Datasets:

Hendrik-a

/

dancer-data

like 0

1011.2096

i

active galactic nuclei ( agn ) are increasingly recognised as a key element in the overall galaxy evolution process ( e.g. * ? ? ? * ) , yet the nature of the link between agn and galaxy evolution is not understood in depth . the link can take two main forms : the triggering of agn as gas is driven into the nuclear regions of galaxies as they evolve ; and the direct impact of the agn - driven outflows on the ism in the galaxy bulges , haloes and any surrounding groups and clusters . the latter agn feedback effect has been invoked to explain the correlations between black hole mass and host galaxy properties ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , as well as the high - end shape of the galaxy luminosity function @xcite . on the other hand , the triggering of agn activity as a result of evolution - driven gas accretion can provide an explanation for the similarity between the redshift evolution of agn activity and that of the global star formation rate of the field galaxy population @xcite . clearly , if we are to incorporate the agn feedback effect accurately into galaxy evolution models , it is important to understand how and when agn are triggered as their host galaxies evolve . deep ground - based imaging observations of powerful radio galaxies show morphological evidence ( tidal tails , fans , bridges and shells etc . ) that a large fraction are triggered in galaxy interactions and mergers @xcite . a merger origin is also supported by the kinematics of the extended emission line regions in some sources @xcite . however , the idea that the activity is always triggered in major galaxy mergers and interactions has been challenged by high resolution hubble space telescope ( hst ) images which provide evidence that the host galaxies of powerful agn of both radio - loud and radio - quiet types are relatively quiescent giant elliptical galaxies @xcite . at least part of this apparent discrepancy between the hst and ground - based results is likely to be a consequence of the fact that shallow hst observations are sensitive to high surface brightness structures close to the nuclei , while the lower resolution ground - based studies are more sensitive to lower surface brightness structures on larger scales ( see discussion in * ? ? ? * ; * ? ? ? while some radio galaxies show clear evidence for triggering in galaxy interactions and mergers , a significant subset have optical morphologies and emission line kinematics that do not support such a triggering mechanism . many such cases are central cluster galaxies surrounded by massive haloes of hot gas @xcite . therefore the infall of warm / cool gas condensing from the hot x - ray haloes in cooling flows has been been suggested as an alternative trigger for the agn activity ( e.g. * ? ? ? in addition , based both on detailed x - ray studies of individual objects and optical studies of large samples of low luminosity radio sources , the direct ( bondi ) accretion of the _ hot _ ism associated with the x - ray haloes has been proposed to explain the fuelling of weak line radio galaxies ( wlrg ) in the local universe @xcite . although the morphologies and emission line kinematics provide important information about the triggering events , this information is generally qualitative . for example , it is difficult to use such information to quantify when agn are triggered in major galaxy mergers relative to the time of coalescence of the merging nuclei . fortunately , another facet of the gas accretion events that trigger agn activity is that they are also likely to be associated with star formation in the host galaxies ; therefore , by studying the young stellar populations in the predominantly early - type host galaxies of powerful radio sources , we can obtain key information about the nature of the triggering events . substantial recent progress has been made in quantifying the degree of recent star formation activity in radio galaxies using both optical / uv observations of direct starlight @xcite and far - ir observations of dust - reprocessed starlight @xcite . concentrating on optical / uv spectroscopic studies of complete samples that take full account of contamination of the continuum by agn - related components ( e.g. scattered or direct agn light , nebular continuum ) , as well as intrinsic reddening of the starlight , young stellar populations ( ysp ) are detected spectroscopically in 15 30% of powerful 2jy and 3cr radio galaxies at low and intermediate redshifts @xcite ; the major uncertainties in these numbers are due to objects in which the strength of the direct or scattered agn component makes detection of the ysp difficult . despite the possibility that a substantial proportion of ysp emission may be absorbed by dust at optical / uv wavelengths , analysis of the mid- to far - ir ( mfir ) continuum properties of powerful radio galaxies derived from deep spitzer observations yields a similar proportion of powerful radio galaxies with energetically significant recent star formation activity ( @xmath015 28% : tadhunter et al . 2007 , dicken et al . , 2008 , 2009)10 less at uv wavelengths than optical wavelengths , such observations are sensitive to relatively low levels of recent star formation activity that may be insignificant in terms of their contribution to the masses and energetics of the host galaxies . ] . the identification of ysp in a significant fraction of nearby radio galaxies has opened the possibility of using spectral synthesis modelling of the stellar populations to investigate the agn triggering events and the evolution of the host galaxies . initial results provided a mixed picture . on the one hand , tadhunter et al . ( 2005 ) and @xcite found evidence for intermediate ysp ages in their small sample of four nearby radio galaxies , pointing to a significant delay between the starbursts and the agn activity , similar to those reported for samples of star forming galaxies and radio - quiet agn in the local universe ( e.g. * ? ? ? * ; * ? ? ? on the other hand , a detailed study by @xcite of two intermediate redshift radio galaxies demonstrated the presence of much younger stellar populations in one object , as well as intermediate age stellar populations in both objects . all the spectral synthesis modelling studies of radio galaxies have stressed the following common features . * * masses . * the masses associated with the ysp detected spectroscopically in radio galaxies are significant ( @xmath5 m@xmath3 ) , amounting to typically 1 40% of the total stellar masses of the host galaxies ; if the starbursts and agn are triggered in mergers , then the systems with the more massive ysp must be associated with relatively major mergers , in which at least one of the merging galaxies is gas - rich . * * spatial distribution . * when substantial ysp are detected in the nuclear regions of the radio galaxies , in general they are also detected across the full extents of the galaxies over which it is possible to make spectroscopic observations with the high s / n required for spectral synthesis modellling ( e.g. * ? ? ? * ) . in some cases , the ysp are detected on scales of 10s of kpc . again this is consistent with simulations of gas rich mergers that predict galaxy wide star formation activity ( e.g. * ? ? * ; * ? ? ? * ) , although it does not preclude other triggering mechanisms . * * reddening . * reddening of the optical / uv light of the ysp by dust is important , especially in the nuclear regions of the galaxies ( typically @xmath6 ) ; failure to take such reddening into account leads to inaccurate ages for the ysp and , in particular , to the over - estimation of the ages of the ysp . in this paper we draw together and summarise the results of all the recent spectral synthesis studies of radio galaxies that are based on high quality optical spectra , including the recent investigation of 12 low and intermediate redshift radio galaxies by @xcite . new spectral synthesis results are also presented for a subset of the sample . the properties of the ysp are then discussed in the context of the morphologies of the host galaxies , in order to investigate the nature , timescales , and order of events of the triggering of the activity of an important subset of the population of galaxies with powerful agn . throughout this paper we assume a cosmology with @xmath7 km s@xmath8 , @xmath9 , and @xmath10 .

in this paper we discuss the results of a programme of spectral synthesis modelling of a sample of starburst radio galaxies in the context of scenarios for the triggering of the activity and the evolution of the host galaxies . new optical spectra are also presented for a subset of the objects discussed . [ firstpage ] galaxies : active galaxies : jets galaxies : starburst galaxies : interactions

in this paper we discuss the results of a programme of spectral synthesis modelling of a sample of starburst radio galaxies in the context of scenarios for the triggering of the activity and the evolution of the host galaxies . new optical spectra are also presented for a subset of the objects discussed . the starburst radio galaxies comprising 25% of all powerful extragalactic radio sources frequently show disturbed morphologies at optical wavelengths , and unusual radio structures , although their stellar masses are typical of radio galaxies as a class . in terms of the characteristic ages of their young stellar populations ( ysp ) , the objects can be divided into two groups : those with ysp ages gyr , in which the radio source has been triggered quasi - simultaneously with the main starburst episode , and those with older ysp in which the radio source has been triggered or re - triggered a significant period after the starburst episode . most of former group are associated with large mid- to far - ir ( mfir ) continuum and [ oiii ] emission line luminosities ( l , w ) , while most of the latter have lower luminosities . combining the information on the ysp with that on the optical morphologies of the host galaxies , we deduce that the majority of the starburst radio galaxies have been triggered in galaxy mergers in which at least one of the galaxies is gas rich . however , the triggering ( or re - triggering ) of the radio jets can occur immediately before , around , or a significant period after the final coalescence of the merging nuclei , reflecting the complex gas infall histories of the merger events . although% of starburst radio galaxies are sufficiently bright at mfir wavelengths to be classified as ultra - luminous infrared galaxies ( ulirgs ) , we show that only the most massive ulirgs are capable of evolving into radio galaxies . finally , for a small subset of starburst radio galaxies in rich clusters of galaxies , cooling flows associated with the hot x - ray haloes offer a viable alternative to mergers as a trigger for the radio jet activity . overall , our results provide further evidence that powerful radio jet activity can be triggered via a variety of mechanisms , including different evolutionary stages of major galaxy mergers ; clearly radio - loud agn activity is not solely associated with a particular stage of a unique type of gas accretion event . [ firstpage ] galaxies : active galaxies : jets galaxies : starburst galaxies : interactions

1011.2096

r

detailed discussions of the individual starburst radio galaxies , including the new spectroscopic results , are presented in the appendix . in this section we consider the general results and patterns obtained for the population of starburst radio galaxies as a whole . it is striking that a large proportion of starburst radio galaxies show unusual radio morphologies that place them outside the regular fri / frii morphological classification for extended radio sources : 7 ( 33% ) are compact steep spectrum ( css ) or gigahertz peaked ( gps ) sources whose radio structures are dominated by structures with a diameter @xmath87kpc ( pks0023 - 26 , 3c48 , b2 0648 + 27 , pks1345 + 12 , 3c305 , pks1549 - 79 , pks2135 - 209 ) ; 3 ( 14% ) show unusually prominent compact steep spectrum core components on a scale @xmath88kpc , even if their radio emission is dominated by radio lobes and hotspots on a larger scale ( 3c321 , 3c433 , 3c459 ) ; 6 ( 29% ) show inner high surface brightness steep spectrum structures along with lower surface brightness outer haloes or double structures ( 3c213.1 , 3c218 , 3c236 , cen a , pks1345 + 12 , 3c293 ) ; and 15 ( 71% ) show one or more of these peculiarities . for comparison , the rate of detection of such features in the southern 2jy sample of radio galaxies with redshifts in the range @xmath11 ( see dicken et al . 2008 for sample definition ) is only 28% . although our small sample size makes it difficult to find clear trends in the detailed radio morphologies with the properties of the stellar populations , it is notable that all but one ( 3c305 ) of the 7 css / gps sources in our sample have nuclear spectra that are consistent with relatively young ages for their ysp ( @xmath15 gyr ) . at optical wavelengths most of the objects in our sample of starburst radio galaxies show morphological peculiarities compared with quiescent elliptical galaxies : 17 ( 80% ) show tidal tails , fans , or highly asymmetric / clumpy outer envelopes at relatively high surface brightness levels ; 14 ( 67% ) show dust features ; 5 ( 23% ) have double nuclei or close companions within 15 kpc ; and 20 ( 95% ) show one or more of these optical peculiarities . this rate of incidence is much higher than in the general population of massive elliptical galaxies observed with similar surface brightness sensitivity ( e.g. * ? ? ? however , at this relatively crude level of morphological classification , a similar rate of morphological disturbance has recently been found in the general population of powerful 2jy radio galaxies at intermediate redshifts ( including non - starburst objects : ramos almeida et al . 2010 ) . the ages of the ysp detected in radio galaxies can provide key information about the order - of - events and the triggering of the agn / jet activity . therefore it is interesting to examine the distribution of luminosity - weighted ysp ages determined from the two component fits to the optical spectra of the full sample of starburst radio galaxies described in section 2 . the top panel of figure 1 shows the distribution of luminosity - weighted ages for the nuclear apertures of the starburst radio galaxies . for comparison we also show the ysp age distribution for a complete sample of ulirgs with redshifts @xmath89 representing the extreme starburst population in the local universe which have been modelled using identical techniques by @xcite . note that , in some apertures of some starburst radio galaxies it proved possible to model the optical spectra with ysp covering a wide range of ages . in such cases we have used the mean age over the range of models that provided good fits . since the upper limiting ages in the latter group were often large ( @xmath131gyr ) , this will tend to skew the age distribution to larger ages . several features are apparent from table 2 and figure 1 . * * nuclear apertures . * considering the nuclear apertures ( figure 1 top ) , 9 ( 43% ) of sources have relatively young ysp ages : @xmath15 gyr . this group is interesting because the typical timescale of the starburst in a major galaxy merger is @xmath00.1 gyr ( e.g. * ? ? ? * ) , and powerful extragalactic radio sources are generally considered to have maximum lifetimes in the range 0.01 0.1 gyr . for such objects the results are consistent with the starburst and agn / jet activity occurring quasi - simultaneously , with little evidence for a major time lag between the starburst and the agn / jet activity . on the other hand , there is also a group of 8 objects ( 36% of sample ) with well - determined older ysp ages ( @xmath90 gyr ) , in which the agn / jet activity appears to have been triggered or re - triggered a significant period _ after _ the major star formation episode in the nuclear regions ( see also the discussion in section 5.1 ) . the latter group includes 3c305 and 3c293 , which were discussed in detail in @xcite . * * extended vs. nuclear apertures . * considering only the apertures with well - determined ysp ages , there is little evidence for a gradient in the ysp ages from the nuclear to the extended regions ; in most cases the nuclear and extended apertures have luminosity - weighted ysp ages that are consistent given the ( sometimes large ) uncertainties . the exception is 3c459 for which the intermediate - aged ysp component becomes more significant off - nucleus @xcite , in common with the trend found for other ulirgs in the local universe @xcite . * * comparison with ulirg ysp ages . * the overwhelming majority of nuclear apertures in the ulirgs modelled by @xcite yield relatively young luminosity - weighted ysp ages : 88% have ysp ages @xmath15 ( figure 1 bottom ) . this is consistent with the group of 9 radio galaxies indentified above with younger ysp ages . indeed , four of the radio galaxies with younger ysp ages 3c48 , pks1345 + 12 , pks1549 - 79 , 3c459 qualify as ulirgs based on their far - infrared luminosities . moreover , our modelling is consistent with young ysp ages for the one other radio galaxy in our sample with a ulirg - like far - ir luminosity pks2135 - 20 even if the ysp age in that case can not be determined with any accuracy , due to the presence of strong nuclear agn emission . * * links with level of agn activity . * it is notable that _ all _ of the objects that have both highly powerful radio emission with @xmath91 w hz@xmath8 and luminous [ oiii ] line emission with @xmath92 } \ge 10^{35}$ ] w luminosity corresponds to luminous quasar - like nuclear activity ( e.g. * ? ? ? ] have spectra consistent with young ysp ages ( @xmath15 gyr ) . all 7 of these objects ( 33% of the sample ) with powerful jets and luminous agn are also luminous at far - ir wavelengths ( @xmath93 w ) . on the other hand , all but one of the objects ( ngc612 is the exception ) that have low radio powers with @xmath94 w hz@xmath8 have spectra consistent with older , intermediate - age ysp . thus , there appears to be a link between the level of agn / jet activity and the age of the ysp , although the relationship is not perfect . objects that do not fit in with the general trend include 3c321 , which has highly luminous [ oiii ] and far - ir emission but intermediate age ysp , and 3c218 which has weak emission lines but much younger ysp . interestingly both of the latter objects fall off the correlation between radio power and emission line luminosity : 3c321 is unusually emission line luminous for its radio power , whereas 3c218 has an unusually low emission line luminosity for its relatively high radio power , perhaps as a consequence of the effect of its rich cluster environment boosting its radio luminosity . we further note that a substantial subset of radio galaxies with quasar - like levels of nuclear activity show no evidence for sgnificant recent star formation activity ; these objects are discusssed further in section 5.4 . llllllll + object & ysp model & mag & ref & @xmath95 & @xmath96 & @xmath97 & ysp mass contr . + & ( age , e(b - v ) ) & type & & ( @xmath98 ) & ( @xmath98 ) & ( @xmath98 ) & + + pks0023 - 26 & ( 0.03,0.9 ) & @xmath99 & 1 & @xmath100 & @xmath101 & @xmath102 & 17% + ngc612 & ( 0.05,1.2 ) & v@xmath103 & 2 & @xmath104 & @xmath105 & @xmath106 & 18% + 3c48 & ( 0.1,0)@xmath107 & f555w & 3 & @xmath108 & @xmath109 & @xmath110 & 2% + fornax a & & r@xmath111 & 4 & & @xmath112 & @xmath112 & + pks0409 - 75 & ( 0.02,0.7 ) & @xmath113 & 1 & @xmath114 & @xmath115 & @xmath105 & 5% + pks0620 - 52 & ( 0.7,0.0 ) & r@xmath116 & 7 & @xmath117 & @xmath118 & @xmath118 & 1% + b20648 + 27 & ( 0.3,0.3 ) & m@xmath119 & 5 & @xmath26 & @xmath120 & @xmath121 & 28% + 3c213.1 & ( 0.6,0.0 ) & @xmath99 & 6 & @xmath47 & @xmath122 & @xmath123 & 11% + 3c218 & ( 0.05,0.4 ) & r@xmath116 & 7 & @xmath124 & @xmath125 & @xmath126 & 4% + 3c236 & ( 0.05,1.4 ) & @xmath99 & 6 & @xmath38 & @xmath109 & @xmath127 & 28% + 3c285 & ( 0.2,0.2 ) & @xmath99 & 6 & @xmath128 & @xmath102 & @xmath129 & 17% + centaurus a & & r@xmath103 & 8 & & @xmath130 & @xmath130 & + pks1345 + 12 & ( 0.05,0.8 ) & r & 11 & @xmath131 & @xmath112 & @xmath132 & 8% + 3c293 & ( 2.0,0.4 ) & @xmath99 & 6 & @xmath104 & @xmath133 & @xmath120 & 57% + 3c305 & ( 0.4,0.6 ) & @xmath99 & 6 & @xmath26 & @xmath134 & @xmath135 & 19% + 3c321 & ( 0.6,0.2 ) & @xmath99 & 6 & @xmath124 & @xmath136 & @xmath137 & 6% + pks1549 - 79 & ( 0.05,0.4 ) & r & 9 & @xmath138 & @xmath104 & @xmath104 & 3% + pks1932 - 46 & & @xmath99 & 1 & & @xmath73 & @xmath73 & + 3c433 & ( 0.05,0.7 ) & v@xmath139 & 10 & @xmath63 & @xmath134 & @xmath140 & 7% + pks2135 - 209 & ( 0.2,0.2 ) & @xmath113 & 1 & @xmath141 & @xmath142 & @xmath143 & 15% + 3c459 & ( 0.05,0.2 ) & @xmath99 & 1 & @xmath144 & @xmath104 & @xmath122 & 8% + + in order to compare the starburst radio galaxies with other types of star forming galaxies in the local universe it is important to consider their stellar masses . we have estimated the total stellar masses by using the monochromatic continuum fluxes derived from the best available total photometric magnitudes to scale the stellar masses derived from our spectral synthesis modelling of the spectra . in each case we used the best - fitting ysp+osp model to derive the stellar masses for the nuclear spectroscopic aperture , then assumed that the same model was appropriate for the entire stellar halo of the galaxy sampled by the photometric aperture . this assumption is justified on the basis that our spectra show little evidence for major gradients in the stellar populations across the halos of most of the galaxies in our sample ( e.g. * ? ? ? * ) . although the major source of uncertainty in this procedure is likely to be related to the choice of a single stellar model for each galaxy , experiments involving the adoption of extreme models ( e.g. assuming that the halos are dominated by osps ) suggest that the derived total stellar masses are accurate to within a factor of two . the results for the starburst radio galaxies are presented in table 4 and figure 2 . they demonstrate that most starburst radio galaxies are giant elliptical galaxies in terms of their total stellar masses . considering the galaxy mass function derived by @xcite m@xmath3 , adapted to our cosmology ] , the majority of starburst radio galaxies are super - m@xmath145 : the mean and median stellar masses are @xmath146 m@xmath3 ( 4@xmath147m@xmath145 ) and @xmath140 m@xmath3 ( 3.3@xmath147m@xmath145 ) . these results are consistent with those derived for the general population of powerful radio galaxies at all redshifts ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? for example , based on the near - ir photometry measurements presented in @xcite , the general population of nearby ( @xmath148 ) 2jy radio galaxies has stellar masses in the range @xmath149 m@xmath3 . however , as highlighted in @xcite , it is dangerous to generalise , and a minority of radio galaxies have stellar masses that are significantly lower ( @xmath150 ) . figure 2 also shows a comparison between the total stellar masses of starburst radio galaxies ( top panel ) and nearby ulirgs from the @xmath89 complete sample of @xcite ( bottom panel ) , derived using identical techniques . in making this comparison it is important to recognise that the estimated total stellar masses of the ulirgs have been derived using osp+ysp models ( modelling combination i in * ? ? ? * ) , which tend to maximise the osp combination ( and hence the total stellar masses ) , whereas in fact the nuclear spectra of many of ulirgs can be adequately modelled by combinations of intermediate age and young ysp , without any contribution from an osp ( combination iii in * ? ? ? * ) , similar to the case of 3c459 amongst the starburst radio galaxies @xcite . despite the fact that the masses of ulirgs in figure 12 may be over - estimated , most radio galaxies have total stellar masses that are greater than those of most ulirgs , although there is a significant overlap between the two distributions . using a k - s two sample test we can reject the null hypothesis that the two samples have the same mass distributions at the @xmath1399.5% level of significance . overall , this comparison provides a clear demonstration of the fact that , although some radio galaxies _ are _ ulirgs and others may have _ evolved from _ ulirgs ( see * ? ? ? * ) , not all ulirgs can evolve into radio galaxies and vica versa ; only the most massive 50% of ulirg systems are capable of harbouring powerful radio jets . in this context it is notable that , out of the complete sample of 26 @xmath89 ulirgs investigated by @xcite , only one is a radio galaxy , and that object pks1345 + 12 ( also in our sample of starburst radio galaxies ) has the largest total stellar mass of all the ulirgs .

25% of all powerful extragalactic radio sources frequently show disturbed morphologies at optical wavelengths , and unusual radio structures , although their stellar masses are typical of radio galaxies as a class . in terms of the characteristic ages of their young stellar populations ( ysp ) , the objects can be divided into two groups : those with ysp ages gyr , in which the radio source has been triggered quasi - simultaneously with the main starburst episode , and those with older ysp in which the radio source has been triggered or re - triggered a significant period after the starburst episode .

in this paper we discuss the results of a programme of spectral synthesis modelling of a sample of starburst radio galaxies in the context of scenarios for the triggering of the activity and the evolution of the host galaxies . new optical spectra are also presented for a subset of the objects discussed . the starburst radio galaxies comprising 25% of all powerful extragalactic radio sources frequently show disturbed morphologies at optical wavelengths , and unusual radio structures , although their stellar masses are typical of radio galaxies as a class . in terms of the characteristic ages of their young stellar populations ( ysp ) , the objects can be divided into two groups : those with ysp ages gyr , in which the radio source has been triggered quasi - simultaneously with the main starburst episode , and those with older ysp in which the radio source has been triggered or re - triggered a significant period after the starburst episode . most of former group are associated with large mid- to far - ir ( mfir ) continuum and [ oiii ] emission line luminosities ( l , w ) , while most of the latter have lower luminosities . combining the information on the ysp with that on the optical morphologies of the host galaxies , we deduce that the majority of the starburst radio galaxies have been triggered in galaxy mergers in which at least one of the galaxies is gas rich . however , the triggering ( or re - triggering ) of the radio jets can occur immediately before , around , or a significant period after the final coalescence of the merging nuclei , reflecting the complex gas infall histories of the merger events . although% of starburst radio galaxies are sufficiently bright at mfir wavelengths to be classified as ultra - luminous infrared galaxies ( ulirgs ) , we show that only the most massive ulirgs are capable of evolving into radio galaxies . finally , for a small subset of starburst radio galaxies in rich clusters of galaxies , cooling flows associated with the hot x - ray haloes offer a viable alternative to mergers as a trigger for the radio jet activity . overall , our results provide further evidence that powerful radio jet activity can be triggered via a variety of mechanisms , including different evolutionary stages of major galaxy mergers ; clearly radio - loud agn activity is not solely associated with a particular stage of a unique type of gas accretion event . [ firstpage ] galaxies : active galaxies : jets galaxies : starburst galaxies : interactions

1011.2096

c

it is clear that many of the optical morphological features of starburst radio galaxies are consistent with the idea that both the agn / jet and starburst activity have been triggered as the result of the gas infall associated with galaxy mergers . hydrodynamical simulations of mergers reveal that they are complex events , and it can take a gigayear or more for the merger remnant to relax and achieve the appearance of a normal galaxy . the main gas infall and star formation are predicted to occur in two major peaks : one at or just after the first peri - centre passage of the merging nuclei ; the other as the two nuclei finally coalesce ( e.g. * ? ? ? the relative intensity and separation in time of these two peaks depends on several factors such as the morphologies , mass ratios and gas contents of the precursor galaxies , the merger geometries , and the importance of feedback processes associated with the agn and starbursts @xcite . given that most starburst radio galaxies have massive old stellar populations in addition to their ysp , it is likely their precursors had signifcant stellar bulges . moreover , the relatively large masses and proportional mass contributions of the ysps ( see table 5 ) suggests that at least one of the precursors must have been gas - rich . in such circumstances the models predict that the second star formation peak associated with the coalescence of the two nuclei is likely to be the most intense @xcite . if the agn feedback effects are important , and the agn is triggered concurrently with the starburst , then the star formation will be halted shortly after ( @xmath820.1 gyr ) the final coalescence of the nuclei by powerful agn - induced winds . the time lag between the two star formation peaks is of order 0.3 1.5 gyr , while the major phase of activity associated with the second ( more intense ) peak is expected to last of order 0.1 gyr . however , star formation and agn activity may not only be associated with the two main peaks of activity , but may also occur albeit at reduced intensity at other stages , for example , as the tidal debris rain back down on the merger remnant following the coalescence of the two nuclei . many of the most recent simulations demonstrate that the fuel supply to the central supermasive black holes can be highly irregular over the course of a merger @xcite . it is important to emphasise that , as well as the delivery of gas into the _ general vicinity _ of the supermassive back hole ( within @xmath0100 pc the typical resolution of the hydrodynamical sigmulations ) , there may be other timescales involved in the triggering of the activity . these include the time required for the supermassive black holes from the precursor galaxies to merge , and the time required for the accreted gas to lose sufficient angular momentum to move close enough to the remnant supermassive black hole to fuel the activity ( see discussion in * ? ? ? it has also been suggested that the powerful winds associated with the circum - nuclear star formation activity may disrupt the flow of gas into the nuclear regions and delay the onset of agn activity @xcite . unfortunately the current generation of hydrodynamical simulations do not have sufficient resolution to include these processes in any detail . therefore in what follows we will assume that the black hole accretion and star formation rates are as ( crudely ) predicted by the simulations , with the caveat that the reality is likely be more complex . we now consider whether , based on their ysp properties and optical morphologies , the objects discussed in this paper are consistent with the merger scenario for the triggering of the activity . most of the starburst radio galaxies can be fitted into one of the following three categories , each corresponding to a particular phase of a gas - rich merger . this merger sequence is also illustrated in figure 3 . * * pre - coalescence . * these double nucleus systems are observed after the first peri - centre passage , but immediately before ( within @xmath00.1 gyr ) the coalescence of the two nuclei , as they move together . all of these objects have large agn / jet and far - ir luminosities , reflecting the level of agn and starburst activity associated with the gas infall expected at this stage of a merger . the ysp in these systems represent a combination of the younger ysp formed as a consequence of the fresh gas infall associated with coalescence , and intermediate age stellar populations formed in the first peak of star formation , around the time of the first peri - centre passage . the relative importance of the latter two stellar populations will depend on the details of the encounter , and the extent to which the most recent episode of star formation is obscured by dust . alternatively , any intermediate age stellar populations could be associated with the captured disks of the precursor galaxies . examples : pks0409 - 75 , pks1345 + 12 , 3c321 and 3c433 . * * coalescence . * these single nucleus systems are observed in the 0.1 gyr period immediately following the coalescence of the two nuclei . for major mergers involving gas - rich galaxies with significant bulges , the models predict that this should represent the most active phase of starburst and agn activity . due to the fact that the most recent phase of star formation activity has been particularly intense , and is likely to dominate ( in flux ) over any previous generations of stars , the luminosity - weighted ages in the nuclear regions of these objects are relatively young ( @xmath820.1 gyr ) . the far - ir , [ oiii ] and radio luminosities are large in this phase , reflecting the high level of agn and starburst activity associated with the large concentrations of gas and dust in the nuclear regions ; in some cases ( depending on the details of the merger ) the source may attain a ulirg - like luminosity . examples : 3c48 , pks1549 - 79 , pks2135 - 209 and 3c459 . * * post - coalescence . * these single nucleus systems still bear the morphological hallmarks of a merger in the recent past ( tidal tails , dust lanes , distorted outer isophotes etc . ) , but they have intermediate age ysp ( @xmath151 gyr ) , consistent with them being observed a significant period after the main merger - induced starburst ( i.e. the ysp represent post - starburst stellar populations ) . this is the scenario outlined in @xcite and @xcite . unless the agn / jet activity lasts considerably longer than the 0.1 gyr maximum lifetime that is typically estimated for powerful extragalactic radio sources ( e.g. * ? ? ? * ) , there must have been a time lag between the main merger - induced starburst and the triggering of the current phase of activity . examples : b20648 + 27 , 3c213.1 , 3c285 , 3c293 , 3c305 , centaurus a , fornax a. just as it appears likely that radio - loud agn activity can be triggered at different stages during a merger , it is also possible that there is more than one episode of agn / jet activity in the course of a merger . for example , an individual system may undergo a particularly powerful phase of agn / jet activity as the nuclei coalesce , close to the peak of starburst activity ( the coalescence phase above ) , but the agn / jet activity may also be triggered ( or re - triggered ) earlier or later in the merger sequence , depending on the details of the radial gas flows in the merger . indeed , as noted above , six of the starburst radio galaxies in our sample show evidence for re - triggered radio source activity in the form of high surface brightness inner radio structures and more diffuse and extended outer radio structures ( 3c213.1 , 3c218 , cen a , 3c236 , 3c293 , pks1345 + 12 ) . moreover , in the particular case of 3c236 , @xcite have argued for multiple phases of jet activity , based on both the double - double morphology of its radio source , and the evidence for two major epochs of star formation in its host galaxy . we emphasise that not all of the starburst radio galaxies can be readily accommodated within the merger scheme outlined above ; there are some prominent misfits . most notably , the central cluster galaxies 3c218 and pks0620 - 52 do not show clear morphological signs of major mergers , and 3c218 is also unusual in having relatively young ysp ( @xmath1520.05 gyr ) but low emission line and far - ir luminosities ( the age of the ysp in pks0620 - 52 is not well - determined ) . pks0023 - 26 may also represent an ambiguous case in the sense that it lies at the heart of a rich cluster of galaxies , and has a peculiar amorphous outer envelope that is difficult to classify in terms of the merger sequence ( although a merger can not be entirely ruled out ) . in the case of the one system in our sample that shows evidence for large - scale , and relatively settled , gaseous disk ngc612 it is not clear whether the agn / jet activity has been triggered by interactions with massive galaxies on a large scale in the wider galaxy group ( as may be evidenced by the hi observations ) , or by recent mergers / interactions with closer companion galaxies ( see * ? ? ? the latter seems more likely given that ngc612 shows an optical shell structure , along with ysp that are much younger ( @xmath15 gyr ) than the estimated time since its closest approach to the the massive companion galaxy ngc619 ( @xmath153 gyr ) . clearly , the possibility of multiple interactions and mergers in galaxy groups can complicate the interpretation of the galaxy morphologies and ysp ages in terms of a simple merger sequence . finally we note that , while the properties of the most luminous starburst radio galaxies in particular , the ulirg - like coalescence systems are consistent with triggering in major ( similar mass ) gas - rich mergers , it is difficult to rule out minor mergers as the trigger for some of the other systems . indeed , it has been argued that the large - scale features of centaurus a are consistent with a minor ( 1:10 ) merger between the host radio galaxy and a smaller disk galaxy @xcite . as noted in the previous section , some of the starburst radio galaxies that are situated close to the centres of rich clusters of galaxies are not readily accommodated in the merger sequence . for such objects cooling flows k ) x - ray emitting gas of the cluster to cooler phases of the ism in the central cluster galaxy , where it can form stars and/or be accreted by the central black holes . the direct accretion of the hot gas itself by the central black hole will be discussed in the following section . ] associated with the hot x - ray emitting gas may provide an alternative triggering mechanism for both the visible star formation and the agn / jet activity . this mechanism is supported by the irregular morphologies and kinematics of the emission line gas in central cluster galaxies hosting radio sources @xcite . moreover , while the high velocity dispersions of the galaxies in the centres of massive galaxy clusters can hamper gas accretion via major , gas - rich mergers , there is no such problem for the accretion of warm / hot gas via cooling flows , since the cooling gas will naturally fall towards the centre of the the cluster potential well . although star formation has been discussed as a potential sink for the cooling gas , until recently the apparently large differences between the estimated hot gas cooling rates and the star formation rates in the central cluster galaxies suggested that only a small fraction of the the cooling gas ends up forming stars ( e.g. * ? ? ? however , spectroscopic observations with the new generation of x - ray satellites have led to a major downward revision in estimates of the hot gas cooling rates , so that they are now much closer to the star formation rates . therefore , it is plausible that a significant fraction of the cooling gas does in fact form stars ( see * ? ? ? * ) . in the cases of the three cooling flow candidates in our sample , based on their infrared luminosities and the relation of @xcite , the star formation rates are 5 , 4 and 25 m@xmath3 yr@xmath8 for pks0620 - 52 , 3c218(hydra a ) and pks0023 - 36 respectively . of these three , only 3c218 has published high quality x - ray observations , and its hot gas cooling rate of @xmath155 m@xmath3 yr@xmath8 @xcite proves to be within a factor of 4 of the star formation rate . given the agreement between its star formation and hot gas cooling rates , 3c218 is one of the best candidates for an object in which the activity has been triggered by the warm / cool gas condensing out of a cooling flow . however , even in the case of 3c218 we can not entirely rule out the idea that the activity has been triggered in a galaxy merger or interaction , since it is possible for central cluster galaxies to undergo mergers that could , potentially , form star forming gaseous disks similar to that associated with the dust lane in the central regions of 3c218 @xcite . although such disks ( and the merging galaxies that produced them ) may represent only a small fraction of the total masses of the cd galaxies , the associated gas infall rates may be sufficient to fuel the agn / jet activity in the nuclei on the requisite timescales . note that the large - scale morphological signatures of galaxy mergers ( e.g. tidal tails , fans , shells ) are more difficult to detect against the light of the massive stellar haloes of the central cluster galaxies than they are in lower mass elliptical galaxies ; the tidal features are also likely to be erased on a relatively short timescale by ongoing tidal interactions between all the galaxies in the dense central regions of the galaxy clusters . as a class , low - power fri radio galaxies are almost invariably classified as weak line radio galaxies ( wlrg ) at optical wavelengths . however , a significant proportion of frii galaxies also have wlrg spectra , with [ oiii]@xmath1565007 and mid - ir luminosities that are an order of magnitude lower than narrow- and broad - line radio galaxies ( nlrg / blrg ) of comparable radio power @xcite . on the basis of their nuclear x - ray and emission line properties , and the way that their emission line luminosities and absolute magnitudes correlate with radio power , it has been suggested that the nuclear accretion rate or accretion mode in wlrg is distinct from that in their strong - lined radio galaxy counterparts ( e.g. * ? ? ? * ; * ? ? ? in particular , it has been argued that wlrg represent objects in which the agn / jet activity is fuelled via bondi accretion of the hot x - ray - emitting ism , while strong - lined radio galaxies represent objects in which the activity is fuelled by the accretion cooler phases of the ism . for low power radio galaxies the bondi accretion hypothesis is supported by correlations between galaxy / black hole mass and the fraction of galaxies that are radio - loud , the relatively large proportion of galaxies that are radio - loud at large galaxy / black hole mass ( suggesting a high duty cycle ) , and the fact that the energy input of radio jets fuelled by bondi accretion is sufficient to balance radiative losses of the hot x - ray emitting haloes of the host giant elliptical galaxies @xcite . significant star formation is not expected in the case of triggering via bondi accretion of the hot ism . therefore it is interesting that a significant subset of the starburst radio galaxies are classed wlrg ( ngc612 , pks0620 - 52 , 3c213.1 , 3c218 , 3c236 , 3c293 , fornax a , centaurus a ) . although some such objects ( pks0620 - 52 , 3c218 ) are candidates for fuelling via cooling flows ( see section 5.2 above ) , more than 50% of the wlrg in our sample of starburst radio galaxies can be classified as post - coalescence or late post - coalescence systems , with evidence for a rich ism in the circum - nuclear regions in the form of circum - nuclear dust lanes , as well as other signs that they have been involved in mergers in the recent past . this suggests a possible alternative to fuelling via bondi accretion of the hot ism : accretion of the cool ism at a slow rate from the debris disks of galaxy mergers . as the disks settle it is expected that the shocks associated with the gaseous dissipation process will lead to a net infall of gas , and also produce a liner - type emission line spectrum , similar to those observed in wlrg @xcite . in the later post - merger stages the debris disks may also act as large reservoirs of _ potential _ fuel for the agn / jet activity , but external stimuli , such as interactions with neighbouring galaxies or the accretion of satellite galaxies , may be required to perturb the disks and induce radial gas infalls that are sufficient to trigger the agn . this might help to explain late post - coalescence systems such as the iconic fri radio galaxies centaurus a and fornax a , which appear to have been triggered a substantial period after ( @xmath02 3 gyr after in the case of fornax a ) the mergers associated with the formation of the dust lanes . in such cases , the original merger may not have triggered the current phase of nuclear activity directly , but rather delivered a reservoir of cool gas that was then perturbed by more minor galaxy interactions to produce the observed level of activity . in this context it is notable that centaurus a shows evidence for an ongoing satellite galaxy accretion event in the form of a blue tidal stream @xcite . overall , the assumption that _ all _ wlrg are fuelled by bondi accretion of the hot ism is likely to represent an over - simplification ; for a significant fraction including some fri radio galaxies slow accretion of cooler gas from the debris disks of galaxy mergers represents a viable alternative mechanism . this is consistent with the x - ray and mid - ir evidence for compact , cool dust / gas structures in the nuclear regions of a minority of wlrg , including centaurus a @xcite . the discussion above has concentrated on starburst radio galaxies that show strong evidence for recent star formation activity at optical wavelengths . however , such objects comprise only a small proportion ( @xmath015 25% ) of the full population of powerful radio - loud agn in the local universe . clearly it is important to consider how the agn / jet activity is triggered in the 75 85% majority of powerful radio galaxies that do not show strong signs of optical star formation activity . note that many of the latter belong to the class of strong - lined frii radio sources in which the agn / jet activity is generally considered to be triggered by accretion of the cooler phases of the ism @xcite . one possibility is that the non - starburst radio galaxies are objects in which the agn / jet activity has been triggered or re - triggered in the late post - coalescence phase , @xmath131 gyr after the starburst associated with the coalescence of the nuclei in the merger . as argued in @xcite , after @xmath01 gyr it can be difficult to detect a merger - induced starburst at optical wavelengths against the light of the giant elliptical galaxy host , especially if the ysp comprises a relatively small fraction of the total stellar mass and/or suffers a moderate amount of extinction . in the late post - coalescence phase , the morphological signs of mergers also become more difficult to detect , especially for radio galaxies at intermediate / high redshifts . the main problem with this explanation is that , for strong - lined , non - starburst frii radio galaxies , the moderate rates of gas infall associated with the debris disks may not be sufficient to fuel the prodigious nuclear activity . indeed , many of the starburst radio galaxies that we identified above as post - coalescence systems are wlrg . alternatively , it is possible that the activity in the non - starburst radio galaxies has been triggered by close encounters with gas - rich companion galaxies , or following the first peri - center passages of the merging nuclei in galaxy mergers . in the latter case , hydrodynamical simulations show that the tidal forces following the first encounter induce significant radial infalls of gas into the nuclei for an extended period around ( ( @xmath00.5 1.0 gyr : * ? ? ? * ; * ? ? ? * ) ) the time of closest approach . such infalls may capable of fuelling the prodigious agn / jet activity in strong - lined radio galaxies . however , in cases in which the merging nuclei have significant bulges ( highly likely in the case of radio galaxies ) , only a relatively low level of star formation is expected at this stage . this mechanism may be supported by the finding of a relatively high incidence of tidal bridge features and tidally distorted companion galaxies in deep imaging observations of non - starburst radio galaxies in the 2jy sample @xcite ; it is further supported by detailed studies of individual radio galaxies in interacting groups @xcite . a final possibility is that non - starburst radio galaxies are triggered in relatively minor mergers ( 1:3 or less ) , or in major mergers that are relatively gas poor ( `` dry '' ) . in such cases relatively low levels of star formation are expected , which are likely to be difficult to detect against the light of the old stellar populations in the host galaxies . however , without further theoretical work , it is not clear whether minor or gas - poor mergers would be capable of delivering sufficient gas to the nuclear regions to fuel the quasar - like levels of nuclear activity detected in some non - starburst radio galaxies . an interesting aspect of starburst radio galaxies is that they show a high incidence of unusual radio structures : our sample includes several compact css / gps sources , as well as sources with relatively bright steep spectrum core structures , diffuse outer haloes and double - double structures . what ( if any ) is the relationship between these unusual radio structures and the presence of young stellar populations in the host galaxies ? as already discussed above , double - double sources , and sources with compact high surface brightness inner structures combined with diffuse outer haloes , may represent cases in which the radio jet activity has been re - triggered ( but see morganti et al . 1999 and wise et al . 2007 for counter - arguments in the cases of centaurus a and hydra a ) . given the complexity of the gas infall histories of major gas rich mergers , it is certainly plausible that each merging system undergoes more than one phase of agn / jet activity , thus explaining the presence of such sources in our sample . considering the compact ( css / gps ) radio sources , there is direct observational evidence from measurements of hotspot advance speeds that css / gps radio sources are relatively youthful ( @xmath157 @xmath158 yr ) . however , since the css / gps radio sources are generally estimated to be much younger than the ysps detected in their host galaxies ( @xmath159 @xmath160 yr ) , the youth of the compact sources does not necessarily help to explain their relatively high rate of occurrence in our sample of starburst radio galaxies . alternatively , the high incidence of css / gps sources in the starburst radio galaxies sample may be the consequence of an observational selection effect as follows . we expect a relatively rich and dense ism to be present in the nuclear regions of merging systems , especially around the time of nuclear coalescence . a radio source triggered in a merger will interact particularly strongly with this rich ism in the early stages of the radio source history , as the jets expand through the central regions of the host galaxies ; direct evidence for strong jet - cloud interactions in young radio sources is provided by their extreme emission line kinematics @xcite . the strong interactions between the jets and the rich ism associated with the mergers will not only result in extreme emission line kinematics , but may also affect the conversion of jet power into radio luminosity , boosting the radio luminosities of sources . there is already evidence that interaction with the relatively dense , hot x - ray haloes associated with clusters of galaxies boosts the radio luminosities of jets for a given jet power @xcite , and it is plausible that there will be a similar boosting effect when the jets strongly interact with the ( cooler ) ism in the central regions of merger remnants . indeed , strong enhancements in the radio emission are observed at the sites of interactions between radio jets and warm emission line clouds in the haloes of radio galaxies in the local universe ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? for a given intrinsic jet power , this flux boosting will lead to the compact radio sources that are triggered in young , star forming merger remnants being preferentially selected in flux - limited radio surveys . this in turn could explain the relatively high rate of occurrence of compact radio sources amongst the starburst radio galaxies , as well as the bias of the compact sources towards relatively young ysp ages ( @xmath15 gyr ; see section 4.1 ) . the interaction of the jets with the richer gaseous environments present in merger remnants could also help to explain the relatively high incidence of extended radio sources with compact steep spectrum cores in our sample , since such interactions have the potential to boost the radio emission from the jets , even if the radio lobes are well ouside the central regions of the galaxies .

although% of starburst radio galaxies are sufficiently bright at mfir wavelengths to be classified as ultra - luminous infrared galaxies ( ulirgs ) , we show that only the most massive ulirgs are capable of evolving into radio galaxies . finally , for a small subset of starburst radio galaxies in rich clusters of galaxies , cooling flows associated with the hot x - ray haloes offer a viable alternative to mergers as a trigger for the radio jet activity . overall , our results provide further evidence that powerful radio jet activity can be triggered via a variety of mechanisms , including different evolutionary stages of major galaxy mergers ; clearly radio - loud agn activity is not solely associated with a particular stage of a unique type of gas accretion event .

in this paper we discuss the results of a programme of spectral synthesis modelling of a sample of starburst radio galaxies in the context of scenarios for the triggering of the activity and the evolution of the host galaxies . new optical spectra are also presented for a subset of the objects discussed . the starburst radio galaxies comprising 25% of all powerful extragalactic radio sources frequently show disturbed morphologies at optical wavelengths , and unusual radio structures , although their stellar masses are typical of radio galaxies as a class . in terms of the characteristic ages of their young stellar populations ( ysp ) , the objects can be divided into two groups : those with ysp ages gyr , in which the radio source has been triggered quasi - simultaneously with the main starburst episode , and those with older ysp in which the radio source has been triggered or re - triggered a significant period after the starburst episode . most of former group are associated with large mid- to far - ir ( mfir ) continuum and [ oiii ] emission line luminosities ( l , w ) , while most of the latter have lower luminosities . combining the information on the ysp with that on the optical morphologies of the host galaxies , we deduce that the majority of the starburst radio galaxies have been triggered in galaxy mergers in which at least one of the galaxies is gas rich . however , the triggering ( or re - triggering ) of the radio jets can occur immediately before , around , or a significant period after the final coalescence of the merging nuclei , reflecting the complex gas infall histories of the merger events . although% of starburst radio galaxies are sufficiently bright at mfir wavelengths to be classified as ultra - luminous infrared galaxies ( ulirgs ) , we show that only the most massive ulirgs are capable of evolving into radio galaxies . finally , for a small subset of starburst radio galaxies in rich clusters of galaxies , cooling flows associated with the hot x - ray haloes offer a viable alternative to mergers as a trigger for the radio jet activity . overall , our results provide further evidence that powerful radio jet activity can be triggered via a variety of mechanisms , including different evolutionary stages of major galaxy mergers ; clearly radio - loud agn activity is not solely associated with a particular stage of a unique type of gas accretion event . [ firstpage ] galaxies : active galaxies : jets galaxies : starburst galaxies : interactions

1011.2096

c

in this paper we have discussed the properties of the young stellar populations ( ysp ) in the @xmath015 25% of powerful radio galaxies that show strong evidence for recent star formation activity at optical wavelengths . combined with information about the morphologies of the host galaxies , the ysp properties of most of these starburst radio galaxies are consistent with the triggering of both starburst and agn / jet activity in galaxy mergers in which at least one of the merging galaxies is gas - rich . however , the triggering of the agn / jet activity is not confined to a single evolutionary phase of galaxy mergers . while in a significant subset of objects the agn / jet activity has been triggered within 0.1 gyr of the coalescence of merging nuclei , close to the expected peaks of the merger - induced starbursts , many objects are observed in the post - coalescence phase , @xmath130.2 gyr after the starburst peaks . in the former group the triggering of the activity can be readily identified with the major infalls of gas that are predicted to occur around the time of coalescence . on the other hand , in the latter group the nature of the link between the triggering of the agn / jet and the original starburst - inducing mergers is less clear : late - time infall of merger debris , settling of the debris disks to an equilibrium configuration , and perturbation of the debris disks by minor mergers and encounters , are all possibilities for the triggering of the activity in these , generally lower luminosity , objects . our results clearly demonstrate that luminous radio - loud agn _ can _ be triggered close to the peaks of major gas - rich mergers . however , the relatively low incidence of radio - loud agn in nearby ulirgs suggests that , even under similar conditions of gas infall , it is not inevitable that radio - loud agn activity _ will _ be triggered in such mergers . indeed our comparison of the stellar masses of ulirgs and starburst radio galaxies suggests that the triggering of powerful radio - loud agn activity is most likely to occur in the most massive merger remnants , consistent with other studies of agn host galaxies that provide evidence for a link between host galaxy mass ( and hence black hole mass ) and the incidence of the radio - loud agn population ( e.g. * ? ? ? overall , if we also take into consideration the evidence that some radio - loud agn are triggered by the accretion of gas from the hot x - ray haloes , either via cooling flows or the direct ( bondi ) accretion of hot gas , it appears unlikely that radio - loudness is solely a consequence of a particular mechanism for the delivering of the fuel supply to the nuclear regions . rather , the ability to produce powerful relativistic jets is more likely to be related to the intrinsic properties of energy generating regions ( e.g. the spin and/or mass of the supermassive black hole ) . finally , we emphasise that a considerable fraction of powerful radio galaxies ( @xmath075 85% ) do not show evidence for energetically significant starburst activity at either optical or mfir wavelengths . therefore , in order to complete our understanding of triggering of the activity in radio - loud agn , in the future it will be important to compare the host galaxy properties and environments of the non - starburst majority of radio galaxies , with those of the starburst minority discussed in this paper .

most of former group are associated with large mid- to far - ir ( mfir ) continuum and [ oiii ] emission line luminosities ( l , w ) , while most of the latter have lower luminosities . combining the information on the ysp with that on the optical morphologies of the host galaxies , we deduce that the majority of the starburst radio galaxies have been triggered in galaxy mergers in which at least one of the galaxies is gas rich . however , the triggering ( or re - triggering ) of the radio jets can occur immediately before , around , or a significant period after the final coalescence of the merging nuclei , reflecting the complex gas infall histories of the merger events .

in this paper we discuss the results of a programme of spectral synthesis modelling of a sample of starburst radio galaxies in the context of scenarios for the triggering of the activity and the evolution of the host galaxies . new optical spectra are also presented for a subset of the objects discussed . the starburst radio galaxies comprising 25% of all powerful extragalactic radio sources frequently show disturbed morphologies at optical wavelengths , and unusual radio structures , although their stellar masses are typical of radio galaxies as a class . in terms of the characteristic ages of their young stellar populations ( ysp ) , the objects can be divided into two groups : those with ysp ages gyr , in which the radio source has been triggered quasi - simultaneously with the main starburst episode , and those with older ysp in which the radio source has been triggered or re - triggered a significant period after the starburst episode . most of former group are associated with large mid- to far - ir ( mfir ) continuum and [ oiii ] emission line luminosities ( l , w ) , while most of the latter have lower luminosities . combining the information on the ysp with that on the optical morphologies of the host galaxies , we deduce that the majority of the starburst radio galaxies have been triggered in galaxy mergers in which at least one of the galaxies is gas rich . however , the triggering ( or re - triggering ) of the radio jets can occur immediately before , around , or a significant period after the final coalescence of the merging nuclei , reflecting the complex gas infall histories of the merger events . although% of starburst radio galaxies are sufficiently bright at mfir wavelengths to be classified as ultra - luminous infrared galaxies ( ulirgs ) , we show that only the most massive ulirgs are capable of evolving into radio galaxies . finally , for a small subset of starburst radio galaxies in rich clusters of galaxies , cooling flows associated with the hot x - ray haloes offer a viable alternative to mergers as a trigger for the radio jet activity . overall , our results provide further evidence that powerful radio jet activity can be triggered via a variety of mechanisms , including different evolutionary stages of major galaxy mergers ; clearly radio - loud agn activity is not solely associated with a particular stage of a unique type of gas accretion event . [ firstpage ] galaxies : active galaxies : jets galaxies : starburst galaxies : interactions

0901.0574

i

it is well known that in a chaotic dynamics the pointwise , future behavior of an initial condition is unpredictable and even impossible to be described by using a finite quantity of information . on the other hand many of its statistical properties are rather regular and often described by suitable versions of classical theorems from probability theory : law of large numbers , central limit theorem , large deviations estimations , correlation decay , hitting times , various kind of quantitative recurrence and so on . in this article we consider a class of flows which contain the celebrated geometric lorenz flow and we will study some of its statistical features by a sharp estimation for the decay of correlations of its first return map on a suitable poincar section . this will give a quantitative recurrence estimation and an estimation for the scaling behavior of the time which is needed to hit small targets ( logarithm law ) . let @xmath9 be a @xmath10 flow in @xmath11 . quantitative recurrence estimations and logarithm laws can be seen in the following framework : we are interested in a quantitative estimation of the speed of approaching of a certain orbit @xmath12 ( starting from the point @xmath1 ) of the system to a given target point @xmath13 . let @xmath14 be a ball with radius @xmath4 centered at @xmath13 . we consider the time @xmath15 needed for the orbit of @xmath1 to enter in @xmath14 for the first time and the asymptotic behavior of @xmath16 as @xmath4 decreases to @xmath5 . often this is a power law of the type @xmath17 and then it is interesting to extract the exponent @xmath18 by looking at the behavior of @xmath19 in this way , we have a hitting time indicator for orbits of the system . as @xmath20 ( for the equivalence see @xcite ) . ] if the orbit @xmath21 starts at @xmath13 itself and we consider the second entrance time in the ball @xmath22(because the orbit trivially starts inside the ball ) with the same construction as before , we have a quantitative recurrence indicator . if the dynamics is chaotic enough , often the above indicators converge to a quantity which is related to the local dimension of the invariant measure of the system and in the hitting time case this relation is called _ logarithm law_. hitting time results of this kind ( sometime replacing balls with other suitable target sets ) have been proved in many continuous time dynamical systems of geometrical interest : geodesic flows , unipotent flows , homogeneous spaces , etc . ( see e.g. @xcite ) . for discrete time systems this kind of results hold in general if the system has fast enough decay of correlation ( @xcite ) . mixing is however not sufficient , since this relation does not hold in some slowly mixing system having particular arithmetical properties ( @xcite ) . some further connections with arithmetical properties are shown in interesting examples as rotations and interval exchange maps ( see e.g. @xcite ) . this kind of problem is also connected with the so called dynamical borel cantelli results ( see @xcite and e.g. @xcite ) . moreover , in the symbolic setting , similar results about the hitting time are used in information theory ( see e.g. @xcite ) . about quantitative recurrence , our approach follows a set of results connecting a quantitative recurrence estimation with local dimension ( see e.g. @xcite ) . we remark that the speed of correlation decay for lorenz like flows is not yet known ( although some are proved to be mixing , see @xcite ) hence quantitative recurrence and hitting time results can not be proved directly using this tool , instead of this we will consider a poincar section , estimating its correlation decay and work with return times . let @xmath23 $ ] be a unit interval , we consider a flow @xmath24 on @xmath25 having a poincar section on a square @xmath26 satisfying the following properties : 1 ) : : the flow induces a first return map @xmath27 of the form @xmath28 ( preserves the natural vertical foliation of the square ) and : 1.a ) : : there is @xmath29 and @xmath30 such that , if @xmath31 are such that @xmath32 $ ] then @xmath33 1.b ) : : @xmath34 is @xmath35-lipschitz with @xmath36 ( hence is uniformly contracting ) on each vertical leaf @xmath37 : @xmath38 1.c ) : : @xmath39 is onto and piecewise monotonic , with two @xmath40 increasing branches on the intervals @xmath41,@xmath42 $ ] and @xmath43 where it is defined can be relaxed to @xmath44^{-1}<1 $ ] provided that the map @xmath45 is eventually expanding in the sense of @xcite , chapter 3 . ] . moreover @xmath46 @xmath47 . 1.d ) : : @xmath48 has bounded variation . by the statistical properties of the map @xmath45 , which is piecewise expanding , under the above assumptions , it turns out that @xmath49 has a unique srb measure @xmath50 we then ask the following property for the flow : 2 ) : : the flow @xmath24 is transversal to the section @xmath51 and its return time to @xmath52 is integrable with respect to @xmath53 . in section [ sec : constr - geometr - model ] we will describe the geometric lorenz system and we show that it satisfies these properties . the main results of the paper concern some statistical properties of @xmath24 and @xmath49 , more precisely : * theorem a ( decay of correlation for the poincar map ) * _ the unique srb measure _ @xmath54 _ of _ @xmath49 _ _ has exponential decay of correlation with respect to lipschitz observables . _ this result is proved in section [ 2p1 ] ( theorem [ resuno ] ) where the reader can also find a precise definition of correlation decay . the proof also uses a regularity estimation for the invariant measure @xmath54 which can be found in the appendix i ( lemma 8.1 ) and is proved by sort of lasota - yorke inequality . we remark that a stretched - exponential bound for the decay of correlation for a two dimensional lorenz like map was given in @xcite and @xcite . we say that a point @xmath55 is _ regular _ if there are @xmath56 and @xmath57 such that @xmath58 induces a diffeomorphism between a neighborhood of @xmath59 and a neighborhood of @xmath3 . in section [ sec : sbrfluxo ] we recall how to construct an srb ergodic invariant measure for the flow @xmath24 which will be denoted by @xmath60 . it turns out that this measure has the following property * theorem b ( logarithm law for the flow ) * _ for each regular _ @xmath13 _ such that the local dimension _ @xmath61 _ _ is defined it holds _ _ @xmath62__for a.e . starting point _ _ @xmath1__. _ _ this is proved in section [ sec : loglaw ] ( theorem [ main1 ] ) and uses the above decay of correlation estimation for the first return map @xmath49 , a result from @xcite giving the hitting time estimation for systems having faster than polynomial decay of correlations and finally the integrability of return time is used to get the result for the flow . using the main result of @xcite , by a similar construction , if the flow also satisfies the following property 3 ) : : the map @xmath45 has derivative bounded by a power law near @xmath63 : there is a @xmath64 s.t . @xmath65 is bounded in a neighborhood of @xmath63 we prove ( in section [ sec : recurrpoli ] , corollary 7.4 ) the following estimation for the return time * theorem c ( quantitative recurrence ) * _ if the flow satisfies conditions 1),2 ) , 3 ) above , then for a.e . _ @xmath1 _ it holds _ @xmath66 in the appendix ii we give an auxiliary result , using a theorem by steinberger @xcite showing that the local dimension is defined a.e . for the geometric lorenz system .

in this paper we prove that the poincar map associated to a lorenz like flow has exponential decay of correlations with respect to lipschitz observables . this implies that the hitting time associated to the flow satisfies a logarithm law . its asymptotic behavior is a power law whose exponent is related to the local dimension of the srb measure at : for each such that the local dimension exists , holds for almost each . in a similar way it is possible to consider a quantitative recurrence indicator quantifying the speed of coming back of an orbit to its starting point . similar results holds for this recurrence indicator .

in this paper we prove that the poincar map associated to a lorenz like flow has exponential decay of correlations with respect to lipschitz observables . this implies that the hitting time associated to the flow satisfies a logarithm law . the hitting time is the time needed for the orbit of a point to enter for the first time in a ball centered at , with small radius . as the radius of the ball decreases to its asymptotic behavior is a power law whose exponent is related to the local dimension of the srb measure at : for each such that the local dimension exists , holds for almost each . in a similar way it is possible to consider a quantitative recurrence indicator quantifying the speed of coming back of an orbit to its starting point . similar results holds for this recurrence indicator .

1012.0263

i

two dimensional electronic systems on a honeycomb lattice have seen tremendous activity over the last couple of years . this development was triggered by the experimental isolation of single layer graphene which comes with a variety of fascinating and unusual properties @xcite . commonly , graphene is considered an excellent conductor with extremely high mobilities @xcite . the effective low - energy theory describing the system is given in terms of massless dirac fermions moving at the fermi velocity @xmath0 instead of the speed of light @xmath1 ( @xmath2 ) . most of the experimental findings in graphene to date can be explained in terms of weakly interacting massless dirac quasiparticles @xcite . a most prominent exception is provided by the recently observed fractional quantum hall effect @xcite . despite this predominant lack of signatures of correlation effects , many authors have analyzed the role of local and long - range coulomb interaction and possible interaction driven insulating phases @xcite . in this paper we study transport in the vicinity of a semimetal - to - insulator quantum phase transition , in which the opening of the single - particle gap in the insulating phase is driven by spontaneous sublattice symmetry breaking . the sublattice inversion symmetry breaking is driven by collective instabilities of the charge density or spin density wave type . note that this scenario does not describe the mott transition in the traditional sense due to the additional symmetry breaking @xcite . in that sense the treatment presented here is closer to the excitonic insulator obtained due to long - range coulomb interaction and chiral symmetry breaking @xcite than it is to a pure hubbard model . within this paper we analyze the simplest possible transition from a semimetal to an insulator described by a hubbard like model and discard the possible existence of interesting intermediate phases such as a spin liquid phase @xcite . transport properties at quantum - criticality have traditionally been a very active branch of research in strongly correlated matter . in two dimensions microscopic calculations have been performed with the quantum - critical conductivity being given by a temperature independent universal number @xcite . this has to be expected for dimensional reasons if the critical point of the field theory has relativistic invariance and is located at finite interaction strength . in the context of clean intrinsic graphene , which shares a number of characteristics with a quantum - critical system @xcite , the critical conductivity was shown to diverge in logarithmic manner upon lowering temperature @xcite . this behavior is rooted in the renormalization group fixed point of the system lying at zero interaction , with the interaction parameter describing long - range coulomb interaction being marginally irrelevant , thus flowing to zero logarithmically upon lowering the energy scale . in our problem , the insulating phase is characterized by the presence of collective order of charge density ( cdw ) or spin density wave ( sdw ) type @xcite . the finite order parameter acts like a mass term for the dirac fermions and consequently opens a gap in the electronic excitation spectrum . both sorts of long - range order break sublattice inversion ( @xmath3 ) symmetry ( conventionally referred to as chiral symmetry ) , which is the driving force behind the finite electronic gap . sdw additionally breaks spin rotation symmetry ( su(@xmath4 ) ) . within this paper we choose a simple field theoretic formulation of the gross - neveu type @xcite , which captures the collective instability and the opening of the electronic quasiparticle gap . we consider two related formulations : ( i ) a landau - ginzburg type bosonic order parameter theory coupled to dirac fermions via a yukawa - type coupling ( henceforth referred to as model i ) and ( ii ) a locally interacting theory of dirac fermions ( henceforth referred to as model ii ) . in both cases there is a quantum phase transition of the semimetal - to - insulator type , which is second order and described by an interacting fixed point . in both cases an appropriate order parameter can easily be defined , which is zero in the semimetallic phase and finite in the insulating phase . thinking in terms of the landau - ginzburg description of phase transitions , the order parameter symmetry is @xmath5 with @xmath6 ( ising or @xmath3 ) for cdw and @xmath7 ( heisenberg ) for sdw . microscopically , local interactions can trigger these instabilities : on - site coulomb repulsion favors sdw , whereas repulsion between adjacent sites favors cdw . [ fig : phasediag ] sketches a phase diagram with the vertical axis being temperature and the horizontal axis the local interaction parameter . the strength of local repulsion , denoted @xmath8 , serves as tuning parameter for the quantum phase transition . in the case of a quantum phase transition towards cdw , @xmath8 denotes repulsive interaction between adjacent sites , whereas for the case of a transition towards sdw the repulsion is on - site . our analysis proceeds along the lines of a combination of a semiclassical boltzmann equation combined with renormalization group arguments ( model i ) and a large - n expansion ( model ii ) @xcite . throughout the paper all mathematical expressions are explicitly shown for the cdw case . the sdw expressions differ in combinatorial factors due to the difference in order parameter symmetry , but not in their structure . however , qualitative differences occur at finite temperature due to the absence of long - range order in the sdw case . in the cdw case a finite gap in the electronic excitation spectrum is stable at finite temperatures , whereas there is no hard gap for the sdw . this is discussed in great detail in the conclusions . we calculated the quantum - critical minimal conductivity of graphene at the semimetal - to - insulator transition using two different phenomenological models . furthermore , we estimated crossover functions for the conductivity which obtain upon lowering temperature and entering the semimetal or respectively the insulating phase . most interestingly , we estimate the crossover function for the quantum - critical - to - insulator crossover and compare it to experimental data in graphene . considering two slightly distinct models we find seemingly contrasting transport properties : \(1 ) within model i in contrast to other relativistically invariant critical points at finite interaction strength in two dimensional systems , the d.c . conductivity is not independent of temperature , but instead seemingly diverges upon lowering temperature @xcite . this surprising result obtains because of a conspiracy of matrix elements and kinematical constraints which prohibits electronic current relaxation from the yukawa coupling to _ all _ orders in perturbation theory . this statement , however , is only strictly true if the electrons and bosons are treated as sharp quasiparticles at all times . it turns out that the minimal conductivity ( at charge neutrality ) is eventually determined by a marginally irrelevant operator , namely long - range coulomb interaction . the critical transport to leading order in temperature turns out to be identical to that of a gas of hot dirac electrons interacting solely via long - range coulomb interaction @xcite . \(2 ) within model ii we find a universal temperature independent universal conductivity as has to be expected from dimensional reasoning . however , we find that the prefactor of the inverse relaxation time is extremely small compared to the one associated with the marginally irrelevant long - range coulomb interaction . in contrast to model i , the scattering from the cdw ( sdw ) order parameter fluctuations is not completely inactive , but still extremely small . a simple order of magnitude estimate suggests that for all experimental purposes the universal quantum - critical conductivity is masked by the current relaxation due to long - range coulomb interaction . we comment on the seeming discrepancy between the transport properties of model i and model ii and argue that the two different pictures are actually compatible and describe the same basic physics , with model i overestimating the kinematical blocking . on a more technical note another interesting result obtains within model i , in which bosons and fermions are directly coupled , namely the absence of boson - drag effects for the coupled boltzmann equations . boson - drag constitutes a serious complication in obtaining transport coefficients in field theories of electrons coupled to bosons , where the bosons are an effective degree of freedom , whose dynamics itself is governed by the underlying electrons . an often employed approximation for the calculation of electronic transport properties in such systems is that the bosonic system is assumed to be equilibrated on timescales relevant for electronic transport and drag effects are neglected . this approximation turns out to be exact in our case . finally , the crossover behavior of the conductivity for the the quantum - critical - to - insulator crossover is discussed for both forms of collective ordering , namely the cdw and sdw . as we argued before , in the case of cdw an ising degree of freedom condenses , which is allowed at finite temperature . thus the electronic degrees of freedom have a hard gap , which entails an exponentially suppressed conductivity . in the case of the sdw , on the other hand , a real quasiparticle gap only opens at temperature @xmath9 and finite temperature behavior is not governed by a hard gap , but rather by a `` pseudogap '' , leading to a power - law suppression of the conductivity . both scenarios allow to determine crossover curves which show remarkable similarities to experiments performed on suspended high - mobility graphene samples @xcite . it appears that they are qualitatively and quantitatively widely compatible with a recent analysis of the data sets under the hypothesis of an underlying electronic quasiparticle gap and might thus be a natural starting point for the identification of the fitting parameters discussed in ref . . in sec . [ sec : model ] we introduce the scenario for the semimetal - to - insulator transition and motivate two different phenomenological models , called model i and model ii . during the course of the paper we will switch between model i and model ii , since different aspects of the problem are more conveniently discussed in one or the other formulation . we review the renormalization group treatment of model i following ref . and also the large - n treatment of model ii following ref . we furthermore stress some of the main physical properties of the models . in sec . [ sec : boltzmann ] we introduce the general formalism of the boltzmann approach . we apply the formalism to both models . in sec . [ sec : boltzi ] we consider model i and solve a system of coupled boltzmann equations for the fermionic and bosonic degrees of freedom . the bosonic degrees of freedom capture the physics of the collective instability and are eventually responsible for the opening of the electronic quasiparticle gap . we explicitly show that in this system of coupled transport equations neglecting the effect of `` boson - drag '' is _ exact _ to linear order in the applied electric field and proceed to analyze the boltzmann equation for the massless dirac particles . we find that inelastic scattering due to the yukawa - coupling is kinematically forbidden ( see sec . [ sec : noleadingorder ] ) to _ all _ orders in perturbation theory . this results in the absence of a temperature independent minimal d.c . conductivity . in sec . [ sec : boltzii ] we solve the boltzmann equation of model ii . in contrast to model i we find that there is a finite universal conductivity which does not depend upon temperature . however , we find that the prefactor of the inverse scattering time is tiny . this leads us to sec . [ sec : boltzcomp ] where we compare the results of in model i with those in model ii and argue in which sense the two results are compatible . in sec . [ sec : qcrcon ] we discuss the minimal conductivity in the quantum - critical regime and make an estimate of crossover temperatures . in a final section ( sec.[sec : discussion ] ) we discuss crossover behaviors which obtain upon lowering of temperature . furthermore , we discuss the fundamental difference between the cdw and sdw cases with a special eye on pseudogap behavior in the sdw case . a discussion of experimental conditions and reference to puzzling results of recent experiments on suspended high mobility graphene samples concludes sec . [ sec : discussion ] .

the effect of either order is to break the sublattice inversion symmetry which induces a finite gap for the electronic single - particle excitations . we analyze two related formulations of the model by means of ( i ) a controlled renormalization group calculation and ( ii ) the large - n method , both of which in combination with a boltzmann transport equation . we determine the quantum - critical conductivity and also discuss crossover behavior from quantum critical behavior into the insulating and/or the semimetallic phases . we find that at asymptotically low temperatures the quantum - critical conductivity is given by a temperature independent universal number . over a large temperature window the temperature independent quantum critical conductivity is masked by a logarithmically temperature dependent contribution due to the marginally irrelevant long - range coulomb interaction . furthermore , we consider possible relations of our findings to recent experiments , with a special emphasis on the quantum - critical - to - insulator crossover . we find that our results are in remarkably good qualitative and quantitative agreement with a recent analysis of the data sets under the hypothesis of an underlying gap in the single - particle spectrum .

in this paper we study transport properties of electrons on the two - dimensional honeycomb lattice . we consider a half - filled system in the vicinity of a symmetry - breaking transition from a semimetallic phase towards an insulating phase with either charge density or spin density wave order . the effect of either order is to break the sublattice inversion symmetry which induces a finite gap for the electronic single - particle excitations . phenomenologically , such a scenario is described in the framework of a gross - neveu theory . we analyze two related formulations of the model by means of ( i ) a controlled renormalization group calculation and ( ii ) the large - n method , both of which in combination with a boltzmann transport equation . we determine the quantum - critical conductivity and also discuss crossover behavior from quantum critical behavior into the insulating and/or the semimetallic phases . we find that at asymptotically low temperatures the quantum - critical conductivity is given by a temperature independent universal number . over a large temperature window the temperature independent quantum critical conductivity is masked by a logarithmically temperature dependent contribution due to the marginally irrelevant long - range coulomb interaction . we discuss possible origins of this peculiarity in the two complementary formulations of the model . furthermore , we consider possible relations of our findings to recent experiments , with a special emphasis on the quantum - critical - to - insulator crossover . we find that our results are in remarkably good qualitative and quantitative agreement with a recent analysis of the data sets under the hypothesis of an underlying gap in the single - particle spectrum .

1409.4313

i

many engineering problems such as chemical reaction processes , heat conduction , nuclear reactors , population dynamics etc . are governed by coupled convection - diffusion - reaction partial differential equations ( pdes ) with non - linear source or sink terms . it is a significant challenge to solve such pdes numerically when they are convection / reaction - dominated . as a model problem , we consider the coupled quasi - stationary equations arising from the time discretization of time - dependent non - linear diffusion - convection - reaction equations @xcite [ 1 ] @xmath0 with @xmath1 are bounded , open , convex domains in @xmath2 with boundaries @xmath3 , @xmath4 , @xmath5 are the diffusivity constants , @xmath6 are the source functions , @xmath7 are the velocity fields , @xmath8 are the dirichlet boundary conditions , @xmath9 are the neumann boundary conditions , and @xmath10 and @xmath11 denote the vector of unknowns and normal vector to the boundary , respectively . the coefficients of the linear reaction terms , @xmath12 , stand for the temporal discretization , corresponding to @xmath13 , where @xmath14 is the discrete time - step . moreover , we assume that the non - linear reaction terms are bounded , locally lipschitz continuous and monotone , i.e. satisfy for any @xmath15 , @xmath16 the following conditions @xcite @xmath17 the non - linear reaction terms @xmath18 occur in chemical engineering usually in the form of products and rational functions of concentrations , or exponential functions of the temperature , expressed by the arrhenius law . such models describe chemical processes and they are strongly coupled as an inaccuracy in one unknown affects all the others . hence , efficient numerical approximation of these systems is needed . for the convection / reaction - dominated problems , the standard galerkin finite element methods are known to produce spurious oscillations , especially in the presence of sharp fronts in the solution , on boundary and interior layers . in last two decades several stabilization and shock / discontinuity capturing techniques were developed for linear and non - linear stationary and time dependent problems . for linear convection dominated problems , the streamline upwind petrov - galerkin(supg ) method is capable to stabilize the unphysical oscillations @xcite . nevertheless , in non - linear convection dominated problems , spurious oscillations are still present in crosswind direction . therefore , supg is used with the anisotropic shock capturing technique as supg - sc for reactive transport problems @xcite . it was shown that supg - sc is capable of reducing the unphysical oscillations in cross - wind direction . the parameters of the supg and supg - sc should be designed carefully for the efficient solution of the discretized equations . in contrast to the standard galerkin conforming finite element methods , discontinuous galerkin finite element(dgfem ) methods produce stable discretizations without the need for stabilization strategies , and damp the unphysical oscillations for linear convection dominated problems . in @xcite , several non - linear convection dominated problems of type ( [ 1 ] ) are solved with dg - sc , discontinuous galerkin method with the shock - capturing technique in @xcite . for an accurate solution of non - linear convection dominated problems , higher order finite elements are used because they are less diffusive and avoid artificial mixing of chemical species under discretization , for supg - sc and dg - sc , respectively . the main advantages of dgfem are the flexibility in handling non - matching grids and in designing hp - refinement strategies @xcite , which allow easily adaptive grid refinement . in this paper we extend the adaptive discontinuous galerkin method in @xcite to the convection dominated non - linear problems of type ( 1 ) . we show on several examples the effectiveness and accuracy of dgafem capturing boundary and internal layers very sharply and without significant oscillations . an important drawback is that the resulting linear systems are more dense than the continuous finite elements and ill - conditioned . the condition number grows rapidly with the number of elements and with the penalty parameter . therefore , efficient solution strategies such as preconditioning are required to solve the linear systems . while more robust compared to iterative solvers , direct solvers are usually more memory and time consuming due to fill - in furthermore , they are known to be less scalable on parallel architectures . therefore , in this paper we use an iterative method which is robust and efficient . because the dg method requires more degrees of freedom than the standard galerkin method , in @xcite linear diffusion - convection - reaction equations are discretized near the boundary and inter layers by the interior penalty dg method , away from the layers by continuous galerkin method . it was shown that combination of both methods will not affect the stability of the dg method . another important class of non - linear diffusion - convection equations are those with the non - linear convective term , including the viscous burger s equation . in the recent years , several effective interior penalty dg methods with efficient time integrators and with space and time adaptivity for this class of problems are developed , see for example @xcite . an important class of non - linear convection - diffusion equations are the pellet equations , which model the intra - particle mass and heat transport in porous catalyst pellets . a comprehensive review of weighted residual methods , the orthogonal collocation , galerkin , tau and least squares methods is given in @xcite for solving the the linear and non - linear pellet equations , where the methods are compared with respect to convergence of the residuals and computational efficiency . the rest of this work is organized as follows . in the next two sections , we give the dg discretization and describe the residual based adaptivity for non - linear diffusion - convection - reaction problems . in section 4 , we have compared the dgfem and dgafem with another class of stabilized methods , the glsfem ( galerkin least square finite element method ) for a linear convection dominated problem . section [ linear ] deals with an efficient solution technique for solving the linear system arising from the dg discretization . in section [ numerical ] , we demonstrate the effectiveness and accuracy of dgafem for handling the sharp layers arising in several examples with different type of non - linear reaction mechanisms . the paper ends with some conclusions .

in this work , we apply the adaptive discontinuous galerkin ( dgafem ) method to the convection dominated non - linear , quasi - stationary diffusion - convection - reaction equations . we propose an efficient preconditioner using a matrix reordering scheme to solve the sparse linear systems iteratively arising from the discretized non - linear equations . non - linear diffusion - convection reaction , discontinuous galerkin , adaptivity , matrix reordering , preconditioning

in this work , we apply the adaptive discontinuous galerkin ( dgafem ) method to the convection dominated non - linear , quasi - stationary diffusion - convection - reaction equations . we propose an efficient preconditioner using a matrix reordering scheme to solve the sparse linear systems iteratively arising from the discretized non - linear equations . numerical examples demonstrate effectiveness of the dgafem to damp the spurious oscillations and resolve well the sharp layers occurring in convection dominated non - linear equations . non - linear diffusion - convection reaction , discontinuous galerkin , adaptivity , matrix reordering , preconditioning

1502.02010

i

population dynamics are a fundamental aspect of many biological processes . in this paper , we introduce and investigate a mathematical model for the population dynamics of an invasive species in a three - species food chain model . exotic species are defined as any species , capable of propagating themselves into a nonnative environment . if the propagating species is able to establish a self sustained population in this new environment , it is formally defined as invasive . the survival and competitiveness of a species depends intrinsically on an individual s fitness and ability to assimilate limited resources . often invasive species possess the ability to dominate a particular resource . this allows them to expand their range via out - competing other native species . in the united states damages caused by invasive species to agriculture , forests , fisheries and businesses , have been estimated to be @xmath0120 billion a year @xcite . in the words of daniel simberloff : `` _ _ invasive species are a greater threat to native biodiversity than pollution , harvest , and disease combined . _ _ '' @xcite therefore understanding and subsequently attenuating the spread of invasive species is an important and practical problem in spatial ecology and much work has been devoted to this issue @xcite . more recently , the spread of natural and invasive species by nonrandom dispersal , say due to competitive pressures , is of great interest @xcite . however , there has been less focus , on the actual eradication of an invasive species , once it has already invaded . this is perhaps a harder problem . in the words of mark lewis : _ `` once the invasive species are well established , there is not a lot you can do to control them''_. @xcite it is needless to say however , that in many ecosystems around the world , invasion has already taken place ! some prominent examples in the us , are the invasion by the burmese python in southern regions of the united states , with climatic factors supporting their spread to a third of the united states @xcite . the sea lamprey and round goby have invaded the great lakes region in the northern united states and canada @xcite . these species have caused a severe decline in lake trout and other indigenous fish populations . lastly the zebra mussel has invaded many us and canadian waterways causing large scale losses to the hydropower industry @xcite . another factor attributed to the increase of an invasive population , is that the environment may turn favorable for the invasive species in question , while becoming unfavorable for its competitors or natural enemies . in such situations , the population of the invasive species may rapidly increase . this is defined as an _ outbreak _ in population dynamics @xcite . these rapid changes tend to destabilize an ecosystem and pose a threat to the natural environment . as an illustration , in the european alps certain environmental conditions have enabled the population of the larch budmoth to become large enough that entire forests have become defoliated @xcite . in most ecological landscapes , due to exogenous factors , one always encounters an invasive species and an invaded species . if the density of the former , be it invasive , disease causing , an agricultural pest , defoliator or other , undergoes a rapid transition to a high level in population , the results can be catastrophic both for local and nonlocal populations . biological and chemical controls are an adopted strategy to limit invasive populations @xcite . chemical controls are most often based on direct methods , via the use of pesticides @xcite . biological control comprises of essentially releasing natural enemies of the invasive species / pest against it . these can be in the form of predators , parasitoids , pathogens or combinations thereof @xcite . there are many problems with these approaches . for example , a local eradication effort was made by usgs through a mass scale poisoning of fish in order to prevent the asian carp ( an invasive fish species ) from entering the chicago sanitary and ship canal @xcite . the hope was to protect the fishing interests of the region . however , among the tens of thousands of dead fish , _ biologists found only one asian carp_. thus chemical control is not an exhaustive strategy . however , biological controls are also not without its share of problems . in fact , sometimes the introduced species might attack a variety of species , other than those it was released to control . this phenomena is referred to as a _ non - target effect _ @xcite , and is common in natural enemies with a broad host range . for example , the cane toad was introduced in australia in 1935 to control the cane beetle . however , the toad seemingly attacked everything else but its primary target @xcite ! in addition , the toad is highly poisonous and therefore predators shy away from eating it . this has enabled the toad population to grow virtually unchecked and is today considered one of australia s worst invasive species @xcite . in studies of biological control in the united states estimate that when parasitoids are released as biological controls that @xmath1 of the introduced species will attack non - targets , in canada these numbers are estimated as high as @xmath2 @xcite . in practise it is quite difficult to accurately predict these numbers . the current drawbacks make it clear that alternative controls are necessary . furthermore , that modeling of alternative controls is important to validate the effectiveness of a management strategy that hopes to avoid non - target effects . such modeling is essential to access and predict the best controls to employ , so that the harmful population will decrease to low and manageable levels . this then gives us confidence to devise actual field trials . we should note that in practice actual eradication is rarely achieved . thus there are clear questions that motivate this research : 1 . how does one define a `` high '' level for a population , and further , how well does an introduced control actually work , at various high levels ? 2 . is it possible to design controls that avoid chemicals / pesticides / natural enemy introduction , and are still successful ? this paper addresses these questions through the investigation of a mathematical model that : 1 . blows - up in finite time . given a mathematical model for a nonlinear process , say through a partial differential equation ( pde ) , one says finite time blow up occurs if @xmath3 where @xmath4 is a certain function space with a norm @xmath5 , @xmath6 is the solution to the pde in question , and @xmath7 is the blow up time . therefore `` highest '' level is equated with blow up , and the population passes through every conceivable high level of population as it approaches infinity . 2 . incorporates certain controls that avoid chemicals / pesticides / natural enemy introduction . the controls we examine are : 1 . the primary food source of the invasive species is protected through spatial refuges . the regions that offer protection are called _ prey refuges _ and may be the result of human intervention or natural byproducts , such as improved camouflage . 2 . an overcrowding term is introduced to model the movement or dispersion from high concentrations of the invasive species . densely populated regions have increased intraspecific competition and interference which cause an increase in the dispersal of the invasive species . this is an improvement to current mathematical models and will be seen to be beneficial if used a control . 3 . we introduce role reversing mechanisms , where the role of the primary food source of the invasive species , and the prey of this food source , is switched in the open area ( the area without refuge ) . this models situations where the topography provides competitive advantages to certain species . it will be seen that this also is beneficial if used a control . in effect , this uses the current ecosystem and by modifying the landscape a natural predator in the environment has an advantage in key areas . hence , the invasive species population will adversely be effected . it can also be thought of as introducing a competitor of the invasive species , to compete with it for its prey . note , none of the above rely on enemy release to predate on the invasive species , or a parasite or pathogen release to infect the invasive species . thus potential non - target effects due to such release can be avoided . in the literature finite time blow up is also referred to as an explosive instability @xcite . there is a rich history of blow up problems in pde theory and its interpretations in physical phenomenon . for example , this feature is seen in models of thermal runaway , fracture and shock formation , and combustion processes . thus blow up may be interpreted as the failure of certain constitutive materials leading to gradient catastrophe or fracture , it may be interpreted as an uncontrolled feedback loop such as in thermal runaway , leading to explosion . it might also be interpreted as a sudden change in physical quantities such as pressure or temperature such as during a shock or in the ignition process . the interested reader is referred to @xcite . blow up in population dynamics is usually interpreted as excessively high concentrations in small regions of space , such as seen in chemotaxis problems @xcite . our goal in the current manuscript is to bring yet another interpretation of blow up to population dynamics , that is one where we equate such an excessive concentration or blow up " of an invasive population with disaster for the ecosystem . furthermore , it is to devise controls that avoid non - target effects and yet reduce the invasive population , before the critical blow up time . in the following , the norms in the spaces @xmath8 , @xmath9 and @xmath10 are respectively denoted by @xmath11 in addition , the constants @xmath12 , @xmath13 and @xmath14 may change between subsequent lines , as the analysis permits , and even in the same line if so required . the current manuscript is organised as follows . in section [ 2 ] we formulate the spatially explicit model that we consider . in section [ 3 ] we describe in detail the modeling of the control mechanisms that we propose , and term ecological damping " . here we make three key conjectures [ c1 ] , [ c2 ] and [ c3 ] , concerning our control mechanisms . section [ 4 ] is devoted to some analytical results given via lemma [ lem : wsol ] , theorem [ thm : wsolimproved ] and [ thm : gattr ] . section [ 5 ] is where we explain our numerical approximations and test conjectures [ c1 ] , [ c2 ] and [ c3 ] numerically . in section [ 6 ] we investigate spatio - temporal dynamics in the model . we investigate the effect of overcrowding on turing patterns , and we also confirm spatio - temporal chaos in the model . lastly we offer some concluding remarks and discuss future directions in section [ 7 ] .

in this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three - species food chain . the controls avoid chemical treatments and/or natural enemy introduction , thus eliminating various non - target effects associated with such classical methods . lastly , we confirm the existence of spatio - temporal chaos .

in this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three - species food chain . we allow for finite time blow - up in the model as a mathematical construct to mimic the explosive increase in population , enabling the species to reach disastrous " levels , in a finite time . we next propose various controls to drive down the invasive population growth and , in certain cases , eliminate blow - up . the controls avoid chemical treatments and/or natural enemy introduction , thus eliminating various non - target effects associated with such classical methods . we refer to these new controls as ecological damping " , as their inclusion dampens the invasive species population growth . further , we improve prior results on the regularity and turing instability of the three - species model that were derived in . lastly , we confirm the existence of spatio - temporal chaos . rana d. parshad , kelly black , and emmanuel quansah matthew beauregard

0711.0705

i

the compound channel consists of a set of channels indexed by @xmath1 with the same input and output alphabets but different conditional probabilities . in the setting of the compound channel only one actual channel @xmath2 is used in all transmissions . the transmitter and the receiver know the family of channels but they have no prior knowledge of which channel is actually used . there is no distribution law on the family of channels and the communication has to be reliable for all channels in the family . blackwell et al . @xcite and independently wolfowitz @xcite showed that the capacity of a compound channel consisting of memoryless channels only , and without feedback , is given by @xmath3 where @xmath4 denotes the input distribution to the channel , @xmath5 denotes the conditional probability of a memoryless channel indexed by @xmath2 , and the notation @xmath6 denotes the mutual information of channel @xmath7 for the input distribution @xmath8 , i.e. , @xmath9 the capacity in ( [ eqn : capacitymemorylesscompoundnofb ] ) is in general less than the capacity of every channel in the family . wolfowitz , who coined the term `` compound channel , '' showed that if the transmitter knows the channel @xmath2 in use , then the capacity is given by @xcite @xmath10 where @xmath11 is the capacity of the channel indexed by @xmath2 . this shows that knowledge at the transmitter of the channel @xmath2 in use helps in that the infimum of the capacities of the channels in the family can now be achieved . in the case that @xmath12 is a finite set , then it follows from wolfowitz s result that @xmath13 is the feedback capacity of the memoryless compound channel , since the transmitter can use a training sequence together with the feedback to estimate @xmath2 with high probability . in this paper we show that when @xmath12 is not limited to finite cardinality , the feedback capacity of the memoryless compound channel is given by @xmath14 . one might be tempted to think that for a compound channel with memory , feedback provides a means to achieve the infimum of the capacities of the channels in the family . however this is not necessarily true , as we show in example [ example : compoundge ] , which is taken from @xcite and applied to the compound gilbert - elliot channel with feedback . that example is found in section [ section : compoundge ] . a comprehensive review of the compound channel and its role in communication is given by lapidoth and narayan @xcite . of specific interest in this paper are compound channels with memory which are often used to model wireless communication in the presence of fading @xcite . lapidoth and telatar @xcite derived the following formula for the compound channel capacity of the class of finite state channels ( fsc ) when there is no feedback available at the transmitter . @xmath15 where @xmath16 denotes the initial state of the fsc , and @xmath17 and @xmath18 denote the input distribution and channel conditional probability for block length @xmath19 . lapidoth and telatar s achievability result makes use of a universal decoder for the family of finite - state channels . the existence of the universal decoder is proved by feder and lapidoth in @xcite by merging a finite number of maximum - likelihood decoders , each tuned to a channel in the family @xmath12 . throughout this paper we use the concepts of causal conditioning and directed information which were introduced by massey in @xcite . kramer extended those concepts and used them in @xcite to characterize the capacity of discrete memoryless networks . subsequently , three different proofs tatikonda and mitter @xcite , permuter , weissman and goldsmith @xcite and kim @xcite have shown that directed information and causal conditioning are useful in characterizing the feedback capacity of a point - to - point channel with memory . in particular , this work uses results from @xcite that show that gallager s 4,5 ) upper and lower bound on capacity of a fsc can be generalized to the case that there is a time - invariant deterministic feedback , @xmath20 , available at the encoder at time @xmath21 . in this paper we extend lapidoth and telatar s work for the case that there is deterministic time - invariant feedback available at the encoder by replacing the regular conditioning with the causal conditioning . then we use the feedback capacity theorem to study the compound gilbert - elliot channel and the memoryless compound channel and to specify a class of compound channels for which the capacity is zero if and only if the feedback capacity is zero . the proof of the feedback capacity of the fsc is found in section [ section : converse ] , which describes the converse result , and section [ section : achievability ] , where we prove achievability . as a consequence of the capacity result , we show in section [ section : compoundge ] that feedback does not increase the capacity of the compound gilbert - elliot channel . we next show in section [ section : iff ] that for a family of stationary and uniformly ergodic markovian channels , the capacity of the compound channel is positive if and only if the feedback capacity of the compound channel is positive . finally , we return to the memoryless compound channel in section [ section : memorylesscompound ] and make use of our capacity result to provide a proof of the feedback capacity . the notation we use throughout is as follows . a capital letter @xmath22 denotes a random variable and a lower - case letter , @xmath23 , denotes a realization of the random variable . vectors are denoted using subscripts and superscripts , @xmath24 and @xmath25 . we deal with discrete random variables where a probability mass function on the channel input is denoted @xmath26 and @xmath27 denotes a mass function on the channel output . when no confusion can result , we will omit subscripts from the probability functions , i.e. , @xmath28 will denote @xmath29 .

, we show that feedback does not increase the capacity of the compound gilbert - elliot channel . additionally , we show that for a stationary and uniformly ergodic markovian channel , if the compound channel capacity is zero without feedback then it is zero with feedback . finally , we use our result on the finite - state channel to show that the feedback capacity of the memoryless compound channel is given by . compound channel , feedback capacity , finite state channel , directed information , causal conditioning probability , gilbert - elliot channel , universal decoder , code - trees , types of code - trees , sanov s theorem , pinsker s inequality

in this work we find the capacity of a compound finite - state channel with time - invariant deterministic feedback . the model we consider involves the use of fixed length block codes . our achievability result includes a proof of the existence of a universal decoder for the family of finite - state channels with feedback . as a consequence of our capacity result , we show that feedback does not increase the capacity of the compound gilbert - elliot channel . additionally , we show that for a stationary and uniformly ergodic markovian channel , if the compound channel capacity is zero without feedback then it is zero with feedback . finally , we use our result on the finite - state channel to show that the feedback capacity of the memoryless compound channel is given by . compound channel , feedback capacity , finite state channel , directed information , causal conditioning probability , gilbert - elliot channel , universal decoder , code - trees , types of code - trees , sanov s theorem , pinsker s inequality

1111.2210

i

the study of dirac points , i.e. the contact points between different energy bands with an approximate linear dispersion relation , has become a major issue since the experimental breakthrough in graphene - based electronics @xcite . indeed , the low - energy electronic properties of graphene are governed by a pseudo - relativistic 2d dirac equation for massless fermions situated at the @xmath0 and @xmath1 corners of the brillouin zone @xcite . the dirac points are topologically protected and a gap is opened only when the inversion symmetry of the lattice or the time - reversal symmetry are broken . the possibility to generate topological phase transitions in graphene - like systems has recently attracted a great deal of attention . within a tight - binding description , an anisotropy in the nearest - neighbor hopping parameters makes the dirac points move away from the high - symmetry @xmath0 and @xmath1 points and , under appropriate conditions , merge at time - reversal invariant points in the first brillouin zone @xcite . most saliently , this merging of dirac points is associated with a topological phase transition between a semimetallic phase and a gapped band - insulating phase . an experimental investigation of the merging transition in graphene turns out to be problematic , since in order to appropriately modify the hopping parameters , an unphysically large strain needs to be applied to the graphene sheet @xcite . an alternative system for the study of such topological transitions is that of ultracold atoms trapped in a honeycomb optical lattice . since the seminal realization of the superfluid - mott - insulator transition in the bose - hubbard model , ultracold atoms in optical lattices have become promising systems to emulate condensed - matter physics . indeed , the lattice geometry , the dimensionality , the atomic species , as well as the interactions can be engineered with a high degree of precision . the more involved triangular and honeycomb geometries were recently realized experimentally and exotic correlated states of matter have been observed experimentally @xcite or predicted theoretically @xcite . the application of a time - periodic perturbation on the optical lattice introduces yet another parameter scale into the system . a periodic shaking of the optical lattice , up to the khz frequency range , has been implemented by placing one of the mirrors used to create the optical lattice on a piezoelectric material , such that the mirror can be moved back and forth in the direction of the beam @xcite . the floquet formalism shows that the hopping energy of the atoms in the shaken lattice is renormalized by a bessel function , as a function of the shaking frequency and amplitude , thus allowing both the magnitude and the sign of the hopping parameter to change . this rather counter - intuitive phenomenon , as compared to the standard tight - binding physics , has been experimentally observed in a one - dimensional cold - atomic system @xcite . in this paper , we consider ultracold fermions trapped in a _ shaken _ honeycomb optical lattice . within the floquet formalism , we derive an effective hamiltonian that generalizes that of a graphene - like material under strain . in particular , we find that the alignment and merging of dirac points in momentum space are now accessible with ultracold fermions in the shaken optical lattice and the phase diagram consists of various phases of the corresponding solid - state system that are otherwise difficult to realize . furthermore , by taking into account a hubbard - like interaction for spinful fermions , we study the density profiles for the homogenous and the trapped gas within a hartree - fock theory . the outline of this paper is the following : in sec.[sec01a ] we introduce the time - dependent hamiltonian and in sec.[sec01b ] we derive the time - independent one , by applying the floquet formalism . in sec.[sec02 ] we investigate the merging and alignment of dirac points , when the optical lattice is shaken along specific directions . the description is extended to include interactions in sec.[sec03 ] , where we derive the dependence of the density on the chemical potential . implications of our results for experiments are discussed in sec.[sec04 ] . finally , our conclusions are presented in sec.[conc ] .

inspired by the recent creation of the honeycomb optical lattice and the realization of the mott insulating state in a square lattice by shaking , we study here the shaken honeycomb optical lattice . for a periodic shaking of the lattice , a floquet theory may be applied to derive a time - independent hamiltonian . in this effective description , the hopping parameters are renormalized by a bessel function , which depends on the shaking direction , amplitude and frequency . consequently , the hopping parameters can vanish and even change sign , in an anisotropic manner , thus yielding different band structures . here , we study the merging and the alignment of dirac points and dimensional crossovers from the two dimensional system to one dimensional chains and zero dimensional dimers .

inspired by the recent creation of the honeycomb optical lattice and the realization of the mott insulating state in a square lattice by shaking , we study here the shaken honeycomb optical lattice . for a periodic shaking of the lattice , a floquet theory may be applied to derive a time - independent hamiltonian . in this effective description , the hopping parameters are renormalized by a bessel function , which depends on the shaking direction , amplitude and frequency . consequently , the hopping parameters can vanish and even change sign , in an anisotropic manner , thus yielding different band structures . here , we study the merging and the alignment of dirac points and dimensional crossovers from the two dimensional system to one dimensional chains and zero dimensional dimers . we also consider next - nearest - neighbor hopping , which breaks the particle - hole symmetry and leads to a metallic phase when it becomes dominant over the nearest - neighbor hopping . furthermore , we include weak repulsive on - site interactions and find the density profiles for different values of the hopping parameters and interactions , both in a homogeneous system and in the presence of a trapping potential . our results may be experimentally observed by using momentum - resolved raman spectroscopy .

1111.2210

r

honeycomb optical lattices have recently been realized experimentally , although the existing setups have only been used to investigate bosonic atoms @xcite . shaking of a lattice has been experimentally implemented in a one - dimensional one by a periodic modulation on the position of the reflecting mirrors @xcite . for a honeycomb lattice , the shaking could be realized by means of an acousto - optical device , as proposed for a triangular lattice in ref . @xcite . the magnitude of the nn hopping parameter @xmath71 in a honeycomb optical lattice has been evaluated in ref . @xcite , @xmath162 in terms of the recoil energy @xmath163 and the magnitude of the potential barrier between nearest - neighbor lattice sites @xmath164 . the magnitude of the nnn hopping parameter @xmath107 is not yet known , but could be determined from numerical band structure calculations . in a typical experimental situation , we expect the ratio @xmath165 to be in the @xmath166 range , in agreement with the parameter chosen in the discussion of sec.[sec02c ] . in a typical experiment , the shaking amplitude would be increased from zero to a finite value . fig.[fig : phases - linear ] shows in which order the system goes through the different phases and dimensions upon increasing the shaking amplitude . here , also the values of the shaking amplitude required for the dimensional crossovers are given for the same system as discussed in sec.[sec02c ] and @xmath167 . if the shaking direction is perpendicular to one of the nn vectors , the system will be in the gapped insulating phase beyond a certain value of the shaking amplitude , since the bessel function crosses the value 0.5 only once and never obtains the value -0.5 . if the shaking is parallel to one of the nn vectors , the system will be in the metallic phase beyond a certain value of the shaking amplitude . nevertheless , it is still possible to induce a merging of dirac points and to open up a gap in the spectrum , since the nn hopping parameters are renormalized such that the value of one of them will in general differ from that of the other two . however , whether the system is actually driven into an insulating phase or remains metallic depends on the precise value of the ratio @xmath165 . in nm correspond to the optical lattice discussed in sec.[sec02c ] with @xmath168 , @xmath169khz , @xmath170 nm , and containing @xmath83k atoms . ( a ) shaking perpendicular to one of the nn hopping directions . ( b ) shaking parallel to one of the nn hopping directions . ] in experiments , an overall harmonic trapping potential is imposed to confine the atoms . it is described by @xmath171 where @xmath172 is the trapping frequency , and @xmath9 is the position measured from the center of the trap . by applying the local density approximation ( lda ) , one finds that the chemical potential evolves radially according to @xmath173 . fig.[fig : density - r](a ) shows the density profile for several ratios of @xmath157 , without nnn hopping or interactions . the case with @xmath174 , when the system is in the extreme limit of the band insulating phase , can be well distinguished from the other cases . fig.[fig : density - r](b ) shows that stronger interactions lead to a higher density away from the center of the trap . this effect becomes visible when the density starts to deviate from one particle per lattice site . next - nearest - neighbor hopping leads to a higher density at the edge of the cloud compared to the case without nnn hopping , which can be seen from comparing figs.[fig : density - r](a ) and ( c ) and from fig.[fig : density - r](d ) . the latter shows the effect of nnn hopping on the density profile for the case where the nnn hopping gives rise to the metallic phase for two different shaking vectors . in the first case , @xmath112 , which gives @xmath113 , such that without nnn hopping , the system is in the zero - gapped semi - metallic phase and the dirac points are located very close to the corners of the first brillouin zone . in the second case , @xmath114 , which results in @xmath115 , such that without nnn hopping the system is in the insulating phase and the two energy bands are almost flat . as a function of the distance from the trap s centre @xmath175 , which is expressed in units of the nearest - neighbor distance @xmath144 . the trapping frequency has been chosen such that the trapping potential is given by @xmath176 . the chemical potential @xmath16 for each case has been chosen such that the density at the trap s centre @xmath35 is one particle per site . this corresponds to half - filling , since we consider 2 species of fermions . unless specified otherwise in the figure , the nn hopping parameters @xmath159 , the nnn hopping parameter @xmath86 , the interaction strength @xmath160 , and the inverse temperature @xmath161 . ( a ) effect of the renormalization of the nn hopping parameters . ( b ) effect of the interaction strength @xmath121 for the isotropic case . ( c ) effect of the nnn hopping parameter @xmath116 in the shaken lattice . ( d ) the metallic phase . for the isotropic cases , @xmath112 , whereas for the 0d cases @xmath114 . these systems are in the metallic phase for @xmath116 , whereas for @xmath86 they are in the semi - metallic and the insulating phase , respectively . ] as a function of the distance from the trap s centre @xmath175 , which is expressed in units of the nearest - neighbor distance @xmath144 . the trapping frequency has been chosen such that the trapping potential is given by @xmath176 . the chemical potential @xmath16 for each case has been chosen such that the density at the trap s centre @xmath35 is one particle per site . this corresponds to half - filling , since we consider 2 species of fermions . unless specified otherwise in the figure , the nn hopping parameters @xmath159 , the nnn hopping parameter @xmath86 , the interaction strength @xmath160 , and the inverse temperature @xmath161 . ( a ) effect of the renormalization of the nn hopping parameters . ( b ) effect of the interaction strength @xmath121 for the isotropic case . ( c ) effect of the nnn hopping parameter @xmath116 in the shaken lattice . ( d ) the metallic phase . for the isotropic cases , @xmath112 , whereas for the 0d cases @xmath114 . these systems are in the metallic phase for @xmath116 , whereas for @xmath86 they are in the semi - metallic and the insulating phase , respectively . ] as a function of the distance from the trap s centre @xmath175 , which is expressed in units of the nearest - neighbor distance @xmath144 . the trapping frequency has been chosen such that the trapping potential is given by @xmath176 . the chemical potential @xmath16 for each case has been chosen such that the density at the trap s centre @xmath35 is one particle per site . this corresponds to half - filling , since we consider 2 species of fermions . unless specified otherwise in the figure , the nn hopping parameters @xmath159 , the nnn hopping parameter @xmath86 , the interaction strength @xmath160 , and the inverse temperature @xmath161 . ( a ) effect of the renormalization of the nn hopping parameters . ( b ) effect of the interaction strength @xmath121 for the isotropic case . ( c ) effect of the nnn hopping parameter @xmath116 in the shaken lattice . ( d ) the metallic phase . for the isotropic cases , @xmath112 , whereas for the 0d cases @xmath114 . these systems are in the metallic phase for @xmath116 , whereas for @xmath86 they are in the semi - metallic and the insulating phase , respectively . ] as a function of the distance from the trap s centre @xmath175 , which is expressed in units of the nearest - neighbor distance @xmath144 . the trapping frequency has been chosen such that the trapping potential is given by @xmath176 . the chemical potential @xmath16 for each case has been chosen such that the density at the trap s centre @xmath35 is one particle per site . this corresponds to half - filling , since we consider 2 species of fermions . unless specified otherwise in the figure , the nn hopping parameters @xmath159 , the nnn hopping parameter @xmath86 , the interaction strength @xmath160 , and the inverse temperature @xmath161 . ( a ) effect of the renormalization of the nn hopping parameters . ( b ) effect of the interaction strength @xmath121 for the isotropic case . ( c ) effect of the nnn hopping parameter @xmath116 in the shaken lattice . ( d ) the metallic phase . for the isotropic cases , @xmath112 , whereas for the 0d cases @xmath114 . these systems are in the metallic phase for @xmath116 , whereas for @xmath86 they are in the semi - metallic and the insulating phase , respectively . ] we emphasize that , in the present paper , we only discuss weak correlations that adiabatically affect the density . however , when increasing further the onsite interaction , one may expect correlated phases with inhomogeneous density , even at half - filling . a detailed study of these correlated phases is a vast research issue that is yet ongoing and that is beyond the scope of the present paper . here , we only provide a glimpse on how the density , which we discussed above in the weak - coupling limit , may evolve in view of some phases studied in the literature . mean - field calculations indicate a transition to an antiferromagnetic state above a value of @xmath177 @xcite , whereas more sophisticated quantum monte - carlo calculations indicate an intermediate spin - liquid phase between the semimetal and the anti - ferromagnetic phase @xcite . the spin - liquid phase may be viewed as a mott insulator with a charge localization on the lattice sites , and recent slave - rotor calculations indicate that such spin - liquid phases dominate the phase diagram for @xmath178 @xcite , which is the parameter range where the dirac points would merge in the absence of interactions . the precise transition between the weakly - interacting liquid phases and these strongly - correlated mott insulators could in principle be determined with the help of the above - mentioned density measurements . a more promising technique for detecting dirac - point motion is momentum - resolved raman spectroscopy . this technique has been proposed as an equivalent of angle - resolved photoemission spectroscopy for cold atom systems @xcite . it has not yet been realized experimentally , while momentum - resolved radio - frequency spectroscopy , which is a very similar technique , has already been implemented @xcite . notice further that another very similar technique , momentum - resolved bragg spectroscopy , has been applied to ultracold bosonic atoms in a static optical lattice by ernst _ et al_. @xcite . momentum - resolved spectroscopy can allow us to indirectly visualize the band structure . in momentum - resolved raman spectroscopy , two laser pulses with frequencies @xmath179 and @xmath180 are irradiated upon the system . if the frequency difference is in resonance with a transition @xmath181 between atomic hyperfine states , @xmath182 , some atoms are excited in a second - order process to the higher hyperfine state . then , with state - selective time - of - flight measurements , the dispersion of the atoms in the new state are measured , from which the dispersion of the original atoms can be derived . when the atoms are confined in a trapping potential and the laser pulses are focussed on the center of the trap , the quality of the results obtained by raman spectroscopy is comparable to those of a homogeneous system @xcite . furthermore , raman spectroscopy yields better results for a system with strong interactions compared to standard time - of - flight measurements @xcite . notice that momentum resolved raman spectroscopy was originally proposed to be applied to a gas of ultracold fermionic atoms at equilibrium and not for a shaken lattice . we therefore discuss , in this final paragraph , why we think that this technique may also be applied to the present case . naturally , as long as the frequencies of the additional lasers in the raman - spectroscopy setup are small with respect to the shaking frequency , @xmath183 , even the full system satisfies the condition ( [ eq : condition ] ) for the validity of floquet theory . as in the case of interactions , one needs , however , to avoid resonances between the different laser frequencies that could become critical @xcite . the opposite limit , in which the laser frequencies and that of the hyperfine transition are larger than the shaking frequency , is more delicate . however , even then , the shaken system remains at quasi - equilibrium as long as the intensities of the lasers used in raman spectroscopy are weak , such that they only constitute a small perturbation . the atomic dynamics probed even at high frequencies is therefore still that of the atoms at quasi - equilibrium , with the band strucure obtained from floquet theory . furthermore , in the experimental studies by zenesini _ et al_. @xcite , time - of - flight measurements were used to determine the momentum distribution of bosonic atoms in a shaken lattice . apart from the time - scale considerations , there are also some length scales that need to be taken into account . there are indeed two requirements for the correct size of the focus of the laser beams . on the one hand , it needs to be larger than the lattice spacing , such that sufficiently many atoms can be excited , while on the other hand the focus of the beams should be small enough , in order to have an approximately flat trapping potential inside the focus area . in addition , choosing the length of the pulses could possibly be a problem , since for shorter pulses , the excited atoms will be less affected by the lattice potential , whereas for longer pulses more atoms can be excited , leading to a stronger signal .

furthermore , we include weak repulsive on - site interactions and find the density profiles for different values of the hopping parameters and interactions , both in a homogeneous system and in the presence of a trapping potential . our results may be experimentally observed by using momentum - resolved raman spectroscopy .

inspired by the recent creation of the honeycomb optical lattice and the realization of the mott insulating state in a square lattice by shaking , we study here the shaken honeycomb optical lattice . for a periodic shaking of the lattice , a floquet theory may be applied to derive a time - independent hamiltonian . in this effective description , the hopping parameters are renormalized by a bessel function , which depends on the shaking direction , amplitude and frequency . consequently , the hopping parameters can vanish and even change sign , in an anisotropic manner , thus yielding different band structures . here , we study the merging and the alignment of dirac points and dimensional crossovers from the two dimensional system to one dimensional chains and zero dimensional dimers . we also consider next - nearest - neighbor hopping , which breaks the particle - hole symmetry and leads to a metallic phase when it becomes dominant over the nearest - neighbor hopping . furthermore , we include weak repulsive on - site interactions and find the density profiles for different values of the hopping parameters and interactions , both in a homogeneous system and in the presence of a trapping potential . our results may be experimentally observed by using momentum - resolved raman spectroscopy .

0807.3481

i

recently , considerable experimental progress has been made in the spectroscopy of baryons containing a single heavy quark . the cdf collaboration has observed four bottom baryons @xmath1 and @xmath2 @xcite . the do @xcite and cdf @xcite collaborations have seen the @xmath3 . the babar collaboration discovered the @xmath4 state @xcite . the cdf sensitivity appears adequate to observe new heavy baryons . study of the electromagnetic properties of baryons can give noteworthy information on their internal structure . one of the main static electromagnetic parameters of the baryons is their magnetic moments . magnetic moments of the heavy baryons in the framework of different approaches are widely discussed in the literature . in @xcite the magnetic moments of heavy baryons containing c - quark have been calculated using the naive quark model . in @xcite , the magnetic moments of charm and bottom baryons are computed in quark model and in @xcite heavy baryon magnetic moments are investigated within soliton type approaches . calculation of the magnetic moments of heavy baryons in the framework of relativistic quark model is done in @xcite . in @xcite the magnetic moments of @xmath5 and @xmath6 baryons are estimated in qcd sum rules with external electromagnetic field . the magnetic moments of the @xmath7 , @xmath8 and @xmath9 transition magnetic moments in light cone qcd sum rules are calculated in @xcite . the magnetic moments of @xmath10 in the same framework is studied in @xcite ( a detailed description of this method can be found in @xcite and references theirin ) . in the present work , we study the magnetic moments and masses of the ground state baryons with total angular momentum 3/2 and containing one heavy quark within light cone qcd sum rules . the paper is organized as follows . in section 2 , the light cone qcd sum rules for mass and magnetic moments of heavy baryons are calculated . section 3 is devoted to the numerical analysis of the mass and magnetic moment sum rules and discussion .

inspired by the results of recent experimental discoveries for charm and bottom baryons , the masses and magnetic moments of the heavy baryons with containing a single heavy quark are studied within light cone qcd sum rules method . a comparison of our results on the magnetic moments of these baryons and the hyper central model predictions is presented .

inspired by the results of recent experimental discoveries for charm and bottom baryons , the masses and magnetic moments of the heavy baryons with containing a single heavy quark are studied within light cone qcd sum rules method . our results on the masses of heavy baryons are in good agreement with predictions of other approaches , as well as with the existing experimental values . our predictions on the masses of the states , which are not yet discovered in the experiments , can be tested in the future experiments . a comparison of our results on the magnetic moments of these baryons and the hyper central model predictions is presented . pacs : 11.55.hx , 13.40.em , 14.20.lq , 14.20.mr

1611.01635

c

as demonstrated in refs . @xcite , both the scalar and vector lq scenarios could explain the anomalies observed in @xmath0 and @xmath1 decays and , for each scenario , there exist two best - fit solutions for the operator coefficients , because the other two solutions for scalar lq are already excluded by the @xmath137 decay @xcite . to further explore these two interesting scenarios , in this paper , we have studies their effects in the semi - leptonic @xmath2 decay , which is induced by the same quark - level transition as in @xmath0 decays . besides the branching fraction @xmath3 and the ratio @xmath41 , we have also discussed the @xmath29 distributions of these two observables , as well as the @xmath5 and @xmath6 longitudinal polarizations and the lepton - side forward - backward asymmetry , using the @xmath40 transition form factors from both the qcd sum rules and the latest lattice qcd calculations . using the best - fit solutions for the operator coefficients allowed by the current data of mesonic decays , we have found that the two lq scenarios give the similar amounts of enhancements relative to the sm predictions for the branching fraction @xmath3 and the ratio @xmath41 . the two best - fit solutions in each of the two scenarios are still found to be indistinguishable from each other based only on these two observables . on the other hand , both of the two lq scenarios give nearly the same predictions as the sm for the @xmath5 and @xmath6 longitudinal polarizations , as well as the lepton - side forward - backward asymmetry . as a consequence , we conclude that , while the two lq scenarios could be distinguished from the sm , it is quite difficult to distinguish between them using the semi - leptonic @xmath2 decay . with the large number of @xmath31 produced at the lhc , we expect that , with future measurements of the observables in @xmath2 decay at the lhcb , the two lq scenarios could be further tested , and even differentiated from the other np explanations to the @xmath7 anomalies .

, we study their effects in the semi - leptonic decay . using the best - fit solutions for the operator coefficients allowed by the current data of mesonic decays , we find that ( i ) the two scenarios give the similar amounts of enhancements to the branching fraction and the ratio , ( ii ) the two best - fit solutions in each of the two scenarios are also indistinguishable from each other , ( iii ) both scenarios give nearly the same predictions as the standard model for the longitudinal polarizations of and as well as the lepton - side forward - backward asymmetry . with future measurements of these observables in decay at the lhcb , the two leptoquark scenarios could be further tested , and even differentiated from the other np explanations to the anomalies .

it has been shown that the anomalies observed in and decays can be resolved by adding a single scalar or vector leptoquark to the standard model , while constraints from other precision measurements in the flavour sector can be satisfied without fine - tuning . to further explore these two interesting scenarios , in this paper , we study their effects in the semi - leptonic decay . using the best - fit solutions for the operator coefficients allowed by the current data of mesonic decays , we find that ( i ) the two scenarios give the similar amounts of enhancements to the branching fraction and the ratio , ( ii ) the two best - fit solutions in each of the two scenarios are also indistinguishable from each other , ( iii ) both scenarios give nearly the same predictions as the standard model for the longitudinal polarizations of and as well as the lepton - side forward - backward asymmetry . with future measurements of these observables in decay at the lhcb , the two leptoquark scenarios could be further tested , and even differentiated from the other np explanations to the anomalies .

hep-ph0601139

i

a search through the spires database reveals over 350 articles whose titles contain the expressions ` quark jet(s ) ' or ` gluon jet(s ) ' @xcite . the idea of quark and gluon jets appears so intuitive that it hardly seems necessary to examine the question of what it means . yet , when going beyond leading order perturbative qcd , the concept of quark and gluon jets is only meaningful once a procedure has been defined to classify an ensemble of partons into a set of jets , each with a well - defined flavour a flavour that is insensitive to the addition of extra soft or collinear branchings . to our knowledge the question of how to do this in general has not been addressed in the literature . as well as being of intrinsic interest , the question of how to define the flavour of a partonic jet is becoming of increasing practical importance as the study of qcd is extended to multi - jet ensembles ( by jets we mean both incoming and outgoing ones ) : in studies of @xmath9 jets one knows that the basic @xmath10-jet born configuration consists of quark jets ; but for jet production at hadron colliders , the born configuration involves @xmath10 incoming and @xmath10 outgoing jets and many flavour channels are possible , @xmath11 , @xmath12 , @xmath13 , etc . the ability to assign flavours to the jets is especially useful when combining fixed - order predictions with all - order calculations ( be it for parton showers as in @xcite or for analytical resummation @xcite ) . this is because all - order calculations are carried out for a fixed born configuration , with a single flavour channel at a time , while fixed - order calculations implicitly sum over all flavour channels and can at best be split up a posteriori to match onto the individual flavour channels of the all - order calculation . as a concrete example , consider the calculation of higher - order corrections to the process @xmath14 , fig . [ fig:2to3]a . an all - order calculation treats the addition of any number of soft / collinear gluons and extra @xmath15 pairs implicitly , leaving the underlying @xmath16 flavours unchanged . when trying to supplement this with results of a fixed order calculation one encounters the problem that higher - order contributions can not be uniquely assigned to any given @xmath16 flavour channel the @xmath17 corrections to @xmath14 include e.g. a @xmath18 piece , but a fixed order calculation gives only the squared sum of all @xmath19 diagrams , among them @xmath20 and @xmath21 , illustrated in fig . [ fig:2to3]b and [ fig:2to3]c respectively . there can exist no unambiguous procedure for separating the @xmath22 contribution into its different underlying channels , both because the different channels are not individually gauge invariant and because they interfere when squaring the amplitude . flavour channel for a @xmath23 parton scattering process ; ( b ) higher - order diagram that can be seen as a correction to ( a ) ; ( c ) higher - order diagram that can be seen as a correction to the process @xmath24 , but with the same final - state partons as ( b).,scaledwidth=95.0% ] one therefore needs a prescription to assign @xmath22 either to the @xmath25 or the @xmath26 underlying born @xmath23 process ( or else to declare it irreducibly @xmath27 like ) , it only being in the @xmath25 case that one needs to put it together with the @xmath14 all - order calculation . this reclassification of a @xmath28 event as a @xmath23 event is similar conceptually to what is done in a normal jet algorithm , except that not only should the momenta of the resulting @xmath23 configuration be infrared and collinear safe , but so should the flavours . accordingly we call it a jet - flavour algorithm . an obvious approach to defining jet flavours at the perturbative level would be to start with an existing jet algorithm , such as the @xmath0-clustering @xcite or cone @xcite algorithm , that defines jets such that each particle belongs to at most one jet . one can then determine the net flavour content of each of the jets , as the total number of quarks minus antiquarks for each quark flavour . jets with no net flavour are identified as gluon jets , those with ( minus ) one unit of net flavour are ( anti ) quark jets , while those with more than one unit of flavour ( or both a flavour and a different antiflavour ) can not be identified with a single qcd parton . pair ( @xmath29 , @xmath30 ) with the @xmath31 and @xmath32 then clustered into different jets ( @xmath33 , @xmath34 ) . ] applied to the @xmath0 or cone algorithms , this procedure yields a jet flavour that is infrared ( ir ) safe at ( relative ) order @xmath35 discussed in our example above . however at ( relative ) order @xmath36 a large - angle soft gluon can split into a widely separated soft @xmath37 pair and the @xmath31 and @xmath32 may end up being clustered into different jets , ` polluting ' the flavour of those jets , see fig . [ fig : badjets ] . because this happens for arbitrarily soft gluons branching to quarks , the resulting jet flavours are infrared unsafe from order @xmath36 onwards . we are not aware of this problem having been discussed previously in the literature , though there do exist statements that are suggestive of ir safety issues when discussing flavour @xcite . in section [ sec : k_t - flav - algor ] we shall discuss ir flavour unsafety with respect to the @xmath0 ( or ` durham ' ) algorithm in @xmath38 @xcite . there we shall recall that the @xmath0 closeness measure is specifically related to the divergences of qcd matrix elements when producing soft and collinear gluons . however there are no divergences for the production of soft quarks and , as we shall see , it is the use for quarks of a distance measure designed for gluons that leads to the infrared unsafety of jet flavour in the @xmath0 algorithm . by taking into account the absence of a soft - quark divergence when designing the jet - clustering distance measure , one can eliminate the infrared divergence of the jet flavour . the essence of the modification to the @xmath0 distance is that instead of the @xmath39 factor that appears usually , one needs to use @xmath40 when the softer of @xmath41 is a quark . in section [ sec : flav - algor - hadr ] we will examine how this can be extended to processes with incoming hadrons . there the added difficulty is the need for a particle - beam distance measure . traditionally this involves only one dimensionful scale , related to the squared transverse - momentum @xmath42 of the particle . there is a sense in which this can be understood as @xmath43 , where @xmath44 is some transverse scale associated with the beam that is larger than all @xmath42 and so could up to now be ignored . in order to obtain a sensible jet - flavour algorithm we shall however need to consider also @xmath45 and therefore in section [ sec : flav - algor - hadr ] we shall investigate how to construct sensible ` beam scales ' . as well as explaining how to build jet algorithms that provide an infrared safe jet flavour , we shall also examine how they fare in practice . in @xmath38 it will be possible to carry out tests both with an nlo code ( which explicitly reveals the ir unsafety of flavour in traditional jet algorithms ) and with parton - shower monte carlo codes . for hadron - hadron collisions only parton - shower monte carlo tests will be possible because none of the currently available nlo codes provides access to the final - state parton flavour information .

it is common , in both theoretical and experimental studies , to separately discuss quark and gluon jets . however , even at parton level , widely - used jet algorithms fail to provide an infrared safe way of making this distinction . this can be a powerful tool when combining fixed - order calculations with multi - jet resummations and parton showers . it also has applications to studies of heavy - quark jets .

it is common , in both theoretical and experimental studies , to separately discuss quark and gluon jets . however , even at parton level , widely - used jet algorithms fail to provide an infrared safe way of making this distinction . we examine the origin of the problem , and propose a solution in terms of a new ` flavour- ' algorithm . as well as being of conceptual interest this can be a powerful tool when combining fixed - order calculations with multi - jet resummations and parton showers . it also has applications to studies of heavy - quark jets . hep - ph/0601139 + bicocca - ft-05 - 28 + cavendish - hep-05/25 + cern - ph - th-06/02 + damtp-2005 - 134 + fermilab - pub-06 - 003-t + lpthe-05 - 34 + january 2006 + * * + andrea banfi , gavin p. salam and giulia zanderighi + _ damtp , centre for mathematical sciences , cambridge cb3 0wa , uk_. + _ cavendish laboratory , university of cambridge , cambridge cb3 0he , uk_. + _ university of milano bicocca and infn sezione di milano , 20126 milan , italy_. + _ lpthe : universit pierre et marie curie paris 6 ; + universit denis diderot paris 7 ; cnrs ; 75252 paris 75005 , france . _ + _ theory group , fermilab , p.o . box 500 , batavia , il , us . _ + _ theory division , physics department , cern , 1211 geneva 23 , switzerland . _ +

1107.4029

i

when a low to intermediate mass star exhausts its core supply of hydrogen , contraction and heating of the core causes the outer layers of the star to expand and cool , whereby the star becomes a red giant ( rg ) with an average effective temperature of 5000k or lower . once the core temperature rises to about 3@xmath3k , helium burning begins , and the stellar surface contracts and heats creating the horizontal branch ( for population ii ) or red clump ( for population i ) stars on the color - magnitude diagram . completion of core helium burning and the start of helium shell burning returns the star to a luminous , cooler phase as it evolves onto the asymptotic giant branch ( early- or e - agb ) where the star greatly expands and the hydrogen shell is ( almost ) extinguished . later , as the he - burning shell approaches the h - he discontinuity , a phase of double shell burning begins . recurrent thermal instabilities in this thermally - pulsing asymptotic giant branch ( tp - agb ) phase are driven by helium shell flashes , periodic thermonuclear runaway events in the he - shell the energy released by these pulses expand the star , whereby the hydrogen shell is again basically extinguished during some time . a third dredge up might then occur , and afterward the hydrogen shell will re - ignite ( and a new thermal pulse will occur ) . during these short - lived pulses , nucleosynthesis products from combined h - shell and he - shell burning are dredged up to the outer layers of the star . the complex details of the dredge - up and its outcome are strongly mass - dependent ( and references therein ) , but generally speaking , surface abundance enhancements result in c , he , and the @xmath4-process elements , including ba , la , zr , and y. s and carbon ( c ) stars are traditionally thought to be members of the tp - agb . in addition to possibly elevated c / o ratios , these stars exhibit other unique spectral characteristics as a result of the dredge - up . while m giants often exhibit titanium oxide ( tio ) absorption bands , both carbon and zirconium have a higher affinity to free oxygen . therefore , a higher c / o ratio also results in the disappearance of tio bands and the appearance of zirconium oxide ( zro ) bands . s stars are therefore distinguished primarily by their zro bands , while c stars show strong c@xmath5 and cn bands . the s star spectral class is divided into three subtypes ( in order of increasing carbon abundance ) : ms , s , and sc stars . classification into one particular class is difficult , but is generally based on the c / o ratio and the relative strengths of tio , zro , and cn molecular absorption bands . overall , a star in the s star class is generally defined as having a c / o ratio ( r ) of @xmath6 and strong zro absorption features . pure s stars are those that show only zro bands , and no tio bands @xcite . classification is complicated by the fact that increased intensity of the zro bands may be due to an excess of zr , rather than being exclusively tied to the c / o ratio @xcite . furthermore , many agb s and c giants are highly variable , and since the strength of molecular bands depends on the effective temperature and surface gravity of the star , spectral type can vary significantly with time . s stars whose spectra show lines of the short - lived element @xmath4-process technetium ( tc ) are known as `` intrinsic '' s stars , and are most likely be members of the tp - agb . @xmath7tc is only produced by the @xmath4-process , while the star is on the agb . since the half - life of @xmath7tc is only 2.13 x 10@xmath8 years , and the average duration of the agb phase of stellar evolution is roughly 1 myr , stars exhibiting significant abundances of technetium are almost certainly members of the agb . by contrast , technetium - poor s stars are known as `` extrinsic '' s stars . these stars are likely to be part of binary systems and their unusual chemical abundances probably originated in a past mass - transfer episode . the present extrinsic s star likely once accreted @xmath4-process rich material from its companion , a tp - agb star at the time that has since evolved into a white dwarf . extrinsic s stars therefore display enriched @xmath4-process elements , despite having never produced these elements themselves . most known extrinsic s stars are assumed to be members of the red giant branch ( rgb ) . they can sometimes be distinguished from intrinsic s stars on the basis of color , because they do not necessarily show the red excess characteristic of stars on the agb . while all currently known extrinsic s stars are thought to be giants , these definitions open up the possibility of extrinsic s stars on the main sequence ( hereafter referred to as dwarf s stars ) that have previously accreted @xmath4-process material and carbon from a companion but whose tc has since decayed . analogous to the dwarf c stars @xcite , a faint s star could be shown to be a dwarf if it has a sufficiently large parallax or proper motion ; a large proper motion predicts a tangential velocity greater than the galactic escape speed unless the object is faint and nearby . s stars are very similar to c stars , with the major difference being a slightly lower c / o ratio . faint high galactic latitude carbon ( fhlc ) stars were once assumed be giant stars at large distances . in 1977 , however , g77 - 61 was discovered to have high proper motion and an upper limit absolute magnitude of + 9.6 , therefore making it the first known carbon dwarf star @xcite . in this case , the term dwarf refers to a star on the main sequence . @xcite discovered four other dwarf carbon ( dc ) stars using techniques that selected known carbon stars for high proper motion . now , well over 100 dwarf carbon stars are known @xcite . the local space density of dcs is far higher than all types of c giants combined @xcite . therefore , contrary to previous assumptions , dwarf c stars are the numerically dominant type of carbon star in the galaxy . since dc stars are now known to be so common , we have begun a search for dwarf s stars . there is little reason to believe that dwarf s stars should not exist . in fact , they may be more abundant than dc stars , since less carbon enhancement is required to produce an s dwarf as compared to a c dwarf . on the other hand , if the range of abundance ratios that produces the characteristic features of s stars is narrow , they may be quite rare . furthermore , the range of c / o ratios that produces s star spectral features may be different for giants and dwarfs , given the higher gravities and larger temperature ranges in dwarfs . we use medium - resolution digital spectra of known s stars ( which are probably giants ) to generate corresponding sloan digital sky survey ( sdss ) colors , to see whether their colors might be sufficiently distinctive to search for additional s stars in the sdss with reasonable efficiency . we also use the fast spectra to investigate molecular band spectral indices for classification . our paper is organized as follows : in [ sec : obs ] we briefly review the observations and our data reduction and processing procedures . in section [ sec : spatlas ] we describe the production of a spectral atlas of s stars , and derive spectral indices from the molecular band strengths in [ sec : specind ] . in [ sec : colors ] we describe the generation of sdss colors and analyze the overall colors of the fast sample in order to determine whether an efficient color selection for s stars exist . in [ sec : intext ] we discuss techniques for distinguishing intrinsic and extrinsic s stars and apply them to the fast sample . in [ sec : motion ] we analyze the parallaxes and proper motions of s stars in the sample to characterize upper and lower limit magnitudes and distances . we use colors to generate approximate temperature indices for s stars in [ sec : temp ] . in [ sec : sum ] we summarize our results and present our conclusions .

known bright s stars , recognized as such by their enhanced s - process abundances and c / o ratio , are typically members of the asymptotic giant branch ( agb ) or the red giant branch ( rgb ) . few modern digital spectra for these objects have been published , from which intermediate resolution spectral indices and classifications could be derived . for published s stars we find accurate positions using the two - micron all sky survey ( 2mass ) , and use the fast spectrograph of the tillinghast reflector on mt . we make available a digital s star spectral atlas consisting of 14 spectra of s stars with diverse spectral features . we define and derive basic spectral indices that can help distinguish s stars from late - type ( m ) giants and carbon stars . we convolve all our spectra with the sloan digital sky survey ( sdss ) bandpasses , and employ the resulting magnitudes together with 2mass mags to investigate s star colors . these objects have colors similar to carbon and m stars , and are therefore difficult to distinguish by color alone . using near and mid - infrared colors from iras and akari , we identify some of the stars as intrinsic ( agb ) or extrinsic ( with abundances enhanced by past mass - transfer ) . we analyze the proper motions and parallaxes of our sample stars to determine upper and lower limit absolute magnitudes and distances , and confirm that most are probably giants .

known bright s stars , recognized as such by their enhanced s - process abundances and c / o ratio , are typically members of the asymptotic giant branch ( agb ) or the red giant branch ( rgb ) . few modern digital spectra for these objects have been published , from which intermediate resolution spectral indices and classifications could be derived . for published s stars we find accurate positions using the two - micron all sky survey ( 2mass ) , and use the fast spectrograph of the tillinghast reflector on mt . hopkins to obtain the spectra of 57 objects . we make available a digital s star spectral atlas consisting of 14 spectra of s stars with diverse spectral features . we define and derive basic spectral indices that can help distinguish s stars from late - type ( m ) giants and carbon stars . we convolve all our spectra with the sloan digital sky survey ( sdss ) bandpasses , and employ the resulting magnitudes together with 2mass mags to investigate s star colors . these objects have colors similar to carbon and m stars , and are therefore difficult to distinguish by color alone . using near and mid - infrared colors from iras and akari , we identify some of the stars as intrinsic ( agb ) or extrinsic ( with abundances enhanced by past mass - transfer ) . we also use band and 2mass magnitudes to calculate a temperature index for stars in the sample . we analyze the proper motions and parallaxes of our sample stars to determine upper and lower limit absolute magnitudes and distances , and confirm that most are probably giants .

1303.4218

i

multigraphs arise in many applications including modelling transportation networks @xcite , the structure of rna @xcite and in nonparametric statistics @xcite . we use terminology `` multigraphs '' inclusively , with both multiple edges and ( possibly multiple ) loops allowed . we seek an asymptotic enumeration formula for multigraphs with a given degree sequence , satisfying certain conditions . let @xmath14 be a nonnegative integer for all pairs @xmath15 of integers which satisfy @xmath16 . then for each @xmath17 , let @xmath18 . we usually write @xmath19 instead of @xmath14 . define @xmath20 . we assume that @xmath7 is even for an infinite number of values of @xmath5 , and tacitly restrict ourselves to such @xmath5 . for subsets @xmath21 of @xmath2 , define @xmath22 to be the set of all multigraphs on the vertex set @xmath8 with degree sequence given by @xmath9 such that the multiplicity of every loop belongs to @xmath1 and the multiplicity of every non - loop edge belongs to @xmath0 . loops contribute 2 to the degree of their vertex . also define @xmath23 to be the set of multigraphs on @xmath8 with degree sequence @xmath9 ( and no restrictions on the multiplicities ) . equivalently we may think of @xmath24 as the set of all @xmath25 symmetric matrices @xmath26 with all diagonal entries in @xmath1 , all off - diagonal entries in @xmath0 and with @xmath27 for @xmath28 . note that diagonal entries are weighted by 2 in the row sum . let @xmath29 . we find an asymptotic expression for @xmath30 that holds when @xmath13 . for @xmath31 let @xmath32_r\ ] ] where @xmath33_r = a(a-1)(a-2)\cdots ( a - r+1)$ ] denotes the falling factorial . then @xmath34 and @xmath35 for all @xmath36 . for @xmath37 , define @xmath38 our main result is the following . [ main ] let @xmath0 and @xmath1 be subsets of @xmath2 such that @xmath3 and @xmath4 . suppose that @xmath39 , @xmath40 and @xmath41 . then @xmath42 for convenience , we restate the formula in the regular case . [ regular ] suppose that @xmath43 with @xmath44 even , such that @xmath45 as @xmath39 . then @xmath46 where @xmath47 setting @xmath48 we recapture the asymptotic expression for sparse simple graphs with given degrees presented in ( * ? ? ? * theorem 5.2 ) . similarly , setting @xmath49 , @xmath50 we obtain the asymptotic enumeration by degree sequence of sparse graphs with loops allowed but no multiple edges : this is the second expression in ( * ? ? ? * theorem 1.5 ) . we remark that the conditions @xmath51 and @xmath52 in theorem [ main ] can be replaced by weaker conditions : namely , that @xmath10 is non - empty and that @xmath11 has at least two elements with the smallest two consecutive . let @xmath53 denote the least element of @xmath10 and let @xmath54 be the smallest two elements of @xmath11 . this case is reduced to ours by subtracting @xmath53 from each diagonal element , @xmath55 from each off - diagonal element , and @xmath56 from each @xmath19 , provided the new degree sequence satisfies the conditions of theorem [ main ] . theorem [ main ] is proved using the switching method , building on an asymptotic enumeration of simple graphs with given degrees @xcite . our application of the switching method introduces a novel way of combining several different switching operations into a single computation . the remainder of the paper is structured as follows . the history of this asymptotic enumeration problem is briefly reviewed in section [ ss : history ] , then the new switching theorem is given in section [ s : switchinglemma ] . in section [ s : multigraphs ] we describe 15 types of switchings on multigraphs , which are used to show that certain multiplicities of edges or loops are rare . these switchings are analysed together in subsection [ ss : combine ] using the new switching theorem . in section [ s : pairings ] we complete the enumeration with the help of some calculations performed in @xcite . finally , in section [ s : naive ] we show that a nave argument leads to a formula for @xmath57 which differs asymptotically by a constant factor from the result of theorem [ main ] in the regular case . the constant factor takes two different values , depending on whether @xmath58 . the earliest work on this problem was that of read @xcite , who found exact and asymptotic formulae when @xmath59 , for all four combinations of @xmath60 and @xmath61 . the best result for @xmath62 in the sparse range is that of mckay and wormald @xcite who treated @xmath63 ; see that paper for a survey of the many earlier results on the case . in addition to @xmath64 , bender and canfield @xcite found the asymptotics for @xmath65 when @xmath66 . ( although that paper allows nonzero diagonal entries , they contribute singly to the row sums , not doubly as we have it . ) in @xcite , mckay and wormald considered @xmath64 in the dense domain defined by @xmath67 for @xmath68 and @xmath69 for all @xmath70 , where @xmath71 is the average degree . mckay @xcite found a better error term under the same conditions , while barvinok and hartigan allowed a wider range of degrees @xcite . greenhill and mckay @xcite added the option of loops in both the sparse and dense ranges by considering @xmath72 , @xmath73 . finally , mcleod and mckay @xcite analysed the case of @xmath74 when @xmath75 for @xmath76 . for sparse rectangular matrices which are not necessarily symmetric , see greenhill and mckay @xcite .

we find an asymptotic expression for the number of multigraphs on the vertex set with degree sequence given by , such that every loop has multiplicity in and every non - loop edge has multiplicity in . equivalently , these are symmetric integer matrices with values allowed on the diagonal and off the diagonal . our expression holds when the maximum degree satisfies . we prove this result using the switching method , building on an asymptotic enumeration of simple graphs with given degrees ( mckay and wormald , 1991 ) . our application of the switching method introduces a novel way of combining several different switching operations into a single computation .

let and be subsets of such that and . for infinitely many , let be a vector of nonnegative integers whose sum is even . we find an asymptotic expression for the number of multigraphs on the vertex set with degree sequence given by , such that every loop has multiplicity in and every non - loop edge has multiplicity in . equivalently , these are symmetric integer matrices with values allowed on the diagonal and off the diagonal . our expression holds when the maximum degree satisfies . we prove this result using the switching method , building on an asymptotic enumeration of simple graphs with given degrees ( mckay and wormald , 1991 ) . our application of the switching method introduces a novel way of combining several different switching operations into a single computation .

1006.0444

i

since the seminal work of tutte @xcite maps and graphs on 2-dimensional surfaces have become widely studied combinatorial objects in discrete mathematics . the enumerative and structural problems around maps , i.e. _ embedded _ graphs on a surface , are relatively well settled . starting from the number of planar maps computed by tutte @xcite , the number of rooted maps on surfaces was found by bender , canfield , and richmond @xcite and other classes of maps were extensively enumerated since then . such enumeration results have been used to study typical properties of random maps on surfaces , e.g. the size of the largest components by banderier _ et al . _ @xcite . another important aspect of maps is that they allow nice bijections to the so - called _ well - labeled _ trees . the bijection between planar maps and the well - labeled trees was first studied amongst others by schaeffer @xcite , which was extended by bouttier , di francesco , and guitter @xcite to maps on an orientable surface with positive genus . these bijections are the corner stone of profound results on the topological structure of scaling limits of random maps by chassaing and schaeffer @xcite , le gall @xcite , and schramm @xcite . on the other hand , analogous problems related graphs that are _ embeddable _ on a surface are still wide open . the enumerative properties of random planar graphs have attracted much attention since the work of mcdiarmid , steger , and welsh @xcite who studied random labeled planar graphs with a given number of vertices . let @xmath7 be the number of labeled planar graphs on @xmath1 vertices . mcdiarmid , steger , and welsh @xcite showed amongst other results that the quantity @xmath8 converges to a limit @xmath9 as @xmath10 , which is called the growth constant . an upper bound @xmath11 , based on the triangulations and probabilistic methods , was obtained by osthus , prmel , and taraz @xcite . a lower bound @xmath12 was given by bender , gao , and wormald @xcite who studied the number of labeled 2-connected planar graphs through the singularity analysis of generating functions arising from the decomposition of graphs along connectivity . using a similar method gimnez and noy @xcite proved that @xmath13 , where @xmath14 are explicitly computable constants ( e.g. @xmath15 ) . as for the number @xmath16 of graphs embeddable on a surface with positive genus , mcdiarmid @xcite showed that its growth constant is the same as that of planar graphs while chapuy _ et al . _ @xcite found @xmath16 for all orientable surfaces of positive genus @xmath17 proving that @xmath18 , where @xmath19 and @xmath9 is the growth constant of the labeled planar graphs . mcdiarmid and reed @xcite studied various typical properties of random graphs on surfaces , e.g. subgraph containment and maximum degree . frieze @xcite asked about the asymptotic behavior of the number @xmath20 of labeled planar graphs on @xmath1 vertices with @xmath2 edges . note first that if @xmath21 for some @xmath22 , then a typical graph with @xmath1 vertices and @xmath2 edges is planar , i.e. @xmath23 ( cf . @xcite or @xcite ) gerke _ et al . _ @xcite proved the existence of its growth constant , in the sense that for @xmath24 with @xmath25 , the quantity @xmath26 converges to a limit @xmath27 as @xmath10 . the asymptotic formula for @xmath24 was found by gimnez and noy @xcite who showed that for @xmath28 , there are analytic constants @xmath29 such that @xmath30 . in this paper we deal with the case when @xmath31 . note that for such @xmath32 @xmath33 i.e. , @xmath34 , and a ` naive ' generating function approach does not lead to the asymptotic formula for @xmath20 . we use @xmath20 to study the asymptotic behavior of the uniform random planar graph @xmath0 by which we mean a graph chosen uniformly at random among all labeled planar graphs with @xmath1 vertices and @xmath2 edges ; thus , each of these graphs occurs as @xmath0 with probability @xmath35 . from the results in @xcite it follows that if @xmath36 is bounded away from both @xmath37 and @xmath38 , then @xmath0 has a well ordered structure , for instance , it has a large component of size @xmath39 , and all planar graphs of finite size appear as its subgraphs . thus , it corresponds to late stages of the evolution of the standard uniform random graph @xmath40 , the graph chosen uniformly at random among all graphs with @xmath1 vertices and @xmath2 edges . our goal is to study the typical size and structure of components in @xmath0 in a more interesting range , when @xmath41 . it turns out that , somewhat surprisingly , @xmath0 exhibits two critical ranges , which occur at @xmath4 and @xmath5 . the first critical period corresponds to a phase transition phenomenon observed in the plethora of different random graph models . let us recall some results on one of the most widely used random graph model @xmath40 . it follows from the papers of erds and rnyi @xcite , bollobs @xcite , uczak @xcite , uczak , pittel , and wierman @xcite , janson _ et al . _ @xcite , and janson @xcite ( see also janson , uczak , and ruciski @xcite ) that the giant component ( i.e. the unique largest component ) suddenly emerges at @xmath4 , and nowadays this spectacular phenomenon is well studied and understood . if @xmath42 and @xmath43 , then , a.a.s . ( i.e. with probability tending to 1 as @xmath1 approaches @xmath44 ) @xmath40 consists of isolated trees and unicyclic components , and the largest component is a tree of size @xmath45 . on the other hand , if @xmath46 , then a.a.s . @xmath40 contains exactly one component with more edges than vertices of size @xmath47 , while all other components are of size @xmath48 . furthermore , if @xmath49 , then a.a.s . @xmath40 contains a topological copy of @xmath50 and thus it is not planar , while , as we have mentioned , for @xmath51 , a.a.s . @xmath40 consists of isolated trees and unicyclic components , so it is clearly planar . another random structure relevant to the behavior of @xmath0 is the uniform random forest @xmath52 ( i.e. a forest chosen uniformly at random among all labeled forest with @xmath1 vertices and @xmath2 edges ) . uczak and pittel @xcite found that although the giant component in @xmath52 emerges at @xmath4 , as for @xmath40 , the critical behavior of these two models are somewhat different . let @xmath42 . if @xmath51 , then the structure of both @xmath52 and @xmath40 are similar ; in particular , the size of the largest tree in @xmath52 is a.a.s . however in the supercritical phase , when @xmath49 , the giant tree of @xmath52 is a.a.s . of size @xmath53 , which is roughly half of the size of the largest component of @xmath40 , while the second largest tree of @xmath52 is of size @xmath3 which does not depend much on @xmath54 provided @xmath55 , i.e. it is by far larger than the second largest component of @xmath40 for @xmath56 , which is of size @xmath57 . in the paper we show that as far as @xmath42 , where @xmath49 and @xmath58 is bounded away from @xmath59 , the behavior of @xmath0 is similar to that of @xmath52 . namely , a.a.s . the size of the largest complex component is of the order @xmath53 , while the second largest component has @xmath3 vertices . however , unlike in the case of @xmath52 for which @xmath60 , for @xmath0 we may have @xmath61 , so the rate of growth of the size of complex components must change at some point . we prove that it occurs when @xmath5 , more precisely , if @xmath62 and @xmath63 , then the complex components of @xmath0 have a.a.s . @xmath64 vertices altogether , while for @xmath65 they contain @xmath66 vertices for some computable constant @xmath67 . let us mention that the condition @xmath68 is a result of the proof method we have used and most likely can be replaced by @xmath69 . furthermore , our method can say quite a lot about structure of the largest component very much in the spirit of uczak @xcite . the rest of the paper is organized as follows . in the next section we describe the main idea of our argument . then , in section [ sec : cubicplanar ] we present the first analytic ingredient of the proof : counting specially weighted cubic planar multigraphs using generating functions . here we also describe how to use this result to bound the number of planar multigraphs with minimum degree three . then , in the next section , we estimate the number of planar graph with @xmath70 vertices and @xmath71 edges in which each component has more edges than vertices . finally , in the main chapter of this paper , we use a direct counting to study the number @xmath20 and the asymptotic properties of @xmath0 for different values of @xmath2 .

we study the component structure of . combining counting arguments with analytic techniques , the first one , of width , is analogous to the phase transition observed in the standard random graph models and takes place for , when the largest complex component is formed . then , for , when the complex components cover nearly all vertices , the second critical period of width occurs .

let be a graph chosen uniformly at random from the family of all labeled planar graphs with vertices and edges . in the paper we study the component structure of . combining counting arguments with analytic techniques , we show that there are two critical periods in the evolution of . the first one , of width , is analogous to the phase transition observed in the standard random graph models and takes place for , when the largest complex component is formed . then , for , when the complex components cover nearly all vertices , the second critical period of width occurs . starting from that moment increasing of mostly affects the density of the complex components , not its size .

1510.00129

i

graph theory provide tools to study the algebraic properties of algebraic structures . in particular , there are several graphs associated with groups to study some specific properties of groups , for instance , intersection graph of subgroups of groups , prime graph of groups , non - commuting graphs of groups and permutability graph of subgroups of groups ( see @xcite , @xcite , @xcite , @xcite and the references therein ) . in @xcite , sattanathan and kala defined the order prime graph of a group @xmath0 , which is a graph having the set of all elements of @xmath0 as its vertices , and two distinct vertices are adjacent if and only if the orders of the corresponding subgroups are coprime . they have studied some properties of this graph . this graph was further investigated by xuanlong ma et al @xcite and hamid reza dorbidi @xcite . they called the order prime graph of a group as the coprime graph of a group . the relation of coprimeness of the orders of the subgroups of a group plays a significant role in the determination of the structural properties of that group . also the relation of coprimeness is not transitive on the set of all proper subgroups of a group . in this paper , we define the _ coprime graph of subgroups _ of @xmath0 , denoted by @xmath1 . it is a graph having all the proper subgroups of @xmath0 as its vertices , and two distinct vertices @xmath2 and @xmath3 are adjacent if and only if @xmath4 and @xmath5 are coprime . now we recall some basic definitions and notations of graph theory . we use the standard terminology of graphs ( e.g. , see @xcite ) . let @xmath0 be a simple graph . @xmath0 is said to be @xmath6-partite if the vertex set of @xmath0 can be partitioned to @xmath6 sets such that no two vertices in same partitions are adjacent . a complete @xmath6-partite graph , denoted by @xmath7 , is a @xmath6-partite graph having partition sizes @xmath8 such that every vertex in each partition is adjacent with all the vertices in the remaining partitions . in particular , @xmath9 is called a _ star_. a graph whose edge set is empty is called a _ null _ graph or _ totally disconnected _ graph . @xmath10 denotes the complete graph on @xmath11 vertices . @xmath12 and @xmath13 respectively denotes the path and cycle with @xmath11 edges . we denote the degree of a vertex @xmath14 in @xmath0 by @xmath15 . a graph is said to be _ connected _ if any two vertices of it can be joined by a path . the _ diameter _ of a connected graph is the maximum of the length of the shortest path between any pair of vertices . a _ tree _ is a connected graph with out cycles . @xmath0 is said to be @xmath2-_free _ if @xmath0 has no subgraph isomorphic to @xmath2 . the girth of @xmath0 , denoted by @xmath16 , is the length of its shortest cycle , if it exist ; other wise @xmath17 . an _ independent set _ of @xmath0 is a subset of @xmath18 having no two vertices are adjacent . the _ independence number _ of @xmath0 , denoted by @xmath19 , is the cardinality of the largest independent set . a _ clique _ of @xmath0 is a complete subgraph of @xmath0 . the clique number @xmath20 of @xmath0 is the cardinality of a largest clique in @xmath0 . the _ chromatic number _ @xmath21 of @xmath0 is the smallest number of colours needed to colour the vertices of @xmath0 such that no two adjacent vertices gets the same colour . g is said to be _ weakly @xmath22-perfect _ if @xmath23 . a graph is said to be _ planar _ , if it can be drawn in the plane , so that no two lines intersect except at the vertices ; otherwise it is said to be _ a graph is called _ unicyclic _ , if it contains exactly one cycle . for any integer @xmath24 , @xmath25 denotes the set of all prime divisors of @xmath11 . if @xmath0 is a finite group , then @xmath26 is denoted by @xmath27 . the number of sylow p - subgroups of a group g is denoted by @xmath28 . we denote the order of an element @xmath29 by @xmath30 . moreover , through out this paper , @xmath31 , @xmath32 , @xmath33 , @xmath34 denotes the distinct primes . since the only groups having no proper subgroups are the trivial group , and the groups of prime order , it follows that , we can define @xmath1 only when the group @xmath0 is neither the trivial group nor the group of prime order . so , unless otherwise mentioned , throughout this paper we consider only groups other than the trivial group , and the groups of prime order . we use only elementary methods . in section 2 , we classify all the finite groups whose coprime graph of subgroups are one of totally disconnected , bipartite , connected , complete , complete bipartite , tree , star or path , and show that the coprime graph of subgroups of a finite group can not be a cycle . for a finite group @xmath0 , we obtain the independence number , clique number , chromatic number , diameter , girth of @xmath1 , and show that @xmath1 is weakly @xmath22-perfect . moreover , we obtain the degrees of vertices of @xmath35 , and we show that every simple graph is an induced subgraph of @xmath35 , for some @xmath11 . in section 3 , we classify all the finite groups whose coprime graph of subgroups of groups are one of planar , @xmath36-free , @xmath37-free , @xmath38-free , @xmath39-free , unicyclic .

we define the _ coprime graph of subgroups _ of , denoted by , is a graph whose vertex set is the set of all proper subgroups of , and two distinct vertices are adjacent if and only if the order of the corresponding subgroups are coprime . in this paper , we study some connections between algebraic properties of a group and graph theoretic properties of its coprime graph . [ [ keywords ] ] keywords : + + + + + + + + + coprime graph , finite groups , connectedness , independence number , clique number , planar .

let be a group . we define the _ coprime graph of subgroups _ of , denoted by , is a graph whose vertex set is the set of all proper subgroups of , and two distinct vertices are adjacent if and only if the order of the corresponding subgroups are coprime . in this paper , we study some connections between algebraic properties of a group and graph theoretic properties of its coprime graph . [ [ keywords ] ] keywords : + + + + + + + + + coprime graph , finite groups , connectedness , independence number , clique number , planar . [ [ mathematics - subject - classification ] ] mathematics subject classification : + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 05c25 , 20k27 , 05c69 , 05c10 .

1510.00129

r

[ order prime graph of subgroups 14 ] let @xmath40 and @xmath41 be two groups . if @xmath42 , then @xmath43 . let @xmath44 be a group isomorphism . define a map @xmath45 by @xmath46 , for every @xmath47 . since a group isomorphism preserves the order of subgroups , so it follows that @xmath48 is a graph isomorphism . * remark : * the converse of the above theorem [ order prime graph of subgroups 14 ] , is not true , for if @xmath49 and @xmath50 , then the number of proper subgroups of @xmath40 is four and their orders are @xmath31 , @xmath51 , @xmath52 , @xmath53 ; the number of proper subgroups of @xmath41 is four and their orders are 4 , 4 , 4 , 2 . here @xmath54 , but @xmath55 . [ order prime graph of subgroups of groups 4 ] let @xmath0 be a group of order @xmath56 , where @xmath57 s are distinct primes , @xmath58 . then 1 . @xmath1 is @xmath6-partite ; 2 . @xmath59 , where for each @xmath60 , 2 , @xmath61 , @xmath6 , @xmath62 is the set of all proper subgroups of @xmath0 whose order is divisible by @xmath57 ; 3 . @xmath63 ; in particular , @xmath1 is weakly @xmath22-perfect . let @xmath64 be the set of all proper subgroups of @xmath0 whose order is divisible by @xmath65 . for each @xmath66 , 3 , @xmath61 , @xmath67 , let @xmath68 . then clearly the collection @xmath69 forms a partition of the vertex set of @xmath1 . also no two vertices in a same partition are adjacent in @xmath1 . moreover , @xmath6 is the minimal number such that a @xmath6-partition of the vertex set of @xmath1 is having this property , since @xmath70 . it follows that @xmath1 is @xmath6-partite . now for each @xmath60 , 2 , @xmath61 , @xmath6 , let @xmath62 be the set of all proper subgroups of @xmath0 whose order is divisible by @xmath57 . clearly each @xmath62 is a maximal independent set of @xmath1 . thus @xmath59 . for each @xmath71 , @xmath0 has a subgroup of order @xmath57 . then the set having one subgroup from each of these orders forms a clique in @xmath1 . since @xmath1 is @xmath6-partite , it follows that @xmath72 . obviously , @xmath73 . weakly @xmath22-perfectness of @xmath1 follows from the definition . the next result is an immediate consequence of theorem [ order prime graph of subgroups of groups 4 ] ( 1 ) . [ c1 ] let @xmath0 be a group with @xmath70 . then 1 . @xmath1 is totally disconnected if and only if @xmath74 ; 2 . @xmath1 is bipartite if and only if @xmath75 . [ order prime graph of subgroups of groups 6 ] let @xmath0 be a finite group . then 1 . @xmath1 is complete bipartite if and only if @xmath0 is isomorphic to one of @xmath76 , @xmath77 , @xmath78 or @xmath79 ; 2 . the following are equivalent : 1 . @xmath80 or @xmath77 ; 2 . @xmath1 is a tree ; 3 . @xmath1 is a star . 3 . the following are equivalent : 1 . @xmath80 ; 2 . @xmath1 is complete ; 3 . @xmath1 is a path . in view of part ( 2 ) of corollary [ c1 ] , to prove parts ( 1 ) , ( 2 ) , and @xmath81 of ( 3 ) of this theorem , it is enough to consider the groups of order @xmath82 and @xmath83 . if @xmath84 , then by corollary [ c1](1 ) , @xmath1 is totally disconnected and so it is neither complete bipartite nor a tree . let @xmath85 with @xmath86 . then @xmath87 or @xmath77 . if @xmath87 , then @xmath88 and so @xmath1 is a path . if @xmath89 , then @xmath0 has an unique subgroup of order @xmath32 , and @xmath32 subgroups of order @xmath31 ; also these are the only proper subgroups of @xmath0 . it follows that @xmath90 and so @xmath1 is complete bipartite , star ; but not a path . let @xmath91 . suppose @xmath0 is abelian , then @xmath0 has a subgroup of order @xmath92 and so @xmath1 is disconnected . it follows that @xmath1 is neither complete bipartite nor a tree . now assume that @xmath0 is non - abelian . here we use the classification of groups of order @xmath93 given in @xcite . * case 1 : * @xmath94 : * case 1a : * @xmath95 . by sylow s theorem , it is easy to see that there is no non - abelian group in this case . * case 1b : * @xmath96 but @xmath97 . in this case , there are two non - abelian groups . the first group is @xmath98 . here @xmath40 has an unique subgroup of order @xmath32 ; unique subgroup of order @xmath92 ; @xmath32 subgroups of order @xmath51 and unique subgroups of order @xmath31 ; also these are the only proper subgroups of @xmath40 . therefore , @xmath99 . so @xmath100 is disconnected . hence @xmath100 is neither complete bipartite nor a tree . the second group is @xmath101 . here @xmath41 has a subgroup @xmath102 of order @xmath92 and so @xmath103 is disconnected . hence @xmath103 is neither complete bipartite nor a tree . * case 1c : * @xmath104 . in this case , we have both groups @xmath40 and @xmath41 from case 1b together with the group @xmath105 . here @xmath106 has unique subgroup of order @xmath32 ; unique subgroup of order @xmath92 ; @xmath32 subgroups of order @xmath51 , and @xmath32 subgroups of order @xmath31 . also these are the only proper subgroups of @xmath106 . therefore , @xmath107 and so @xmath108 is disconnected . hence @xmath108 is neither complete bipartite nor a tree . * case 2 : * @xmath109 * case 2a : * @xmath110 . then there is no non - abelian subgroups . * case 2b : * @xmath111 . in this case , we have two groups . the first one is @xmath112 . here @xmath113 has a unique subgroup of order @xmath51 ; unique subgroup of order @xmath31 ; @xmath31 subgroups of order @xmath92 ; @xmath51 subgroups of order @xmath32 . also these are the only proper subgroups of @xmath113 . therefore , @xmath114 and so @xmath115 is disconnected . hence @xmath115 is neither complete bipartite nor a tree . next we have the family of groups @xmath116 . there are @xmath117 isomorphism types in this family ( one for @xmath118 and one for each pair @xmath119 in @xmath120 . we will refer to all of these groups as @xmath121 of order @xmath93 . here @xmath121 has a subgroup @xmath102 of order @xmath92 and so @xmath122 is disconnected . hence @xmath123 is neither complete bipartite nor a tree . * case 2c : * @xmath124 . in this case , we have only one subgroup of order @xmath93 , given by @xmath125 , where @xmath126 has order @xmath32 in @xmath127 . here @xmath128 does not have a subgroup of order @xmath92 . but @xmath128 has an unique subgroup of order @xmath51 ; @xmath129 subgroups of order @xmath31 ; @xmath51 subgroups of order @xmath32 , also these are the only proper subgroups of @xmath128 . hence @xmath130 , which is complete bipartite ; but which is not a tree . note that if @xmath131 , the cases 1 and 2 are not mutually exclusive . up to isomorphism , there are three non - abelian groups of order 12 : @xmath132 , @xmath133 and @xmath79 . in case 1b , we already dealt with the group @xmath134 . it is easy to see that @xmath135 and @xmath136 . these three graphs are not trees and the only complete bipartite graph is @xmath137 . if @xmath138 , @xmath139 , then let @xmath140 , @xmath141 be elements in @xmath0 of order @xmath31 , @xmath32 respectively . here @xmath142 is a proper subgroup of @xmath0 whose order is divisible by @xmath31 and @xmath32 . therefore , @xmath1 is disconnected . hence @xmath1 is neither complete bipartite nor a tree . if @xmath143 , @xmath144 , @xmath145 , then @xmath0 has a subgroup with prime index , since @xmath0 is solvable and so @xmath1 is disconnected . hence @xmath1 is neither complete bipartite nor a tree . combining all the above cases together , the proof of parts ( 1 ) , ( 2 ) , and @xmath81 of ( 3 ) of this theorem follows . now , we prove @xmath146 of part ( 3 ) : clearly @xmath147 . so assume that @xmath1 is complete . then by theorem [ order prime graph of subgroups of groups 4 ] , each partition @xmath148 , @xmath149 of @xmath1 must contain exactly one subgroup of distinct prime order and so these subgroups are normal in @xmath0 . if @xmath150 , then @xmath0 must contain a subgroup whose order is a product of @xmath6 distinct primes , so this subgroup is an isolated vertex in @xmath1 , which is not possible . hence @xmath151 and so by part ( 1 ) of this theorem , it turns out that @xmath80 . this completes the proof . [ order prime graph of subgroups of groups 8 ] if @xmath0 is a finite group , then @xmath152 , for @xmath153 . suppose @xmath1 is the cycle @xmath154 of length @xmath11 . since @xmath155 , so without loss of generality , we assume that , @xmath156 , @xmath157 and @xmath158 or @xmath82 . if @xmath158 , then @xmath159 , @xmath160 , @xmath161 are adjacent and so @xmath1 is complete , which is not possible , by theorem [ order prime graph of subgroups of groups 6](3 ) . if @xmath162 , then @xmath163 implies that @xmath164 or @xmath33 . if @xmath165 , then @xmath159 , @xmath160 , @xmath166 are adjacent , which is not possible . so we have @xmath164 . then @xmath167 and so @xmath159 and @xmath166 are adjacent in @xmath1 . it follows that @xmath168 and @xmath143 , @xmath144 , @xmath169 . now we check the existence of such a group . if @xmath170 , then @xmath0 has at least five proper subgroups , which is not possible . if @xmath171 , then @xmath91 or @xmath92 . in this case , we have shown in the proof of theorem [ order prime graph of subgroups of groups 6 ] that @xmath1 can not be a cycle . this completes the proof . [ order prime graph of subgroups of groups 3 ] let @xmath0 be a finite group . then @xmath1 is connected if and only if @xmath0 does not have a proper subgroup @xmath2 with @xmath172 . in this case , @xmath173 . suppose @xmath0 has a subgroup , say @xmath2 with @xmath172 . then @xmath4 is not relatively prime to any other subgroups of @xmath0 . therefore , @xmath1 is disconnected . conversely , assume that @xmath0 does not have a subgroup @xmath2 with @xmath172 . suppose @xmath1 is complete , then @xmath1 is connected and @xmath174 . now assume that @xmath1 is not complete . let @xmath2 and @xmath3 be two non - adjacent vertices in @xmath1 . then by assumption , @xmath175 and @xmath176 , and so there exist @xmath57 , @xmath177 such that @xmath178 and @xmath179 . if @xmath180 , then there is a path @xmath181 , where @xmath159 is a subgroup of @xmath0 of order @xmath57 . if @xmath182 , then there is a path @xmath183 , where @xmath159 , @xmath160 are subgroups of @xmath0 of orders @xmath57 , @xmath184 respectively . it follows that @xmath1 is connected and @xmath185 . note that @xmath186 , @xmath187 and @xmath188 , so it shows that the diameter of @xmath1 takes all the values in @xmath189 . this completes the proof . from the above theorem , for a given finite group @xmath0 , if @xmath1 is disconnected , then @xmath0 has a proper subgroup @xmath2 with @xmath172 . it turns out that such a subgroup @xmath2 will be an isolated vertex of @xmath1 . as a consequence , we have the following result . let @xmath0 be a finite group . if @xmath1 is disconnected , then @xmath190 , where @xmath191 is a connected component of @xmath1 , and @xmath33 is the number of proper subgroups @xmath2 of @xmath0 with @xmath172 . [ order prime graph of subgroups 9 ] if @xmath0 is a finite group , then @xmath192 . let @xmath0 be a group of order @xmath193 , where @xmath57 s are distinct primes and @xmath58 . if @xmath194 , then any three subgroups of @xmath0 of distinct prime orders are mutually adjacent in @xmath1 and so @xmath1 contains @xmath195 as a subgraph . it follows that @xmath196 . if @xmath197 , then by corollary [ c1](2 ) , @xmath1 is bipartite and so @xmath1 can not contain an odd cycle . now we consider the following cases : * case a : * @xmath143 , @xmath144 , @xmath198 . here @xmath0 has subgroups of orders @xmath31 , @xmath51 , @xmath32 , @xmath199 , let them be @xmath159 , @xmath160 , @xmath161 , @xmath166 respectively . then @xmath200 contains the cycle @xmath201 and so @xmath202 . * case b : * @xmath138 , @xmath203 . suppose sylow @xmath32-subgroup of @xmath0 is not unique , then @xmath0 has at least two sylow @xmath32-subgroup , let them be @xmath159 , @xmath160 and @xmath0 has subgroups of order @xmath31 , @xmath51 , let them be @xmath161 , @xmath166 respectively . then @xmath1 contains the cycle @xmath201 and so @xmath202 . suppose sylow @xmath32-subgroup of @xmath0 is unique , then in the bipartition of the vertex set of @xmath1 , one partition contains only the sylow @xmath32-subgroup of @xmath0 and another partition contains the remaining subgroups of @xmath0 . it follows that @xmath1 does not contains a cycle , so @xmath204 is @xmath205 . * case c : * @xmath85 . by theorem [ order prime graph of subgroups of groups 6](3 ) , @xmath1 is a path and so @xmath204 is @xmath205 . * case d : * @xmath84 . by corollary [ c1](1 ) , @xmath1 is totally disconnected and so @xmath204 is @xmath205 . proof follows by combining all the above cases together . [ order prime graph of subgroups 13 ] let @xmath206 , where @xmath57 s are distinct primes and @xmath58 . if @xmath2 is a proper subgroup of @xmath207 of order @xmath208 , then @xmath209 . it is well known that for every divisor @xmath210 of @xmath11 , @xmath207 has a unique subgroup of order @xmath210 . let @xmath3 be a subgroup of @xmath207 which is adjacent with @xmath2 in @xmath35 . then @xmath211 and @xmath212 , with @xmath213 , @xmath214 , @xmath61 , @xmath215 . but for each @xmath216 , the power of @xmath184 can be chosen in @xmath217 ways . it follows that , such a subgroup @xmath3 can be chosen in @xmath218 ways . excluding the trivial subgroup , we have @xmath219 subgroups in @xmath207 which are adjacent with @xmath2 in @xmath35 . this completes the proof . [ order prime graph of subgroups 15 ] if @xmath191 is a simple graph on @xmath220 vertices , then there exist @xmath221 such that @xmath191 is an induced subgraph of @xmath222 . let @xmath11 be the number of maximal independent sets of @xmath191 . now assign @xmath11 distinct primes for each of these maximal independent sets . let @xmath14 be a fixed vertex of @xmath191 . if @xmath14 belongs to @xmath223 maximal independent sets of @xmath191 , then label to @xmath14 , the product of primes which are assigned to these @xmath223 maximal independent sets . similarly we can label the other vertices of @xmath191 . if all these labeling are distinct , then keep them as it is . otherwise , in order to make the labeling distinct , we relabel the vertices by using different powers of these primes . now let @xmath224 be the least common multiple of the labels assigned to vertices of @xmath191 . again relabel each of these labels by subgroup of @xmath225 whose order is the same label . then it turns out that @xmath191 is an induced subgraph of @xmath225 . hence the proof . now we illustrate theorem [ order prime graph of subgroups 15 ] in the following example . consider the graph @xmath191 as shown in figure [ fig : f3 ] . ] here @xmath226 , @xmath227 are the only maximal independent subsets of @xmath191 . first we assign prime @xmath57 to @xmath228 for each @xmath60 , 2 . here @xmath229 , so label @xmath230 by @xmath65 ; @xmath231 , so label @xmath232 by @xmath233 ; @xmath234 , so label @xmath235 by @xmath65 ; @xmath236 , so label @xmath237 by @xmath65 ; @xmath238 , so label @xmath239 by @xmath233 . since @xmath230 , @xmath235 , @xmath237 have the same label , and @xmath232 , @xmath239 have the same label , so we relabel them in the following way : label @xmath230 , @xmath235 , @xmath237 by @xmath65 , @xmath240 , @xmath241 respectively , and @xmath232 , @xmath239 by @xmath233 , @xmath242 respectively . let @xmath243 . again relabel each of these labels by subgroup of @xmath244 whose order is the same label . it follows that @xmath191 is the induced subgraph of @xmath244 .

let be a group . [ [ mathematics - subject - classification ] ] mathematics subject classification : + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 05c25 , 20k27 , 05c69 , 05c10 .

let be a group . we define the _ coprime graph of subgroups _ of , denoted by , is a graph whose vertex set is the set of all proper subgroups of , and two distinct vertices are adjacent if and only if the order of the corresponding subgroups are coprime . in this paper , we study some connections between algebraic properties of a group and graph theoretic properties of its coprime graph . [ [ keywords ] ] keywords : + + + + + + + + + coprime graph , finite groups , connectedness , independence number , clique number , planar . [ [ mathematics - subject - classification ] ] mathematics subject classification : + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 05c25 , 20k27 , 05c69 , 05c10 .

0903.0079

i

an international array of first - generation long - baseline laser interferometric gravitational - wave ( gw ) detectors ( ligo @xcite , virgo @xcite , geo @xcite and tama @xcite ) are reaching their design sensitivities . these michelson interferometers have been built to measure gw - driven relative length changes ( within a detection band from 10hz to 10khz ) between the mirror - endowed test masses which are hung as pendulums with an eigenfrequency far below the detection band . resonant cavities are used to enhance the sensitivity by increasing the circulating optical power and the signal storage time . in michelson interferometers usually the total differential mode of motion between the arm cavity mirrors , in the following always represented by the position operator @xmath3 ( for the nomenclature see fig.[fig : advligo ] ) is measured via a homodyne detection of the modulation fields ( also called side - band fields ) leaking out at the dark port of the interferometer . current gw interferometers are already quantum limited at high frequencies by the shot noise . next generation interferometers , such as the planned advanced ligo detector @xcite ( cf . fig.[fig : advligo ] ) , are expected to be quantum noise limited at nearly all frequencies in the detection band . advanced ligo will therefore operate at its free mass _ standard quantum limit _ ( sql ) @xcite at which the back - action noise is comparable to the shot noise level . the position - referred spectral density of the sql at the sideband frequency @xmath4 is given by @xmath5 the sql is the minimum noise spectrum achievable by a linear quantum measurement of the position with uncorrelated sensing and back - action noise . here @xmath6 is the reduced mass of all arm cavity mirrors , or @xmath7 of the individual mirror mass . improvement of sensitivities to gws beyond advanced ligo will require to surpass the sql significantly in a broad frequency band . various conceptual strategies exist for building interferometers with broadband sub - sql quantum noise @xcite , while there is also much effort devoted to lowering classical noise below the sql . for example , ( i ) the clio interferometer is currently being cooled down to a few tens of kelvin , and has a theoretical thermal noise budget below the sql @xcite , ( ii ) non - spherical mirrors are being developed that support non - gaussian modes which average better over mirror surfaces and are thus less susceptible to thermal noise @xcite , ( iii ) coating structures are also being optimized for coating thermal noise @xcite . this paper , however , is devoted not to the improvement of the detector s sensitivity to gws , but to the study of quantum mechanical behavior of its test masses . recently , it has been reported by the ligo scientific collaboration in ref . @xcite that a certain ( controlled ) mode of the mirror s differential motion in the ligo detector located in hanford was experimentally cooled down to @xmath8k , with an effective occupation number of around 200 . furthermore , there is a number of other experiments considering different smaller - scale mechanical structures @xcite . the goal of such _ cold damping _ @xcite experiments is to reach the oscillator s ground state . as a real pure quantum state is approached , the semiclassical model as used in the above references will certainly break down and the quantum noise effects in the measurement process have to be included . one aim of this paper is at providing a mathematical foundation guiding future experimental efforts of quantum - state preparation one that is straightforward to apply to experimental situations . note that our general formulation applies not only to gravitational - wave detectors but to the whole bunch of experiments related to quantum state preparation . quantum mechanically , we consider a problem in which an object is being continuously measured by the optical field , while it is simultaneously subject to noisy forces . for such problems , the stochastic master equation ( sme ) @xcite is a readily available tool to simulate quantum - state preparation in quantum mechanical systems ; a riccati equation associated with the sme provides the remaining uncertainty of the object , when all measurement data are taken into account . formally , this approach only treats markovian systems ( since only markovian systems allow us to project the optical field being measured and trace off the noise fields at every infinitesimal time step , resulting in a closed - form evolution of the test - mass density operator ) , while non - markovianity is prevalent in experiments such as in gw detectors : virtually none of the noise sources are white , and we have the added complexity that the cavity mode often couples strongly with the test masses , i.e. it can not be _ adiabatically eliminated _ @xcite , and must be evolved together with the test masses . since we only consider linear systems with gaussian noise , and we only care about the test masses state after the initial transient has died down , the sme and the riccati equation , which also characterizes the exact way of the transient decays , are not entirely necessary . instead , we have found that a wiener filtering approach , in which the measurement data is filtered with the optimal causal wiener filter to obtain instantaneous optimal estimates for position and momentum of the test masses @xcite , suffices , and is most straightforwardly connected with experimental calibration of the system . an example of the power of the wiener filtering approach has already been demonstrated in ref . @xcite , where an optimal controller that yields a steady quantum state with minimum uncertainty ( or von neumann entropy ) has been derived for a general linear ( markovian as well as non - markovian ) quantum measurement process . a direct application of the wiener filtering approach is to explore how quantum a macroscopic test mass can be prepared in a certain environment , which is the second aim of this paper . we measure the _ purity _ of the quantum state of an individual test mass ( or a single mechanical degree of freedom ) through the heisenberg uncertainty product or the following quantity @xmath9 which is unity for a pure state . this quantity can also be converted into an effective occupation number . here @xmath10 , @xmath11 and @xmath12 are the second - order moments of position and momentum of the gaussian state . we will show that a low classical noise budget which is completely below the sql for a broad frequency band allows the quantity @xmath13 to become close to unity . in particular for simple systems with a total classical noise spectrum @xmath14 which is dominated by a white sensing noise and a white force , we have obtained the simple relation @xmath15 but we will also explore how a realistic noise budget for the planned advanced ligo detector as well as an extension of advanced ligo with plausible improvement can best be taken advantage of through an optimized optical configuration that minimizes @xmath13 . when two independent mechanical degrees of freedom are considered , the formalism , which we present in this paper , has already been applied to show that the production of quantum entanglement between the macroscopic end mirrors is possible for sub - sql laser interferometers @xcite . an experiment testing mqm should be divided into different stages which are separated in time : a preparation stage , where the test mass will be continuously observed ; an optional free - evolution stage ; and a verification stage . one will need to collect statistics from a huge number of identical trials as it is required from quantum mechanics . this present paper is the first one of a paper - series : this one deals with the preparation of macroscopic conditional quantum states ; while a second paper @xcite will study the verification of such macroscopic quantum states . this paper is organized as follows : in sec.[sec : wiener ] we will briefly review the theoretical basics of wiener filtering . in sec.[sec : marko ] we will study analytically the conditional variances of the simplified model using only markovian dynamics . we will introduce a flexible homodyne detection angle and input squeezing . in sec.[sec : macroent ] we will extend the analysis done in ref . @xcite about macroscopic entanglement . in sec.[sec : nonmarko ] we will study test - masses in a cavity with finite bandwidth and we will treat more realistic , non - markovian noise sources . these preliminary studies result in an investigation of quantum - state preparation in advanced ligo in sec.[sec : advligo ] . finally , in sec.[sec : con ] we will summarize our main conclusions .

this result , along with the prospect for further improvements , heralds the new possibility of experimentally probing macroscopic quantum mechanics ( mqm ) quantum mechanical behavior of objects in the realm of everyday experience using gravitational - wave detectors . in this paper , we provide the mathematical foundation for the first step of a mqm experiment : the preparation of a macroscopic test mass into a nearly minimum - heisenberg - limited gaussian quantum state , which is possible if the interferometer s classical noise beats the sql in a broad frequency band . our formalism , based on wiener filtering , allows a straightforward conversion from the classical noise budget of a laser interferometer , in terms of noise spectra , into the strategy for quantum state preparation , and the quality of the prepared state . using this formalism , we consider how gaussian entanglement can be built among two macroscopic test masses , and the performance of the planned advanced ligo interferometers in quantum - state preparation

long - baseline laser - interferometer gravitational - wave detectors are operating at a factor of ( in amplitude ) above the standard quantum limit ( sql ) within a broad frequency band ( in the sense that ) . such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150hz and an occupation number of . this result , along with the prospect for further improvements , heralds the new possibility of experimentally probing macroscopic quantum mechanics ( mqm ) quantum mechanical behavior of objects in the realm of everyday experience using gravitational - wave detectors . in this paper , we provide the mathematical foundation for the first step of a mqm experiment : the preparation of a macroscopic test mass into a nearly minimum - heisenberg - limited gaussian quantum state , which is possible if the interferometer s classical noise beats the sql in a broad frequency band . our formalism , based on wiener filtering , allows a straightforward conversion from the classical noise budget of a laser interferometer , in terms of noise spectra , into the strategy for quantum state preparation , and the quality of the prepared state . using this formalism , we consider how gaussian entanglement can be built among two macroscopic test masses , and the performance of the planned advanced ligo interferometers in quantum - state preparation

1612.07297

i

the last two decades have seen an explosion in the study of complex systems , caused by the increasing relevance for society of such large interconnected structures , and by an unprecedented availability of data to analyze them . many of these systems can be modelled as networks , in which the system elements are represented as nodes , and their interactions as connections , or edges , linking them @xcite . the network representation of complex systems has been used in the social sciences @xcite , in biology @xcite , and in studies of technological systems @xcite and communication systems @xcite . more recent work has focussed on the multilayer nature of complex networks , introducing a new framework that is particularly useful for the analysis of large complex data sets @xcite . researchers have applied complex systems techniques to a wide range of disciplines , identifying and analyzing several defining features of complex networks , such as the small world property @xcite , heterogeneous degree distributions @xcite , clustering @xcite , degree - degree correlations @xcite , assortativity @xcite , synchronizability @xcite , and community structure @xcite . communities were originally studied in the context of social networks , in which they are formed by groups of people that share close friendship relations . however , communities of densely connected modules have been observed in several real - world and model networks of diverse nature @xcite , where , in general , they are defined as groups of nodes whose internal connections are denser or stronger than those that link nodes belonging to different groups . in all these cases , the presence of communities directly influences the behaviour of the system , where there is often a correspondence between communities and functional units . ever since the discovery of community structure in real - world networks , a plethora of techniques devoted to their detection has been introduced @xcite . the challenge is both theoretical , in proposing a good mathematical definition of what constitutes a community , and computational , in developing good heuristics that can detect communities in a reasonable time . a common way of investigating the community structure of networks starts with the definition of a quality function , which assigns a score to any network partition . larger scores correspond to better partitions , and algorithms are created to find the partition with the largest score . by far , the most common and used of such quality functions is modularity @xcite , that works by comparing the number of links inside each community to the number of links that would be expected if the nodes were connected at random , without any preference for links within or outside the community . a partition with a large modularity indicates that the communities have many internal links and few external ones , when compared to a randomized version of the network . however , despite its success , modularity also has some shortcomings , decreasing its general usefulness . in this article , we study a new quality function , _ modularity density _ , that was originally introduced in @xcite and that has been shown to address the limitations of traditional modularity . we present a detailed analysis of its properties on synthetic networks typically used to evaluate quality functions , as well as on random graphs , which are a commonly used benchmark to test community detection methods . we also present some limitations that need to be taken into consideration when using methods based on modularity density . in addition , we describe a new community detection algorithm based on this metric , whose computational complexity is quadratic in the number of nodes , and validate it on synthetic and real - world networks , showing that it performs better that other currently available methods . also , we argue that the nature of modularity density allows for a direct quantitative comparison of community structures across networks of different sizes .

many real - world complex networks exhibit a community structure , in which the modules correspond to actual functional units . identifying these communities is a key challenge for scientists . a common approach is to search for the network partition that maximizes a quality function . here in addition , we show that modularity density allows an easy comparison between networks of different sizes , and we also present some limitations that methods based on modularity density may suffer from .

many real - world complex networks exhibit a community structure , in which the modules correspond to actual functional units . identifying these communities is a key challenge for scientists . a common approach is to search for the network partition that maximizes a quality function . here , we present a detailed analysis of a recently proposed function , namely modularity density . we show that it does not incur in the drawbacks suffered by traditional modularity , and that it can identify networks without ground - truth community structure , deriving its analytical dependence on link density in generic random graphs . in addition , we show that modularity density allows an easy comparison between networks of different sizes , and we also present some limitations that methods based on modularity density may suffer from . finally , we introduce an efficient , quadratic community detection algorithm based on modularity density maximization , validating its accuracy against theoretical predictions and on a set of benchmark networks . _ keywords _ : complex networks , community detection , network algorithms , modularity density

1612.07297

c

communities are a fundamental structure that is often present in real - world complex networks . thus , the ability to accurately and efficiently detect them is of great relevance to the analysis of complex data sets . despite their success , traditional methods based on modularity have been shown to suffer from limitations . we have presented a detailed analysis of the properties of modularity density , an alternative quality function for community detection , showing that it does not suffer from the drawbacks that affect traditional modularity . in particular , modularity density does not depend separately on the size of the network or the number of edges , but only on the combination of these two properties in terms of the density of links within the communities . as a consequence , it allows a direct quantitative comparison of the community structure across networks of different sizes and number of edges . at the light of these considerations , we have introduced a new community detection algorithm based on modularity density maximization . investigating its performance on erds - rnyi and heterogeneous random networks , we showed that it correctly identifies them as containing no actual communities . moreover , our algorithm outperforms the other existing modularity - density - based method on every benchmark network that we tested . the high level of accuracy it reaches , its low computational complexity , and the ability to properly identify networks with no ground - truth communities make it a powerful tool to investigate complex systems and extract meaningful information from the network representation of large data sets , giving it a broad range of application throughout the physical sciences . at the same time , we have also identified some limitations of modularity density that were not previously known . more specifically , we found that the theoretical maximum of modularity density for ring lattices and pure random trees does not correspond to the trivial partition , but rather to partitions with more than one community . we find this particularly intriguing , since erds - rnyi graphs are locally tree - like . thus , these results seem to suggest a certain relevance of long - distance links for a correct behaviour of modularity density . since most real - world networks are not pure trees or ring lattices , and indeed do feature shortcut links , we believe these limitations do not affect the suitability of modularity density and methods based on it in the analysis and modelling of complex systems . we will further investigate these limitations in future work . additionally , we will also extend this method to other types of networks , such as bipartite graphs , which require a redefinition of the concept of community itself . an implementation of our algorithm is freely available for download at www.fedebotta.com . fb acknowledges the support of uk epsrc ep / e501311/1 . cidg acknowledges support by eins , network of excellence in internet science , via the european commission s fp7 under communications networks , content and technologies , grant no .

, we present a detailed analysis of a recently proposed function , namely modularity density . we show that it does not incur in the drawbacks suffered by traditional modularity , and that it can identify networks without ground - truth community structure , deriving its analytical dependence on link density in generic random graphs . finally , we introduce an efficient , quadratic community detection algorithm based on modularity density maximization , validating its accuracy against theoretical predictions and on a set of benchmark networks .

many real - world complex networks exhibit a community structure , in which the modules correspond to actual functional units . identifying these communities is a key challenge for scientists . a common approach is to search for the network partition that maximizes a quality function . here , we present a detailed analysis of a recently proposed function , namely modularity density . we show that it does not incur in the drawbacks suffered by traditional modularity , and that it can identify networks without ground - truth community structure , deriving its analytical dependence on link density in generic random graphs . in addition , we show that modularity density allows an easy comparison between networks of different sizes , and we also present some limitations that methods based on modularity density may suffer from . finally , we introduce an efficient , quadratic community detection algorithm based on modularity density maximization , validating its accuracy against theoretical predictions and on a set of benchmark networks . _ keywords _ : complex networks , community detection , network algorithms , modularity density

1408.4767

i

recently , a class of two - dimensional integrate and fire type models have been developed which can be fit to properties of real neurons . this class of models includes the adapting , leaky integrate and fire neuron ( lif ) @xcite , the izhikevich model @xcite , the quartic integrate and fire model @xcite , and the adaptive exponential integrate and fire model ( adex ) @xcite . the models in this class are far simpler to fit and simulate than traditional conductance based models . nevertheless , these models still replicate the more complex behaviors of real neurons @xcite . these models have been fit to several different neuron types so that the behavior of large networks of these neuron models may be studied through numerical exploration of the parameter space . for example , this approach has been used to determine the role of various parameters in the generation of adaptation induced bursting in networks of ca3 pyramidal neurons @xcite while the numerical simulation of integrate and fire networks is far simpler and faster than that of conductance based models , numerical exploration of the parameter space is still a time - consuming process . furthermore , one can not easily perform direct bifurcation analysis on large networks . fortunately , a system of mean field equations has been derived for these large networks of two - dimensional integrate and fire neurons @xcite . this derivation assumes that the networks are all - to - all coupled and the neuronal parameters are homogeneous within the network . the resulting mean field system is a set of non - smooth differential equations governing the first moments of the adaptation variable and the synaptic coupling variable . the mean field system of equations is analytically derived from the original network , without any further fitting . thus , one can conduct bifurcation analysis ( either analytically or numerically ) on the mean field system with confidence that the results are representative of the behavior of the original network of model neurons , and possibly the original network of actual neurons . such a level of correspondence between the parameters for the individual neurons , and the resulting behavior of the full network is currently not possible with more sophisticated types of neuron models . however , analysis of the derived mean field system has an added level of difficulty as the system of equations is non - smooth . both classical bifurcation theory and the newer field of non - smooth bifurcation theory must be used to adequately understand the behavior of the mean field system , and thus the full network . here we explore , both analytically and numerically , many of the non - smooth bifurcations and phenomena that occur in the mean field system of equations from @xcite . the primary mean field system we use is that of the izhikevich model , with the neuronal models fit to hippocampal area ca3 pyramidal neuron data @xcite . we modify the parameters slightly as the neuronal model used in @xcite was an alteration of the default izhikevich model to better fit the action potential half - width observed in the data . we use this model primarily for two reasons : it is the most analytically tractable and the parameters have been fit to neuronal data . however , as we will see , many of the non - smooth bifurcations are present in the other models in the general class of two - dimensional adapting integrate and fire neurons . whenever possible we present our results in terms of this general class .

mean - field systems have been recently derived that adequately predict the behaviors of large networks of coupled integrate - and - fire neurons . the mean - field system for a network of neurons with spike frequency adaptation is typically a pair of differential equations for the mean adaptation and mean synaptic gating variable of the network . these differential equations are non - smooth , and in particular are piecewise smooth continuous ( pwsc ) . here

mean - field systems have been recently derived that adequately predict the behaviors of large networks of coupled integrate - and - fire neurons . the mean - field system for a network of neurons with spike frequency adaptation is typically a pair of differential equations for the mean adaptation and mean synaptic gating variable of the network . these differential equations are non - smooth , and in particular are piecewise smooth continuous ( pwsc ) . here , we analyze the smooth and non - smooth bifurcation structure of these equations and show that the system is organized around a pair of co - dimension two bifurcations that involve , respectively , the collision between a hopf equilibrium point and a switching manifold , and a saddle - node equilibrium point and a switching manifold . these two co - dimension 2 bifurcations can coalesce into a co - dimension 3 non - smooth bifurcation . as the mean - field system we study is a non - generic piecewise smooth continuous system , we discuss possible regularizations of this system and how the bifurcations which occur are related to non - smooth bifurcations displayed by generic pwsc systems .

1408.4767

c

through our analysis of the mean field systems for large networks of coupled neurons , a number of new non - smooth bifurcations have been discovered that have been previously been unknown in the literature . these include two co - dimension 1 branches of boundary equilibrium bifurcations that have homoclinic limit cycles at the bifurcation point , and can be thought of as generating / destroying non - smooth limit cycles . additionally , a pair of co - dimension 2 bifurcations have also been discovered that result from the collision of classical smooth branches of bifurcations with non - smooth bifurcations . these occur when either a hopf equilibrium point , or a saddle - node equilibrium point collide with a switching manifold . we have determined locally in a neighbourhood of these bifurcation points the resulting behavior of the system through analytical and numerical results . additionally , a global - codimension 2 bifurcation and the collision of a bogdanov - takens equilibrium point with a switching manifold was also discovered by analyzing these systems , however we leave their analysis for later work . given the analysis we have performed , then there are several predictions we can make , using the bifurcation curves for all the necessary branches . for example , it appears that the time scales @xmath221 and @xmath325 are crucial for determining the presence of bursting . if @xmath218 , then no bursting can occur , while if @xmath220 , there is a bell shaped region of bursting for @xmath134 , and @xmath207 . thus , if the adaptation time scale is smaller then the time scale of the synapses , adapting , recurrently coupled networks would not burst . this can be the case for example for weakly adapting neurons coupled together with nmda synapses , which have a long time scale . unfortunately however , while much of these bifurcations can be at least derived , one can not easily determine whether or not even the smooth bifurcations are generic in any sense . this is due to the fact that these particular systems can not be diagonalized very easily , due to the presence of the @xmath326 term , which has an unbounded derivative as @xmath327 . thus , center manifold theory can not be directly applied , and many of the genericity conditions can not be verified . in addition to these problems with regards to smooth bifurcations , one can not easily apply the existing non - smooth theory to these systems . the systems in the form @xmath328 are clearly piecewise smooth continuous , however unlike the vast majority of pwsc systems discussed in the literature , they fail to satisfy one critical constraint that these other systems have . in normal piecewise smooth continuous systems , given by @xmath329 where @xmath330 on @xmath331 , it is assumed that both @xmath332 and @xmath333 exists everywhere , and are smooth . in our system , @xmath326 only exists when @xmath334 and its first derivative only exists when @xmath254 . this renders much of the analysis on pwsc systems inapplicable . indeed , this system can not even be regularized in the normal way , via a teixeira type regularization scheme @xcite due to the fact that @xmath86 is undefined when @xmath335 . however , there are alternate ways to apply both center manifold theory , and simultaneously regularize this system . in particular , consider the three - dimensional system given by @xmath336 where @xmath337 is a small constant . in this singularly perturbed system , one can show that as @xmath338 , one recovers the piecewise smooth continuous system as when @xmath337 is small , we can regard @xmath20 and @xmath2 as fixed , and thus @xmath339 rapidly converges to the steady states @xmath82 , or @xmath86 , depending on the sign of @xmath340 . using this type of embedded system , which is entirely polynomial for the izhikevich mean field system , one has regularized the non - smooth system in a sense by embedding it as the fast system in a singular perturbation problem . thus , to actually determine the genericity properties of the bifurcations displayed above , in addition to how the non - smooth bifurcations discovered are related to the general smooth bifurcation theory , one can analyze either directly or numerically the embedded system for finite @xmath337 . preliminarily , we have found that the hopf beb bifurcation seems to be a bautin point under the regularization , and the saddle - node beb bifurcation point seems to be a bogdanov - takens point under the regularization . these are both co - dimension 2 smooth bifurcation , and they also explain the emergence of the non - smooth saddle - node of periodics in the hopf beb , which has a smooth saddle - node of periodics . additionally , the regularized bogdanov - takens has ( generically ) a branch of homoclinic bifurcations , which also exists in a non - smooth form for the saddle - node beb . however , as the embedded system , and its justification as a regularization are outside of the scope of this paper , we leave it for future work . in addition to the embedded regularization , this system is also unusual in the sense that there is a natural regularization for the mean - field system . suppose we consider the voltage equations to be perturbed by white noise : @xmath341 where @xmath342 and @xmath343 . in which case one can rigorously derive a mean - field system for this network of equations which is identical to the original mean - field system given in equations ( [ mfa])-([mfc ] ) only the firing rate is now given by : @xmath344^{-1}\end{aligned}\ ] ] where @xmath345 is an anti - derivative ( in @xmath1 ) of @xmath346 . as we shall do in forthcoming work @xcite one can rigorously show that this expression for @xmath347 is smooth with respect to @xmath20 and @xmath2 , and always defined , and converges to ( [ mfc ] ) as @xmath348 . thus , the mean - field system for a network with noise parameterized by @xmath349 , the variance in the noise , converges to the system ( [ mfa])-([mfc ] ) as the variance of the noise becomes negligible . but , since the mean - field system with noise is smooth , it can be thought of as a natural regularization for the non - smooth mean - field system . we remark that this is unusual in the field of non - smooth theory as generally a regularization is chosen or suggested , and is typically of the teixeira form @xcite . we leave the bifurcation analysis of the system with noise for future work . finally , one may ask if the non - smooth bifurcations we analyze here appear in other non - smooth systems or are generic in any way . to the best of our knowledge , the co - dimension 2 bifurcations are novel in the literature , according to a recent review @xcite . however , a hopf - bifurcation occuring on a discontinuity boundary ( a co - dimension 2 non - smooth bifurcation ) does occur in the example ( in section 6 ) in @xcite ( see figure 29 . ) . however , the system examined in @xcite is a fillipov system , and thus has a higher order of discontinuity . as to whether these bifurcations occur in a more generic system , we intend to explore this further with a more generic piecewise smooth continuous system that does not have undefined derivatives on the switching manifolds . in particular , we note that with a quadratic pwsc system , one can show that as for our saddle - node beb bifurcation , at the intersection between generic branches of persistence and non - smooth fold beb bifurcations , the equilibrium of @xmath333 must have a zero eigenvalue at this co - dimension 2 point . we intend to explore all the possible cases and their possible relationships to the co - dimension 2 non - smooth bifurcations we outline in this paper for future work . r. brette and w. gerstner . adaptive exponential integrate - and - fire model as an effective description of neuronal activity . , 94(5):36373642 , 2005 . a. buzzi , p.r . da silva , and m.a . teixeira a singular approach to discontinuous vector fields on the plane , 231:633655 , 2006 k.a . ferguson , c.y.l . huh , b. amilhon , s. williams , and f.k . skinner simple , biologically - constrained ca1 pyramidal cell models using an intact , whole hippocampus context , 2014 , 3:104 ( doi : 10.12688/f1000research.3894.1 ) w. nicola , and s.a . bifurcations of large networks of two - dimensional integrate and fire neurons , 35 : 87108 , 2013 . . nykamp . and d. tranchina . a population density approach that facilitates large - scale modeling of neural networks : analysis and an application to orientation tuning . , 8:1950 , 2000 . a. omurtag , b.w . knight , and l. sirovich . on the simulation of large populations of neurons . , 8:5163 , 2000 . ( in red ) using @xmath350 for @xmath8 predicted from topological normal form theory ( @xmath351 , green ) , which is only locally valid near the transition to firing from quiescence , or for a more global fit ( @xmath352 , blue ) . the specific @xmath8 used does not matter as it can be merely absorbed into the @xmath76 and @xmath77 parameters and the final bifurcation analysis is the same . ] .parameters for various network types and the mean - field systems . note that parameter above are dimensionless , where as in some of the cited sources they are in dimensional form only . [ cols="^,^,^,^",options="header " , ]

these two co - dimension 2 bifurcations can coalesce into a co - dimension 3 non - smooth bifurcation . as the mean - field system we study is a non - generic piecewise smooth continuous system , we discuss possible regularizations of this system and how the bifurcations which occur are related to non - smooth bifurcations displayed by generic pwsc systems .

mean - field systems have been recently derived that adequately predict the behaviors of large networks of coupled integrate - and - fire neurons . the mean - field system for a network of neurons with spike frequency adaptation is typically a pair of differential equations for the mean adaptation and mean synaptic gating variable of the network . these differential equations are non - smooth , and in particular are piecewise smooth continuous ( pwsc ) . here , we analyze the smooth and non - smooth bifurcation structure of these equations and show that the system is organized around a pair of co - dimension two bifurcations that involve , respectively , the collision between a hopf equilibrium point and a switching manifold , and a saddle - node equilibrium point and a switching manifold . these two co - dimension 2 bifurcations can coalesce into a co - dimension 3 non - smooth bifurcation . as the mean - field system we study is a non - generic piecewise smooth continuous system , we discuss possible regularizations of this system and how the bifurcations which occur are related to non - smooth bifurcations displayed by generic pwsc systems .

cs0609148

i

although low - density parity - check block codes ( ldpc - bcs ) have very good performance under message - passing iterative ( mpi ) decoding , they are known to be subject to decoding failures due to so - called pseudo - codewords . these are real - valued vectors that can be loosely described as error patterns that cause non - convergence in iterative decoding due to the fact that the algorithm works locally and can give priority to a vector that fulfills the equations of a graph cover rather than the graph itself . [ example : introduction ] consider the trivial length-@xmath0 and dimension-@xmath1 code @xmath2 defined by the @xmath3 parity - check matrix @xmath4 and whose tanner graph is shown in fig . [ fig : smallgraph:1 ] ( left ) . a possible cubic cover of this tanner graph is also depicted in fig . [ fig : smallgraph:1 ] ( right ) . because @xmath5 is a valid configuration in this cubic cover , the vector @xmath6 is a pseudo - codeword of the code @xmath7 defined by @xmath8 ( see @xcite ) . it has been shown @xcite that the performance of mpi decoding schemes for ldpc - bcs is largely dominated _ not _ by minimum hamming weight considerations but by minimum _ pseudo - weight _ considerations , where the minimum pseudo - weight in the case of an additive white gaussian noise channel ( awgnc ) is defined as @xmath9 where @xmath10 and @xmath11 are , respectively , the @xmath12-norm and @xmath13-norm , and @xmath14 is the set of all pseudo - codewords for the code @xmath7 defined by @xmath8 . the minimum pseudo - weight is a measure of the effect that decoding failures have on the performance of the code . , the minimum hamming weight may still be a key factor in performance analysis ; however , the larger the gap between @xmath15 and @xmath16 , the greater role the minimum pseudo - weight plays . in any case , the minimum hamming weight is important for quantifying the impact of undetectable errors . ] as a consequence , the large signal - to - noise ratio ( snr ) performance of mpi decoding can be worse than that predicted by the maximum - likelihood decoding union bound , which constitutes a major problem when trying to determine performance guarantees . addressing this problem from the convolutional - code perspective , i.e. , studying the pseudo - codeword problem described above for ldpc convolutional codes ( ldpc - ccs ) , constitutes the major topic of this paper . we investigate a class of time - invariant ldpc convolutional codes derived by `` unwrapping '' certain classes of quasi - cyclic ( qc ) ldpc block codes that are known to have good performance @xcite . unwrapping a qc block code to obtain a time - invariant convolutional code represents a major link between qc block codes and convolutional codes . this link was first introduced in a paper by tanner @xcite , where it was shown that the free distance of the unwrapped convolutional code , if non - trivial , can not be smaller than the minimum distance of the underlying qc code . this idea was later extended in @xcite . more recently , a construction for ldpc convolutional codes based on qc - ldpc block codes was introduced by tanner et al . @xcite , and a sliding - window mpi decoder was described . in that paper it was noted that the ( non - trivial ) convolutional versions of these codes significantly outperformed their block code counterparts in the waterfall region of the bit error rate ( ber ) curve , even though the graphical representations of mpi decoders were essentially equivalent . throughout this paper we mainly take the approach of @xcite , which connects the presence of pseudo - codewords in mpi decoding and linear programming ( lp ) decoding . lp decoding was introduced by feldman , wainwright , and karger @xcite and can be seen as a relaxation of the maximum - likelihood decoding problem . more precisely , maximum - likelihood decoding can be formulated as the solution to an optimization problem , where a linear cost function is minimized over a certain polytope , namely the polytope that is spanned by the set of all codewords . for general codes , there is no efficient description of this polytope and so feldman et al . suggested replacing it with an ( efficiently describable ) relaxed polytope , which in the following will be called the `` fundamental polytope '' . in other words , the decoding result of the lp decoder is the point in the fundamental polytope that minimizes the above - mentioned linear cost function . in order to analyze the behavior of unwrapped ldpc convolutional codes under lp decoding , we need to examine the fundamental polytope @xcite of the underlying qc - ldpc block codes . ( because of symmetries , it is actually sufficient to study the structure of the fundamental polytope around the zero codeword , i.e. , it is sufficient to study the so - called fundamental cone . ) our goal is to formulate analytical results ( or at least efficient procedures ) that will allow us to bound the minimum pseudo - weight of the pseudo - codewords of the block and convolutional codes . the paper aims at addressing this question and related issues . in the following sections , we will study the connections that exist between pseudo - codewords in qc codes and pseudo - codewords in the associated convolutional codes and show that this connection mimics the connection between the codewords in qc codes and the associated convolutional codes . as a motivational example we simulated a rate @xmath17 @xmath18-regular ldpc - cc with syndrome former memory @xmath19 , together with three wrapped block code versions : a @xmath20 $ ] @xmath18-regular qc - ldpc block code , a @xmath21 $ ] code , and a @xmath22 $ ] code , with parity - check matrices of increasing circulant sizes @xmath23 , @xmath24 , and @xmath25 , respectively , while keeping the same structure within each @xmath26 circulant @xcite ( see section [ sec : link : qc : and : conv : codes:1 ] ) . ( note that increasing the circulant size of the qc code increases its complexity , i.e. , its block length . also note that each of the three block codes has rate slightly greater than @xmath27 . ) a sliding - window mpi decoder as in @xcite was used to decode the convolutional code . conventional ldpc - bc mpi decoders were employed to decode the qc - ldpc block codes . all decoders were allowed a maximum of @xmath28 iterations . the resulting ber performance of these codes on a binary - input awgn channel is shown in fig . [ fig : compare:1 ] . we note that , particularly in the low - to - moderate snr region , where the complete pseudo - weight spectrum plays an important role , the unwrapped ldpc - cc performs between @xmath29 and @xmath30 better than the associated qc - ldpc block codes . also , as the circulant size increases , the performance of the block codes approaches that of the convolutional code . these performance curves suggest that the pseudo - codewords in the block code that result in decoding failures may not cause such failures in the convolutional code , which suggests that ldpc - ccs may have better iterative decoding thresholds than comparable ldpc - bcs ( see also @xcite and @xcite ) . in order to underline the influence of pseudo - codewords under mpi decoding , we consider the following experiment . let @xmath31 be a _ minimal pseudo - codeword _ @xcite for the above - mentioned @xmath17 @xmath18-regular ldpc - cc , i.e. , a pseudo - codeword that corresponds to an _ edge of the fundamental cone _ of that ldpc - cc . moreover , we define the log - likelihood ratio vector @xmath32 to be is not squared , therefore this ratio does not correspond to the awgnc pseudo - weight of @xmath31 ( see sec . [ sec : pseudo : weight : comparison:1 ] ) , although it is closely related to that value . ] @xmath33 we then run the mpi decoder that is initialized with @xmath34 and count how many iterations it takes until the decoder decides for the all - zero codeword as a function of @xmath35 and @xmath36 . the results are shown in fig . [ fig : alphabetaplot:1 ] . the meaning of @xmath32 is the following . if @xmath37 , then @xmath38 corresponds to the log - likelihood ratio vector that the receiver sees when the communication system operates at a signal - to - noise ratio @xmath39 and when the noise vector that is added by the binary - input awgn channel happens to be the all - zero vector ( see , e.g. , the discussion in ( * ? ? ? 3 ) ) . for non - zero @xmath35 the expression for @xmath40 has been set up such that the lp decoder has a decision boundary at @xmath41 : for @xmath42 the all - zero codeword wins against the pseudo - codeword @xmath31 whereas for @xmath43 the all - zero codeword loses against the pseudo - codeword @xmath31 under lp decoding . the simulations in fig . [ fig : alphabetaplot:1 ] were obtained using a search algorithm that looked for a low - pseudo - weight minimal pseudo - codeword @xmath31 in the fundamental cone of the above - mentioned ldpc - cc . the @xmath31 that we found has awgnc pseudo - weight @xmath44 , which happens to be smaller than the free distance . secondly , we ran the mpi decoder for various choices of @xmath35 and @xmath36 : fig . [ fig : alphabetaplot:1 ] left shows the number of iterations needed using a sum - product - algorithm - type mpi decoder whereas fig . [ fig : alphabetaplot:1 ] right shows the number of iterations needed using a min - sum - algorithm - type mpi decoder . ( note that the decisions reached by the latter are independent of the choice of @xmath36 , @xmath45 . ) because of the more oscillatory behavior of the min - sum - algorithm - type mpi decoder close to decision boundaries of the lp decoder , observed empirically , it is advantageous to run that decoder for many iterations in our scenario , whereas in the case of the sum - product - algorithm - type mpi decoder it hardly pays to go beyond @xmath46 iterations . in this paper , we provide a possible explanation for the performance difference observed in the motivational example above . based on the results of @xcite that relate code performance to the existence of pseudo - codewords , we examine the pseudo - codeword weight spectra of qc - ldpc block codes and their associated convolutional codes . we will show that for a non - trivial ldpc - cc derived by unwrapping a non - trivial qc - ldpc block code , the minimum pseudo - weight of the convolutional code is at least as large as the minimum pseudo - weight of the underlying qc code@xcite , i.e. , @xmath47 this result , which parallels the well - known relationship between the free hamming distance of non - trivial convolutional codes and the minimum hamming distance of their non - trivial quasi - cyclic counterparts @xcite , is based on the fact that every pseudo - codeword in the convolutional code induces a pseudo - codeword in the block code with pseudo - weight no larger than that of the convolutional code s pseudo - codeword . this difference in the weight spectra leads to improved ber performance at low - to - moderate snrs for the convolutional code , a conclusion supported by the simulation results presented in fig . [ fig : compare:1 ] . the paper is structured as follows . in sec . [ sec : ps : qc : and : conv : codes:1 ] we develop the background necessary to describe the connection between pseudo - codewords in unwrapped ldpc convolutional codes and those in the associated qc - ldpc codes . thus , in sec . [ sec : link : qc : and : conv : codes:1 ] we briefly discuss the connection between convolutional codes and their associated qc codes , especially how codewords in the former can be used to construct codewords in the latter , and in sec . [ sec : fundam : cone : par : check : matrix:1 ] we define the fundamental polytope / cone of a matrix and show how we can describe the fundamental cone of a polynomial parity - check matrix through polynomial inequalities . we end the section by showing how pseudo - codewords in unwrapped ldpc convolutional codes yield pseudo - codewords in the associated qc - ldpc codes . in sec . [ sec : pseudo : weight : comparison:1 ] , we compare the pseudo - weights of unwrapped convolutional and their associated qc block codes . sec . [ sec : pseudo : weight : definitions:1 ] introduces various channel pseudo - weights and sec . [ sec : pseudo : weight : inequality:1 ] presents the main result , namely that the minimum awgn pseudo - weight , the minimum binary erasure channel ( bec ) pseudo - weight , the minimum binary symmetric channel ( bsc ) pseudo - weight , and the minimum max - fractional weight of a convolutional code are at least as large as the corresponding minimum pseudo - weights of a wrapped qc block code . [ sec : analysis : problematic : pseudo : codewords : conv : codes:1 ] discusses a method to analyze problematic pseudo - codewords , i.e. , pseudo - codewords with small pseudo - weight . the method addresses the convolutional code case . it introduces two sequences of `` truncated '' pseudo - weights and , respectively , `` bounded pseudo - codeword '' pseudo - weights , that play an important role in identifying the minimum pseudo - weight of the convolutional code , similar to the role that column distances and row distances play in identifying the free distance . we end with some conclusions in sec . [ sec : conclusions:1 ] . throughout the paper we will use the standard way of associating a tanner graph with a parity - check matrix and vice - versa . we will use the following notation . we let @xmath48 , @xmath49 , @xmath50 , and @xmath51 be the galois field of size @xmath13 , the field of real numbers , the set of non - negative real numbers , and the set of positive real numbers , respectively . if @xmath52 is a polynomial over some field and @xmath53 is some positive integer then @xmath54 denotes the polynomial @xmath55 of degree smaller than @xmath53 such that @xmath56 . we say that a polynomial @xmath57 with real coefficients is non - negative , and we write @xmath58 , if all its coefficients @xmath59 satisfy @xmath60 . similarly , a polynomial vector @xmath61 is non - negative , and we write @xmath62 , if all its polynomial components @xmath63 satisfy @xmath58 for all @xmath64 . moreover , a polynomial matrix @xmath65 is non - negative , and we write @xmath66 , if all its entries are non - negative polynomials . finally , for any positive integer @xmath53 and for any @xmath67 , @xmath68 will represent the @xmath69-times cyclically left - shifted identity matrix of size @xmath70 .

message - passing iterative decoders for low - density parity - check ( ldpc ) block codes are known to be subject to decoding failures due to so - called pseudo - codewords . these failures can cause the large signal - to - noise ratio performance of message - passing iterative decoding to be worse than that predicted by the maximum - likelihood decoding union bound . in this paper we address the pseudo - codeword problem from the convolutional - code perspective . in particular , we compare the performance of ldpc convolutional codes with that of their `` wrapped '' quasi - cyclic block versions and we show that the minimum pseudo - weight of an ldpc convolutional code is at least as large as the minimum pseudo - weight of an underlying quasi - cyclic code . this result , which parallels a well - known relationship between the minimum hamming weight of convolutional codes and the minimum hamming weight of their quasi - cyclic counterparts , is due to the fact that every pseudo - codeword in the convolutional code induces a pseudo - codeword in the block code with pseudo - weight no larger than that of the convolutional code s pseudo - codeword . this difference in the weight spectra leads to improved performance at low - to - moderate signal - to - noise ratios for the convolutional code , a conclusion supported by simulation results . * index terms * convolutional codes , quasi - cyclic codes , low - density parity - check ( ldpc ) codes , linear programming decoding , message - passing iterative decoding , pseudo - codewords , pseudo - weights .

message - passing iterative decoders for low - density parity - check ( ldpc ) block codes are known to be subject to decoding failures due to so - called pseudo - codewords . these failures can cause the large signal - to - noise ratio performance of message - passing iterative decoding to be worse than that predicted by the maximum - likelihood decoding union bound . in this paper we address the pseudo - codeword problem from the convolutional - code perspective . in particular , we compare the performance of ldpc convolutional codes with that of their `` wrapped '' quasi - cyclic block versions and we show that the minimum pseudo - weight of an ldpc convolutional code is at least as large as the minimum pseudo - weight of an underlying quasi - cyclic code . this result , which parallels a well - known relationship between the minimum hamming weight of convolutional codes and the minimum hamming weight of their quasi - cyclic counterparts , is due to the fact that every pseudo - codeword in the convolutional code induces a pseudo - codeword in the block code with pseudo - weight no larger than that of the convolutional code s pseudo - codeword . this difference in the weight spectra leads to improved performance at low - to - moderate signal - to - noise ratios for the convolutional code , a conclusion supported by simulation results . * index terms * convolutional codes , quasi - cyclic codes , low - density parity - check ( ldpc ) codes , linear programming decoding , message - passing iterative decoding , pseudo - codewords , pseudo - weights .

astro-ph0009078

i

ngc 1068 is a nearby heavily obscured seyfert 2 galaxy with a bright active galactic nucleus ( agn ) which has been studied in nearly every available wavelength band and at many spatial resolutions . its classification as a seyfert 2 nucleus rests on the basis of narrow emission lines . antonucci & miller ( 1985 ) have , however , discovered broad , polarized emission lines indicative of a broad line region , which suggests the presence of a seyfert 1 nucleus hidden by a thick circumnuclear torus or a heavily warped disk , a possibility we shall henceforth include in the word `` torus '' . barthel ( 1989 ) suggested that ngc 1068 might be a prototype for many classes of agns . thus ngc 1068 has provided the framework for a unification scheme based on a dense disk of molecular gas and dust surrounding a broad line region and seyfert 1 nucleus ; see e.g. , krolik ( 1999 ) and references therein . in this model , seyfert 1 and 2 galaxies are substantially similar objects viewed at different orientations . an alternative to the torus geometry that has been suggested by cameron et al . ( 1993 ) , is that the molecular material in the nuclear vicinity is distributed in such a way that the bulk of the gas and dust lies @xmath1100 pc or so from the nucleus . we take the distance to ngc 1068 as 14.4 mpc ( tully 1988 ) so that 1@xmath0 = 72 pc ; we assume h@xmath4 to be 75 km s@xmath5 mpc@xmath5 throughout this paper . since antonucci & miller ( 1985 ) suggested that ngc 1068 contains an obscuring torus , there have been numerous theoretical studies of thick tori in agns . three that have focused on ngc 1068 , mainly constrained by the energetics , are efstathiou , hugh & young ( 1995 ) , pier & krolik ( 1993 ) and granato , danese , & franceschini ( 1997 ) ; these give numerous references to other theoretical models and issues . recently , observations of the nucleus of ngc 1068 at a range of wavelengths with high spatial resolution have been published . differences exist between different images , but most find strong nuclear emission in a roughly north - south direction ; the putative torus is presumed to lie in roughly an east - west plane . hubble space telescope ( hst ) observations of the inner 3@xmath0 of ngc 1068 in an [ oiii ] filter by evans et al . ( 1991 ) and macchetto et al . ( 1994 ) resolve the narrow line region into a conical shape oriented northeast by southwest . spectral observations by crenshaw & kraemer ( 2000a , b ) and kraemer & crenshaw ( 2000 ) of the [ oiii ] emitting gas have further delineated the cone . speckle observations at the 2.2 @xmath2 m diffraction limit of the keck 10-meter telescope show that about half of the nuclear flux at 2.2 @xmath2 m within a diameter of @xmath11@xmath0 comes from an extended region , essentially north - south but orientated slightly west of north , 0.3@xmath0 ( 22 pc ) in length on either side of a point source which is less than 0.03@xmath0 ( 2 pc ) in size ( weinberger et al.1999 ) . rouan et al . ( 1998 ) have used adaptive optics to obtain images at 1.2 , 1.6 and 2.2 @xmath2 m with higher dynamic range but poorer spatial resolution than weinberger et al . and see evidence of elongated structure at a position angle of p.a . @xmath6 102@xmath3 which might be tracing the putative torus . marco & alloin ( 2000 ) , observing at 3.5 and 4.8 @xmath2 m , see an unresolved core with a full width at half maximum ( fwhm ) @xmath7 0.2@xmath0 ( 16 pc ) , a north - south elongation about 1@xmath0 ( 70 pc ) in length , plus a `` disk - like '' structure with a diameter @xmath11.0@xmath0 ( 70 pc ) at a p.a . @xmath1 100@xmath3 which they interpret as the dusty torus invoked in unification schemes . gallimore et al . ( 1996a ) and gallimore , baum , & odea , ( 1996c ) have summarized the sub - arcsecond radio structure of ngc 1068 as consisting of three components in a northeast by southwest line . a 10@xmath0 ( kiloparsec ) scale radio jet joins the southern and central radio components and traces emission to sub - arcsecond ( tens of pc ) scales . the southern - most radio peak consists of two clumps , the brighter of which has a relatively flat radio spectrum and is associated with h@xmath8o and oh masers characterizing warm and dense molecular gas and showing keplerian motion . gallimore et al . ( 1996c ) consider this region ( called s1 ) as most likely being at the location of the central engine of ngc 1068 because of these features . gallimore , baum & odea ( 1997 ) have imaged s1 at 8.4 ghz and give the first direct image of a pc - scale ionized gas disk surrounding the agn in ngc 1068 when they trace a set of compact sources of overall extent 0.15@xmath0 at a position angle of @xmath1110 . s1 appears to also coincide with the apex of the [ oiii ] cone within the astrometric uncertainties between the visual and radio images ( 0.2@xmath0 ; evans et al . 1991 ) . at millimeter wavelengths , schinnerer et al . ( 2000 ) see two emission knots in the @xmath9co(2 - 1 ) line about 1@xmath0 east and west of the nucleus surrounded by a ring of emission with radius @xmath11.5@xmath0 ( 100 pc ) . the bolometric luminosity of ngc 1068 is determined mainly in the mid infrared where it is extremely bright ; its flux distribution peaks at @xmath125 @xmath2 m . if the infrared emission is isotropic , the bolometric luminosity of ngc 1068 is @xmath12.53.0@xmath1010@xmath11l@xmath12 , most of which is emitted between 10 and 100 @xmath2 m . this includes , however , the emission from the `` 3 kpc ring '' , a disk about 30@xmath0 in diameter , which was observed at 10 , 60 and 158 @xmath2 m by telesco et al . ( 1984 ) and found to account for almost half the luminosity of ngc 1068 . telesco et al . attributed this emission to a molecular cloud with ongoing star formation . subsequent radio measurements by planesas , scoville & myers ( 1991 ) and papadopoulos , seaquist & scoville ( 1997 ) further delineated the properties of the molecular cloud . finally , laurent et al . ( 2000 ) obtained cvf spectra between 5 and 16 @xmath2 m which allowed them to clearly separate the mid - infrared emission from the nucleus and from the outer ring . based on the observations detailed below we will take the bolometric luminosity of the central area 4@xmath0 in diameter of ngc 1068 to be 1.5@xmath1010@xmath11l@xmath12 . hard x - ray observations of ngc 1068 provide another estimate of the intrinsic agn luminosity . a strong fe k line , first detected with ginga by koyama et al . ( 1989 ) , indicates that the observed x rays are scattered and reflected emission , and that the direct line of sight to the agn is completely blocked by a compton - thick material , a result confirmed by observations with asca ( ueno et al . 1994 ) and bepposax ( matt et al . the intrinsic 210 kev luminosity of ngc 1068 is estimated to be on the order of @xmath11.1@xmath1010@xmath13l@xmath12 ( iwasawa et al . 1997 ; rescaled to h@xmath4 = 75 km s@xmath5 mpc@xmath5 ) . if l@xmath14l@xmath15 ( matt et al . 2000 ) , the intrinsic agn bolometric luminosity is estimated to be @xmath16l@xmath17 . the reduced obscuration at mid - infrared wavelengths allows a detailed examination of the nuclear structure , and means that mid - infrared observations are crucial in determining the morphology of the nucleus . the previous mid - infrared observations of ngc 1068 with the highest spatial resolution are those of bock et al . ( 1998 ) who made diffraction limited observations ( fwhm @xmath10.5@xmath0 ) with the hale 200-inch telescope at 8.8 , 10.3 and 12.5 @xmath2 m ; see bock et al . for references to previous mid - infrared work . bock et al . report a central peak with structures extending about 1@xmath0 north - south which is unresolved east - west and coincides with one wall of the ionization cone seen by evans et al . in this paper we report similar observations but made at wavelengths from 7.9 @xmath2 m to 24.5 @xmath2 m with the 10-meter keck telescope and accordingly having twice the raw spatial resolution as the palomar observations . the present observations were limited to the inner 4@xmath0 of the galaxy and pertain to this extreme nuclear region only .

mid - infrared observations of the central source of ngc 1068 have been obtained with a spatial resolution in the deconvolved image of 0.1 ( pc ) . about two - thirds of its flux can be ascribed to a core structure which is itself elongated north - south and does not show a distinct unresolved compact source .

mid - infrared observations of the central source of ngc 1068 have been obtained with a spatial resolution in the deconvolved image of 0.1 ( pc ) . the central source is extended by in the north - south direction but appears unresolved in the east - west direction over most of its length . about two - thirds of its flux can be ascribed to a core structure which is itself elongated north - south and does not show a distinct unresolved compact source . the source is strongly asymmetric , extending significantly further to the north than to the south . the morphology of the mid - infrared emission appears similar to that of the radio jet , and has features which correlate with the images in [ oiii ] . its 12.524.5 m color temperature ranges from 215 to 260k and does not decrease smoothly with distance from the core . silicate absorption is strongest in the core and to the south and is small in the north . the core , apparently containing two - thirds of the bolometric luminosity of the inner 4 diameter area , may be explained by a thick , dusty torus near the central agn viewed at an angle of to its plane . there are , however , detailed difficulties with existing models , especially the narrow east - west width of the thin extended mid - infrared `` tongue '' to the north of the core . we interpret the tongue as re - processed visual and ultraviolet radiation that is strongly beamed and that originates in the agn .

astro-ph0009078

c

an overview of the energetics of ngc 1068 and how the present observations fit into the luminosity of ngc 1068 is provided by figure 2 which compares the flux per octave of the keck observations with the overall spectral energy distribution measured from ngc 1068 . the latter has been determined from the published literature and reflects large beam measurements such as the iras measurements . figure 2 establishes that the wavelengths used in the present observations sample the bulk of the emission from ngc 1068 . the arrows in figure 2 indicate upper limits on the flux per octave measured in a gaussian of fwhm equaling the east - west width of ngc 1068 . in the four wavelength bands they represent 35 , 14 , 21 and 21% of the total , and represent estimates of the emission which can be ascribed to an unresolved point source . the estimate is an upper limit since the width of ngc 1068 is certainly greater than the fwhm of the deconvolved psf . we are forced to the conclusion that only a small fraction of the observed luminosity in ngc 1068 comes from a point like nucleus ; even in close to the central peak there is a significant component of extended emission . emission from the low surface brightness disk @xmath135@xmath0 in diameter corresponding to a 3 kpc diameter ring of molecular clouds in which star formation is occurring , is included in the overall fluxes in figure 2 ( telesco et al . telesco et al . conclude that about half the bolometric luminosity of ngc 1068 comes from the 3 kpc ring and estimate that at 10 @xmath2 m @xmath120% of the observed flux density comes from the disk . the disk is much colder than the nuclear source ; telesco et al . estimate that the 8 25 @xmath2 m radiation from the disk is only about 20% of the total . in contrast , at 100 @xmath2 m , most of the emission is from the disk and only a small fraction is from the nucleus . from the keck data and figure 2 we estimate that @xmath1two - thirds of the bolometric luminosity comes from the central area with 4@xmath0 diameter . i.e. , the 3 kpc ring contributes only @xmath1one - thirds the bolometric luminosity . this apparent discrepancy between the keck data and the data of telesco et al . can be attributed to the uncertainties in the models and in the calibrations , including the wide bandwidths , plus the inherent difficulties of observations in the far infrared . it is best resolved with high spatial resolution observations at 60 and 100 @xmath2 m such as will be available with the sofia mission . since it does not affect the following discussion , it will not be pursued further . figure 3 shows the 12.5 @xmath2 m contour map from the keck observations superimposed on the hst [ oiii ] image of macchetto et al . since no absolute astrometry was obtained for the keck images , the juxtaposition of the infrared central peak with the apex is uncertain . the mid - infrared peak was located at the scattering center as determined by kishimoto ( 1999 ) who has recently carried out a reanalysis of the polarization data ( capetti et al . 1997 ) to determine the position of the nucleus of ngc 1068 as defined by ultraviolet polarimetry . independent determinations of the position of the nucleus from astrometry at near - infrared wavelengths ( thatte et al . 1997 ) and mid - infrared wavelengths ( braatz et al . 1993 ) agree within the quoted uncertainties . with the choice of kishimoto s central position , the line of the 12.5 @xmath2 m emission lies just inside the ionization cone , adjacent to one `` wall '' . also , this choice of alignment gives a good correlation between the mid - infrared emission and [ oiii ] clouds b - f , and thus provides independent confidence in the efficacy of the adopted deconvolution . the 12.5 @xmath2 m contour is superimposed on the 5 ghz map of gallimore et al . ( 1996c ) in figure 4 . again , since no absolute astrometry was obtained for the keck images , the juxtaposition of the infrared central peak with the radio features is uncertain . a shift of 0.3@xmath0 would more completely overlay the mid - infrared features with the radio jet and can not be ruled out . the 12.5 @xmath2 m central peak has been located on s1 , the brighter of the southern components contained in the radio nucleus and the source gallimore et al.identify with the center of ngc 1068 . it has a flatter radio spectrum than the other radio sources and is the location of the torus observed by gallimore et al . the qualitative agreement of the central portions is striking . both images show a bend to the east , although the infrared bend is further to the north than the radio bend . at the brighter levels , the appearance of the present mid - infrared images agrees qualitatively with the near - infrared images of marco & alloin ( 2000 ) in showing extended emission along the north - south direction , the preferential direction of the axis of the radio emission and of the ionizing cone . as in the mid infrared , the central core is unresolved in the near - infrared images ( fwhm @xmath240.12@xmath0 ) . the agreement at the lower intensity contours is not so good . at both 3.5 and 4.8 @xmath2 m , marco & alloin ( 2000 ) see evidence both @xmath10.5@xmath0 east and west of the central peak for a putative torus at an intensity level roughly 1% of the peak surface brightness observed . the flux density at 4.8 @xmath2 m of the clumps defining this torus is @xmath10.15 jy . no sign of this torus is seen in the present mid - infrared observations . if the radiation is thermal , at a reasonable temperature , it should also be present in the 7.9 @xmath2 m deconvolved image . tests made by placing an artificial point source 0.5@xmath0 from the central peak of ngc 1068 indicate that at 7.9 @xmath2 m a source with a flux density of @xmath10.1 jy or 0.5% of the total observed flux density at 7.9 @xmath2 m could easily be seen ; see the appendix . calculations using the thermal parameters of draine & lee ( 1984 ) show that ordinary astronomical graphite grains emitting 0.1 jy at 7.9 @xmath2 m would have to be hotter than 600 k to emit 0.15 jy at 4.8 @xmath2 m . ordinary astronomical graphite grains re - radiating thermal radiation after being heated by a source with a luminosity of 1.5@xmath1010@xmath25l@xmath12 and 35 pc distant , would come to a temperature @xmath1 245 k. thus , the grains can not be heated purely by the central source unless the emissivities are vastly different from commonly accepted values , or the lumps derive their energy from an entirely different source . kleinmann , gillett & wright ( 1976 ) obtained a spectrum of ngc 1068 from 8 to 13 @xmath2 m with @xmath12% spectral resolution in a 5@xmath0 diameter beam which demonstrated that ngc 1068 has a pronounced absorption feature centered at @xmath19.7 @xmath2 m attributed to silicates . more recent iso - sws spectra by sturm et al . ( 2000 ) have delineated a broad absorption feature extending from @xmath18.6 @xmath2 m to @xmath110.0 @xmath2 m which is centered at 9.4 @xmath2 m rather than 9.7 @xmath2 m , but the spectrum is probably contaminated because of the large iso beam . the wavelength range of the 10.3 @xmath2 m band used in the present observations overlaps about half of this absorption and thus provides a measure of any strong silicate absorption morphology . figure 5 gives the spectral energy distribution at the five locations shown . these locations were chosen to approximate local maxima in the 12.5 @xmath2 m image after the four deconvolved images of figure 1 were smoothed to @xmath10.2@xmath0 fwhm . it should be noted that , because the images at all four wavelengths were smoothed to the lowest resolution , this is a robust result . the figure shows strong absorption on the peak and just to the south . there is a smooth continuum , perhaps even silicate emission , to the north and northeast . the most straight forward explanation is that we are seeing an attenuating screen of silicate which is more concentrated over the central peak of mid - infrared emission than in other regions . the absence of a silicate absorption feature in certain regions of the image could , of course , be due to purely geometrical effects such as the lack of temperature gradients along the line of sight . in order to estimate the brightness temperature of the central peak , the source size was taken as that area which contained pixels in the deconvolved image with a flux density per pixel greater than half the maximum value . for the 12.5 @xmath2 m image , that with the best resolution , the size of this area was @xmath10.4 pc ( 0.006 @xmath0 ) and the resulting brightness temperature was 193 k. brightness temperatures for the other wavelengths , similarly defined , ranged from from 118 k at 24.5 @xmath2 m , with a source size @xmath12.7 pc , to 205 k at 7.9 @xmath2 m , with a source size @xmath11.8 pc . a 12.5 to 24.5 @xmath2 m color temperature was calculated from the deconvolved images at these wavelengths after first smoothing the data to a common fwhm of 0.2@xmath0 . only flux densities per pixel larger than three times the estimated noise per pixel , i.e. 0.03@xmath10[maximum flux density / pixel ] at 12.5 @xmath2 m and 0.12@xmath10[maximum flux density / pixel ] at 24.5 @xmath2 m were used . the resultant color temperatures , shown in figure 6 , are quite sensitive to the alignment of the two images , but in the central portion are @xmath1265 k. the color temperature is highest in the central peak at 269 k and , significantly , there is no smooth dropping of the temperature along the extended north - south emission . in fact , the color temperature north of the central peak falls to @xmath1 216 k @xmath10.25@xmath0 ( 20 pc ) north of the peak and then rises again to @xmath1263 k @xmath10.4@xmath0 ( 30 pc ) north of the peak . calculations using the averaged emissivity parameters of draine & lee ( 1984 ) indicate that an optically thin cloud of pure silicate grains in thermal equilibrium with a central source of 1.5@xmath1010@xmath25l@xmath12 would have 12.5 to 24.5 @xmath2 m color temperatures of 270 k and 220 k at distances of 20 and 30 pc . if graphite grains were assumed , the color temperatures the same distances from the source would be 320 k and 270 k. the physical temperatures are predicted to be about 10 to 20 k cooler . thus the measured color temperatures are in the range as expected for heating by a central source , but do not show a smooth behavior with radial distance expected for a uniform distribution of dust grains in such a situation . an obvious possibility is that the warm emission is from single photon heated small grains . this has , for example , been invoked in the starburst galaxy m82 to explain an increase in the color temperature with distance from the center ( telesco et al . although this possibility can not be excluded , we consider it unlikely since if it were the explanation for the warm emission , it would also be necessary to explain why , in figure 5 , there is no sign of the pah emission which is ubiquitous with single photon heating . of course , beaming of a central source could increase the predicted temperature . an explanation for the results of antonucci & miller ( 1985 ) could invoke beaming of the central source . baldwin , wilson & whittle ( 1987 ) have shown that the intensity of the central source could be as much as 200 times greater along the radio axis than to the earth . if * f * is the `` beaming factor '' by which the luminosity of the central source in the direction of the dust cloud exceeds that towards earth , the resultant temperature would be increased by a factor of * * f**@xmath26 . thus temperatures as high as 500 k could be obtained with beaming factors in the hundreds , although we do not consider such extreme beaming necessary . the most prominent feature of the present observations is the highly asymmetric almost linear nature of the images , the well resolved extent north - south , and the extreme narrowness east - west . a dominant feature of this emission is a relatively constant 12.5 to 24.5 @xmath2 m flux ratio or color temperature . we will designate the narrow lobe to the north of the dashed line in figure 1b as the `` tongue '' . also prominent is a `` core '' , a name we assign to the region south of the dashed line in figure 1b . we acknowledge that the dividing line between the two areas is arbitrary and is partially based on the model described below . the core contains about two - thirds the flux per octave in the mid infrared which we identify with the bolometric luminosity of the central source within an area 4@xmath0 in diameter , while the tongue contains about one - third . the core is aligned so its north - pointing axis points in a direction slightly west of north while the emission in the tongue curves slightly east of north . as a corollary to the feature noted above , we emphasize that the mid - infrared observations , by their small extent , convincingly associate a significant fraction , more than half , of the bolometric luminosity of ngc 1068 with an agn rather than with star bursts . our interpretation of the images is divided into a discussion of the core and a discussion of the tongue . the core region is itself asymmetrical ; the brightness of the emission in the north of the core is significantly greater than that to the south . the emission coming from the core can be understood if there is a very dense torus originating within a parsec or so of the agn . granato et al . ( 1997 ) have proposed a simple model consisting of a torus extending from @xmath10.2 pc to tens of pc . ( note , however , that this assumes that the torus has uniform density whereas the hcn observations of e.g. tacconi et al . ( 1994 ) suggest that the gas observed at @xmath1100pc is quite inhomogeneous . ) the asymmetric structure of the core image is a natural consequence of the inclination of the plane of the torus to the line of sight . we are seeing emission from the heated inside edge to the north , while the heated southern side is partly obscured by the torus itself . granato et al . invoke an observation angle of 65@xmath3 and predict an asymmetry of @xmath114:1 intensity ratio between the flux in a 0.2@xmath0 diameter beam at the peak of the core and one in the lobe to the south . the observations yield a ratio of @xmath110:1 for the flux density within a 0.2@xmath0 diameter beam at the core and at the lobe to the south ( positions b and a in figure 5 ) . the predictions of granato et al . give a separation of 0.3@xmath0 between the core peak and the southern lobe , in good agreement with the measured separation of 0.4@xmath0 . although the observations and models for the core region are in excellent agreement in some aspects , in others they differ . the models are clearly not attuned to the small scale structure observed . the east - west width of the radiation pattern in the model of granato et al . ( 1997 ) is significantly larger than observed . the modeled 10 @xmath2 m surface brightness has an east - west fwhm @xmath10.15@xmath0 while the deconvolved 12.5 @xmath2 m observations are barely , if at all , resolved east - west with an east - west fwhm @xmath270.05@xmath0 . the modeled 10 @xmath2 m surface brightness drops to 10% at a full width of 0.4@xmath0 , while in the deconvolved 12.5 @xmath2 m image the measured full width at 10% is closer to 0.1@xmath0 . the model clearly requires significantly deeper silicate absorption in the spectral energy distribution of the southern component compared to that of the northern source in the core . figure 5 shows silicate absorption at both the southern locations ( positions a and b ) , but whether the extreme southern source displays the increased absorption required to attenuate the signal from the near side of the torus is uncertain , depending on the continuum temperature at the two locations . the high aspect ratio of the mid - infrared images , and whether the southern lobe we identify as part of the core is indeed associated with a torus remain challenges for torus models to address . the tongue is a powerful mid - infrared component in ngc 1068 associated with the western boundary of both the [ oiii ] emission and the radio continuum emission ( evans et al . 1991 ; macchetto et al . 1994 ; gallimore et al . 1996c ) . on spectral grounds we identify this with re - emission by dust of visual and ultraviolet radiation concentrated in an ionization cone which most likely originates in the nucleus of ngc 1068 . at this stage we note and comment upon three explanations for the formation of the ionization cone in ngc 1068 . relativistic beaming : : the ultraviolet continuum could be produced nonthermally by a pair of relativistic jets and beamed along the jet direction through relativistic aberration . there is no evidence , however , that the jets associated with seyfert galaxies , in contrast to those associated with spiral galaxies , are relativistic and we consider that this explanation is unlikely . dust absorption : : the ultraviolet continuum may be produced in a roughly isotropic source , like an accretion disk , and cool dusty gas at low latitudes the torus then remove most of it only permitting escape along the two polar directions . as the solid angle subtended by the ionization cone is @xmath10.1 of the sky , we would expect the power radiated by the torus to be at least ten times that associated with the ionization cone . we have already shown , however , that the power re - radiated at mid - infrared wavelengths from the northern ionization cone is one third that from the core , and this is a lower bound on the luminosity flowing along the ionization cone . as the core luminosity is dominated by the mid - infrared power reported here , we conclude that the core is under - luminous by at least an order of magnitude for dust absorption to account for the formation of the cones . ( see storchi - bergmann , mulchaey , & wilson ( 1992 ) for a related argument . ) electron scattering : : free electrons have a very high albedo at ultraviolet wavelengths , and a hot , ionized torus , probably orbiting inside a cool dusty torus will scatter most of the radiation from an isotropic ultraviolet source into the polar directions . this is our favored explanation for the ionization cone . ( see miller , goodrich & matthews , 1991 . ) note that the x - ray observations also suggest the presence of a hot torus . the above picture is strengthened by the observations of capetti et al . ( 1995 ) who measured wavelength - dependent , polarized visual and near ultraviolet continuum emission from the ionization cone which appears to be concentrated at the edges of the radio emission ( capetti et al . 1997 ) , just as in the mid - infrared observations reported here . this suggests that we are under - estimating the luminosity of the ionization cone . in view of the energetic considerations given above , it is appropriate to compare the potential luminosities with the eddington luminosity of ngc 1068 . the eddington luminosity is based on the observations of gallimore et al . ( 1996b ) and greenhill et al . ( 1996 ) who used water maser emission lines to estimate the mass of the black hole in ngc 1068 . unfortunately , the estimates of the two groups differ by a factor of three . gallimore et al.s measurements result in an eddington luminosity of 1@xmath1010@xmath9l@xmath12 while those of greenhill et al . give 3@xmath1010@xmath25l@xmath12 . both these luminosities are less than the putative isotropic bolometric luminosity of @xmath2225@xmath1010@xmath25l@xmath12 derived above , but we can strongly discount this value only if we accept greenhill et al.s value of the black hole mass . it should be noted that either value of the eddington luminosity is only somewhat larger than the total mid - infrared luminosity suggesting that the accretion onto the black hole is almost eddington - limited and that any gas within the ionization cone will be accelerated outward by radiation pressure as the flux there must exceed the eddington flux . the radiation pressure should also sweep the ionization cone clean of dust , although there is evidence ( miller et al . 1991 ) that the grains are continuously being replenished . the time scale for such clearing would be quite short so an evacuated cone with dust at the edges might result . thus , with the exception of the dust in a hypothesized central torus , the mid - infrared emitting dust would be distributed in a thin shell around the surface of the ionization cone , and thereby appear as linear features since the line - of - sight path length is maximized at the edges of the shell . the observations would most likely imply a very patchy shell . this would obviate the need to invoke any beaming of the ultraviolet radiation which heats the dust , other than the relatively broad ionization cone . although the morphological resemblance of the radio and mid - infrared emitting regions might suggest the radio jet being the heating source of the dust in the tongue , we argue that this is unlikely based on the energetics . observation shows that the plasma responsible for the scattering of the agn light is moving outward from the nucleus at a velocity of 3001200 km / s ( miller et al . if we take this plasma velocity as the shock speed , mid - infrared emission can be produced by shocks in this flow through two dust - heating mechanisms : direct collisions between the plasma and dust particles ( draine 1981 ) and absorption of ultraviolet radiation produced by the post - shock cooling plasma ( cf . dopita & sutherland 1996 ) . however , unless the efficiency of converting the shock energy into infrared emission is extremely high , we can not avoid the conclusion that this shock carries a mechanical luminosity comparable to the eddington limit , which seems unlikely . there is no evidence that jets in seyfert galaxies are this luminous . furthermore , regardless of which mechanism dominates the dust heating , such a fast shock is bound to produce a substantial ultraviolet radiation . therefore , the absence of strong ultraviolet sources near the mid - infrared emitting region ( recall that the ultraviolet radiation in the nuclear region is mostly scattered agn light ) also argues against the shock heating by the radio jet unless the ultraviolet radiation is perfectly shielded by dust . our picture , then , is of a thick , radiation - dominated accretion disk close to the central black hole that emits an ultraviolet power somewhat larger than the total mid - infrared luminosity which , primarily through electron scattering , with perhaps some dust absorption , is collimated into a pair of roughly anti - parallel cones . it is likely that these cones are not just framed by a single accretion torus but are defined successively on many scales from the radius of the black hole to the radius of the narrow line region . indeed , the partial occultation of the ionization cone by the dense , dusty gas that we are observing may be just a final stage in this process . why is the mid - infrared emission only found mainly on one side of the ionization cone and the radio jet ? we suspect that this is because the gas flow on all scales may be quite irregular and the beam of the ionizing radiation is far from axisymmetric . precession of the central accretion disk may also contribute to this outcome . this can also account for the otherwise surprising observation that the color temperature actually increases along the tongue . suppose that the intensity in the northern ionization cone is quite non - uniform due to the irregular scattering and absorption associated with its formation . the hotter dust observed near the end of the tongue might then be associated with an unusually intense pencil impacting a dense and dusty cloud , where the radiation flux is larger than the radiation flux that heats dust closer to the core despite the inverse square law dilution . in this way , we believe that we can account qualitatively for the observed morphology from radio to ultraviolet wavelengths . if the interpretation presented above survives further scrutiny , it suggests an explanation as to why seyfert galaxies ( and most quasars ) are radio - quiet ( not silent ) . specifically the radiation drag close to the black hole and within the ionization cone may prevent the outflow from attaining ultra - relativistic speed . future observations of other nearby seyfert galaxies will be necessary to see if total luminosities are as large as found for ngc 1068 . in order to substantiate this picture it would be useful to show that the agn has sufficient x - ray , ultraviolet , and visual luminosity to provide for the observed mid - infrared luminosity . observations of visual polarization , like those of capetti et al ( 1995 ) , should be able to give this since it is presumably due to dust scattering . if we assume that the grains are similar to galactic grains , their blue polarized flux should correlate with the mid - infrared flux . we can use the albedo and polarization expected from dust scattering to estimate the luminosity absorbed . this should give a lower limit on the luminosity in the ionization cone .. the luminosities measured in the present images are , as noted , close to the eddington luminosity for ngc 1068 . if the tight correlation between the bulge velocity dispersion and black hole mass ( ferrarese & merritt 2000 ; gebhardt et al . 2000 ) is substantiated , black hole masses may be inferred in other galaxies from velocity dispersion measurements . by comparing the corresponding eddington luminosity with the agn luminosity derived from infrared observations similar to those presented here , we will be able to determine which agn are accreting at the eddington rate . this should enhance our understanding of how black holes are fueled in galactic nuclei . finally , a consequence of the picture presented above is that a significant fraction of the luminosity of ngc 1068 is not associated with a torus _ per se _ , but is produced by re - processing radiation with dusty gas located @xmath140 pc away from the central source whose characteristics may be unique to ngc 1068 . this complexity makes any interpretation of agns invoking a common morphology more difficult .

the source is strongly asymmetric , extending significantly further to the north than to the south . the morphology of the mid - infrared emission appears similar to that of the radio jet , and has features which correlate with the images in [ oiii ] . there are , however , detailed difficulties with existing models , especially the narrow east - west width of the thin extended mid - infrared `` tongue '' to the north of the core .

mid - infrared observations of the central source of ngc 1068 have been obtained with a spatial resolution in the deconvolved image of 0.1 ( pc ) . the central source is extended by in the north - south direction but appears unresolved in the east - west direction over most of its length . about two - thirds of its flux can be ascribed to a core structure which is itself elongated north - south and does not show a distinct unresolved compact source . the source is strongly asymmetric , extending significantly further to the north than to the south . the morphology of the mid - infrared emission appears similar to that of the radio jet , and has features which correlate with the images in [ oiii ] . its 12.524.5 m color temperature ranges from 215 to 260k and does not decrease smoothly with distance from the core . silicate absorption is strongest in the core and to the south and is small in the north . the core , apparently containing two - thirds of the bolometric luminosity of the inner 4 diameter area , may be explained by a thick , dusty torus near the central agn viewed at an angle of to its plane . there are , however , detailed difficulties with existing models , especially the narrow east - west width of the thin extended mid - infrared `` tongue '' to the north of the core . we interpret the tongue as re - processed visual and ultraviolet radiation that is strongly beamed and that originates in the agn .

astro-ph0009078

i

\1 ) mid - infrared observations of ngc 1068 at the diffraction limit of the keck 10-m telescope show a bright core containing about 1/3 the total flux accompanied by north - south emission about 70 pc long which is unresolved in the east west direction . thus most of the emission from the nuclear region of ngc 1068 comes from the elongated , highly asymmetric north - south structure . \2 ) at wavelengths between 7.9 and 24.5 @xmath2 m , essentially all the nuclear flux of ngc 1068 , as distinct from that in the 3 kpc ring , is contained within a diameter of 300 pc of the central core . \3 ) the 12.5 to 24.5 @xmath2 m color temperature of the radiation is @xmath1270 k and does not decrease smoothly with distance from the core , but has a secondary maximum close to 270 k after dropping to @xmath1215 k. \4 ) the absorption by silicates is lumpy even within the central region of ngc 1068 . there is evidence for increased silicate absorption over the central core and to the south ; there is less silicate extinction to the knots of emission to the north . \5 ) the low level mid - infrared emission , when located using the scattering center determined by kishmoto ( 1999 ) , lies near one wall of the conical region depicted in [ oiii ] ( evans et al . 1991 ; macchetto et al . 1994 ) , and features in the near - infrared emission correlate with clumps in the [ oiii ] emission . the mid - infrared emission mimics the radio jet observed by gallimore et al . ( 1996a ) . \6 ) no evidence for the putative outer torus present at 3.5 and 4.8 @xmath2 m ( marco & alloin 2000 ) is seen in these mid - infrared images . two thirds of the mid - infrared emission the core is interpreted as being the result of re - radiation of the agn luminosity by a dusty torus viewed at an angle so we see one heated face almost directly while the other face is obscured . most of the ultraviolet power of the nucleus appears to be redirected into the ionization cone by electron scattering.there are , however , significant details which need to be addressed before this picture can be accepted . the remaining third of the mid - infrared emission in ngc 1068 the tongue is associated with the western boundary of both the [ oiii ] emission and the radio continuum emission . we identify this with re - emission by dust of visual and ultraviolet radiation which originates in the core of ngc 1068 and is strongly beamed along the ionization cone . the ability to perform ground - based imaging photometry of active galaxies in the mid infrared is opening up several scientific opportunities . the most immediate is that observations such as these will greatly improve our estimates of the cosmological luminosity density of accreting black holes . x - ray observations have demonstrated that there is a large population of heavily obscured agn . x - ray observations however , are not able to measure the absorbed power with any precision , and for this , infrared observations are crucial . we suspect that most re - radiation by dust in obscured agn emerges in the mid infrared . by contrast , most emission from star forming regions may occur at longer wavelengths . in order to test this hypothesis , it will be necessary to perform additional , high resolution observations in the mid infrared of active galaxies , like those described here . if the hypothesis is confirmed , then sirtf will be able to measure the re - radiation in a much larger sample and provide the first accurate measurement of the luminosity density of active galaxies . we thank the staff of the keck observatory , especially bob goodrich , for their assistance in making these observations possible . we also thank pat shopbell for discussions about the x - ray observations of ngc 1068 and lee armus , bob goodrich , nick scoville , kris sellgren , and dave thompson for discussions about various aspects of the interpretation . we thank ski antonnucci and makoto kisimoto for their helpful comments as referees . the w. m. keck observatory is operated as a scientific partnership between the california institute of technology , the university of california and the national aeronautics and space administration . it was made possible by the generous financial support of the w. m. keck foundation . b.t.s . , k.m . and e.e . are supported by grants from the nsf and nasa . is supported by the sirtf science center at caltech . sirtf is carried out at j.p.l . , operated by caltech under an agreement with nasa . this work was carried out in part ( j.j.b.,m.w.w . and m.e.r . ) at j.p.l . the development of mirlin was supported by nasa s office of space science .

its 12.524.5 m color temperature ranges from 215 to 260k and does not decrease smoothly with distance from the core . silicate absorption is strongest in the core and to the south and is small in the north . the core , apparently containing two - thirds of the bolometric luminosity of the inner 4 diameter area , may be explained by a thick , dusty torus near the central agn viewed at an angle of to its plane . we interpret the tongue as re - processed visual and ultraviolet radiation that is strongly beamed and that originates in the agn .

mid - infrared observations of the central source of ngc 1068 have been obtained with a spatial resolution in the deconvolved image of 0.1 ( pc ) . the central source is extended by in the north - south direction but appears unresolved in the east - west direction over most of its length . about two - thirds of its flux can be ascribed to a core structure which is itself elongated north - south and does not show a distinct unresolved compact source . the source is strongly asymmetric , extending significantly further to the north than to the south . the morphology of the mid - infrared emission appears similar to that of the radio jet , and has features which correlate with the images in [ oiii ] . its 12.524.5 m color temperature ranges from 215 to 260k and does not decrease smoothly with distance from the core . silicate absorption is strongest in the core and to the south and is small in the north . the core , apparently containing two - thirds of the bolometric luminosity of the inner 4 diameter area , may be explained by a thick , dusty torus near the central agn viewed at an angle of to its plane . there are , however , detailed difficulties with existing models , especially the narrow east - west width of the thin extended mid - infrared `` tongue '' to the north of the core . we interpret the tongue as re - processed visual and ultraviolet radiation that is strongly beamed and that originates in the agn .

astro-ph9903158

i

most attempts at modeling the emission from accreting black hole systems typically assume that the particle energy distribution responsible for the emission is either purely `` thermal '' ( i.e. , a maxwellian ) or purely `` non - thermal '' ( i.e. , a power law ) . this is partly due to the desire for convenience and simplicity , and partly due to our continued ignorance as to when and how non - thermal particles exchange energy and thermalize with neighboring particles . despite our ignorance , however , the reality is that nature probably never makes particle distributions that are strictly of one type or the other . as a concrete example which may be very relevant to the process of black hole accretion , consider solar flares . ( many analogies have been made between magnetic reconnection and flare events in the solar corona , and those that might occur in accretion disk coronae , e.g. , galeev , rosner , & vaiana 1979 . ) the watch instrument on the granat satellite has recently collected a large sample of flare events observed at energies above @xmath0 kev ( crosby et al . 1998 ) . many of those observations were made in coincidence with the goes satellite which measures solar flare at lower @xmath1 kev . while the goes observations usually can be adequately interpreted in terms of purely thermal emission , in many instances watch sees a significant high - energy excess over the emission predicted from the goes spectral model . in other words , many solar flare events are produced by particle distributions with not only a strong thermal component , but also a significant non - thermal tail : the emitting plasma is a `` hybrid '' thermal / non - thermal plasma . if the solar corona - accretion disk corona analogy is correct , then something similar may well occur near black holes and could have important consequences for black hole emission models . the goals of this contribution are to review the arguments for and against the existence of similar particle distributions in the context of accreting black hole systems , to see what the practical consequences of having a hybrid plasma might be , and then finally to ask whether we have any concrete concrete evidence that such plasmas play a role in the observed emission . in 2 below , i examine the theoretical arguments for and against having a purely thermal electron distribution in a black hole accretion disk corona . in 3 , i examine some of the consequences of having a hybrid plasma and present model spectra calculated assuming varying amounts of thermal heating and non - thermal acceleration power are supplied to the plasma . in 4 , i argue that we may already have strong evidence for hybrid plasmas in the spectra of galactic black hole candidates , especially in spectra obtained during their soft state . i show how a simple phenomenological model based on a hybrid plasma can explain the spectra of cyg x-1 in its soft , hard , and transitional states in terms of one basic parameter , a critical radius outside of which the accretion disk is a cold sunyaev - shakura ( 1973 ) disk , and inside of which the disk is a hot , adaf - like ( narayan & yi 1995 ) corona . i summarize my conclusions concerning the importance and relevance of hybrid plasmas in 5 .

here , i review the arguments for `` thermal '' versus `` non - thermal '' plasmas in accreting black hole systems and discuss the physics and emission properties of `` hybrid '' plasmas , where the particle distribution energy is approximately a maxwellian plus a power law tail . using results from a new emission code , i then show that such plasmas may be relevant to explaining recent observations , particularly those of galactic black hole candidates in their soft state .

models of the continuum radiation from accreting hot plasmas typically assume that the plasma heating mechanism produces energetic particles distributed in energy either as a maxwellian ( the `` thermal '' models ) or as an extended power law ( the `` non - thermal '' models ) . the reality , however , is that neither description is probably accurate . in other astrophysical contexts where we have been able to observe the actual particle energy distributions , e.g. solar system plasmas , and in many particle acceleration theories , the heating mechanism supplies only some fraction of the available energy to very energetic particles . the remainder goes into producing lower energy particles which settle into a quasi - maxwellian energy distribution . here , i review the arguments for `` thermal '' versus `` non - thermal '' plasmas in accreting black hole systems and discuss the physics and emission properties of `` hybrid '' plasmas , where the particle distribution energy is approximately a maxwellian plus a power law tail . using results from a new emission code , i then show that such plasmas may be relevant to explaining recent observations , particularly those of galactic black hole candidates in their soft state . = = = 1=1=0pt = 2=2=0pt = 2=2=0pt

astro-ph9903158

i

most attempts at modeling the emission from accreting black hole systems have typically assumed the underlying particle energy distribution is either a maxwellian ( `` thermal '' ) or a power law ( `` non - thermal '' ) . while such an assumption may be convenient analytically , it is no longer required given the advent of powerful computers , and more importantly , it is does not appear to be well - justified . there are several examples in nature , e.g. , the phenomenon of solar flares , where it is clear the underlying distribution is neither a maxwellian nor a power law , but rather a quasi - maxwellian at low energies with a high - energy approximately power - law tail . this is exactly the type of particle energy distribution that is often predicted by theoretical particle heating / acceleration models . ( the acceleration process typically kicks only a few particles in the high energy tail of the particle distribution to much higher energies . ) re - examining the process of electron thermalization under the physical conditions likely to be found near a black hole , we find that the likely thermalization time scales are likely to be quite long unless some ( unknown ) collective plasma process is more effective than two - body coulomb collisions at exchanging energy between electrons . in particular , because the radiation field is likely to be so intense near an accreting black hole , the coulomb relaxation time for even moderately relativistic electrons may be much longer than the relevant cooling times . depending on the exact plasma parameters , they may also be longer than the characteristic source variability time . thus , the old arguments made against thermal models still stand . these arguments were largely brushed aside and forgotten when it became clear many of the classical non - thermal sources like ngc 4151 ( an agn that was supposed to have strong mev emission ) in fact showed strong cutoffs at @xmath171 kev energies and had spectra that could be successfully fit using purely thermal comptonization models . now that we are seeing hints that the emission in galactic black holes candidates may indeed extend to much higher energies ( albeit at much lower levels than previously thought ) , `` hybrid '' models involving both thermal particle heating and non - thermal particle acceleration are beginning to creep back . one of the strongest cases for the existence of a non - thermal particle distribution near black holes is the soft spectral state of galactic black hole candidates . in this state , one sees very strong , quasi - blackbody emission at @xmath1 1 kev , with a steep @xmath1 power law tail extending to at least @xmath1 511 ( @xmath7 ) in several objects . particularly in the case of cyg x-1 , such emission is very hard to explain either via pure thermal comptonization or bulk comptonization in the accretion flow . this has not been completely appreciated . data from future missions with improved sensitivity in the @xmath87 kev - @xmath172 mev range ( e.g. , integral and astro - e ) should be conclusive . if we relax the assumption that the energy distribution of the comptonizing electrons is a strict maxwellian , then many problems go away . using a newly developed , self - consistent hybrid plasma code , we show that the spectrum in the soft state ( as well as in the other spectral states ) can easily be modeled . with the proviso that there is always some small amount of non - thermal acceleration going on ( compared to the total source luminosity ) , models that explain the cyg x-1 state transitions in terms of a moving transition radius between cold and hot disk phases appear to work fairly well . ( as cui points out in these proceedings , however , these models only attempt to explain _ time - averaged _ spectra . what such a spectrum and the deductions one makes from such a spectrum have to do with reality is not yet clear , particularly if this time - averaged emission is the superposition of many individual flare events , e.g. , as discussed here by poutanen & fabian as well as mineshige & negoro . if we follow theoretical prejudice and assume that particle energy distributions are indeed not completely thermal , then we must explain why so many black hole sources still manage to look so thermal . clearly , one part of the answer must be that the efficiency with which power is channeled into relativistic electrons ( lorentz factors @xmath142 ) is relatively low . why this is so , depends on the unknown details of the acceleration mechanism . another part of the answer , however , may have to do with comptonization and pair plasma physics . if a source photon gains most of its energy in a single scattering event before escaping , then clearly the emergent radiation spectrum depends critically on the underlying scattering electron energy spectrum . however , if multiple compton scattering is important , i.e. , a photon gains its energy in several small steps before it escapes , then the exact details of the energy distribution turn out not to matter . to first order , if the scattering electrons have the same mean energy , be they thermal or non - thermal , then they tend to produce the same mean energy change in a scattered photon , which results in a spectrum with the same shape . ( one can imagine doing a fokker - planck expansion of the relevant equations . ) the details of the distribution typically only matter at the high - energy and low - energy tails of the output spectrum . the types of sources where multiple compton is most important are those that are relatively photon - starved , i.e. , where the power supplied to electrons is much larger than the power initially supplied to the low energy target photons . in this case , as long as the bulk of the heated / accelerated electrons do not have lorentz factors @xmath173 it is largely irrelevant whether the electrons thermalize or not before they cool . ( note that if the source is very optically thick to gamma - ray pair production , and many generations of pair cascading are important , then the condition that most electrons have low lorentz factors is automatically guaranteed even if the accelerated electrons which initiate the cascading have high initial energies . ) to model cyg x-1 completely , for example , we may need a non - thermal power law source of energetic electrons . to match the data , however , the non - thermal acceleration must also produce a very steep power law in energy , i.e. , most of the power resides in the lowest energy electrons . if we add such a particle distribution to , say , a hot background thermal plasma distribution , and then make the source photon starved , we will see virtually no difference in the final spectrum , except perhaps at the highest energies @xmath174 kev . ( for connoisseurs of pair plasmas , though , note that differences in the high energy photon spectrum can mean big differences in the pair balance and the pair thermostat . ) it is probably no accident , then , that the photon - starved hard state of galactic black holes looks so thermal , while the photon - rich soft state does not . in sum , whether we realize it or not , hybrid plasmas may be all around us !

models of the continuum radiation from accreting hot plasmas typically assume that the plasma heating mechanism produces energetic particles distributed in energy either as a maxwellian ( the `` thermal '' models ) or as an extended power law ( the `` non - thermal '' models ) . the reality , however , is that neither description is probably accurate . in other astrophysical contexts where we have been able to observe the actual particle energy distributions , e.g. solar system plasmas , and in many particle acceleration theories ,

models of the continuum radiation from accreting hot plasmas typically assume that the plasma heating mechanism produces energetic particles distributed in energy either as a maxwellian ( the `` thermal '' models ) or as an extended power law ( the `` non - thermal '' models ) . the reality , however , is that neither description is probably accurate . in other astrophysical contexts where we have been able to observe the actual particle energy distributions , e.g. solar system plasmas , and in many particle acceleration theories , the heating mechanism supplies only some fraction of the available energy to very energetic particles . the remainder goes into producing lower energy particles which settle into a quasi - maxwellian energy distribution . here , i review the arguments for `` thermal '' versus `` non - thermal '' plasmas in accreting black hole systems and discuss the physics and emission properties of `` hybrid '' plasmas , where the particle distribution energy is approximately a maxwellian plus a power law tail . using results from a new emission code , i then show that such plasmas may be relevant to explaining recent observations , particularly those of galactic black hole candidates in their soft state . = = = 1=1=0pt = 2=2=0pt = 2=2=0pt

hep-ph0608140

i

theoretical models constructed to understand physics beyond the standard model ( sm ) ( most notably string theory ) frequently imply the existence of extra dimensions . it has been a particular challenge in phenomenology to understand how these extra dimensions would be realized and manifested in our observable @xmath2 dimensional world . the number , shape and size of these dimensions , as well as the particles allowed to propagate in them give rise to several different models , all having different phenomenological implications . we will be considering universal extra dimensions ( ued ) where the sm fields propagate in all the extra dimensions . for toroidal compactification , this would imply a tower of kaluza - klein ( kk ) particles for every sm particle , each carrying kk number . momentum conservation in the extra dimensions implies kk number conservation . however , the requirement of obtaining the proper sm chiral modes at low energies leads to constraints on the possible compactification geometries . an example for @xmath3 is the orbifold @xmath4 where the @xmath5 projects out half of the zero modes , leaving only sm fields . additionally , this breaks translation invariance along the extra dimensions , so kk number is no longer conserved . a residual symmetry , kk - parity , is still present and it is sufficient to ensure the stability of the lightest kk particle ( lkp ) . it also ensures that kk particles are always produced in pairs , allowing for good agreement between theory and experiment for small values of the compactification scale , of the order of a few hundred gev @xcite . the stability of the lkp allows for an interesting candidate for dark matter ( dm ) @xcite . the lkp is expected to be weakly interacting and electrically neutral if it is to be considered a candidate for dark matter . the usual candidate is @xmath6 , the kk partner of the hypercharge gauge boson . for @xmath7 tev , @xmath6 gives excellent agreement with the observed relic density . there have been many further analyses of the relic density in ued , including a more proper treatment of coannihilation effects , and the impact of the inclusion of second kk level resonances @xcite . however , most of these studies ignore the gravitational sector . we shall mostly work within the context of one extra dimension . the gravitons couple extremely weakly and therefore are generally considered to be unimportant for collider studies . cosmologically , however , they can have a significant effect , and they can also be a candidate for the lkp @xcite . we are interested in investigating the inclusion of the graviton tower in the scenario with @xmath6 as the lkp . the gravitons do not evolve thermally , and have very long lifetimes , so if they are present , we expect them to decay to the lkp sometime after big bang nucleosynthesis ( bbn ) . the preservation of the light element abundances sets a bound on the amount of energy that can be released in a decay @xcite . secondly , since the gravitons decay ultimately into the lkp , we expect the relic density to increase . therefore , the mass of the lkp consistent with the observed relic density is lowered . additionally , if any of the gravitons decay after matter domination , we have to consider the effects of non - thermalized photons released in the decays on the spectrum of the diffuse photon flux ( dpf ) @xcite . this article is organized as follows . in section 2 , we review the standard calculation for relic density . section 3 reiterates the calculation for the density of gravitons presented in ref . @xcite , emphasizing the points relevant for our analysis . in section 4 , we analyze the lifetimes for the decay of the graviton tower and study its implication on the diffuse photon spectrum . section 5 goes over the constraints on the energy released in the decay of the kk gravitons to the lkp . in section 6 , we combine the above results with the standard relic density calculation . our goal is to analyze the effect of the gravitons on the predicted mass of the lkp consistent with the known dark matter density . we will show that , in fact , almost any value of @xmath8 lower than the one obtained in the absence of gravitons would be allowed , provided the reheating temperature , @xmath9 , is large enough . for the calculation of the relic density of @xmath6 , we ignore complicating factors such as coannihilation and second kk level resonance effects @xcite . since these effects can be parameterized in the effective cross - section , we present the effect the graviton tower will have on the mass of the lkp without the gravitons , @xmath10 , and note that as @xmath11 increases , the contribution due to the graviton tower becomes large , and should be included in any precise calculation of @xmath8 . we also find that all the gravitons , except for @xmath0 , decay right after bbn . at these early times , the electromagnetic bbn constraints are very weak . however it has been shown that at small lifetimes , the hadronic constraints are very stringent @xcite . therefore , including constraints from both hadronic and electromagnetic decays , requiring consistency with bbn light element predictions , we find a stringent limit on the mass difference between @xmath12 and the lkp mass , @xmath13 . since the @xmath0 is long - lived , we also derive another constraint on the mass difference such that the observed spectrum of the dpf is not destroyed . comparing the two constraints , we find that there exists a region of parameter space where both constraints are satisfied and which gives mass differences of the same order of magnitude as that obtained by radiative loop corrections to @xmath14 @xcite . additionally , we observe that if experimental evidence for ued is found , and the relic density induced by standard interactions of the kk modes is found to be lower than the one observed experimentally , the reheating temperature may be determined by assuming that the graviton kk modes provide the contribution necessary to achieve consistency between theory and experiment . alternatively , including the possibility of other unobserved exotic particles contributing to the relic density , an upper bound on the reheating temperature is obtained .

models of universal extra dimensions ( ued ) at the tev scale lead to the presence of kaluza klein ( kk ) excitations of the ordinary fermions and bosons of the standard model that may be observed at hadron and lepton colliders . a conserved discrete symmetry , kk - parity , ensures the stability of the lightest kk particle ( lkp ) , which , if neutral , becomes a good dark matter particle .

models of universal extra dimensions ( ued ) at the tev scale lead to the presence of kaluza klein ( kk ) excitations of the ordinary fermions and bosons of the standard model that may be observed at hadron and lepton colliders . a conserved discrete symmetry , kk - parity , ensures the stability of the lightest kk particle ( lkp ) , which , if neutral , becomes a good dark matter particle . it has been recently shown that for a certain range of masses of the lkp a relic density consistent with the experimentally observed one may be obtained . these works , however , ignore the impact of kk graviton production at early times . whether the is the lkp or not , the tower thus produced can decay to the lkp , and depending on the reheating temperature , may lead to a modification of the relic density . in this article , we show that this effect may lead to a relevant modification of the range of kk masses consistent with the observed relic density . additionally , if evidence for ued is observed experimentally , we find a stringent upper limit on the reheating temperature depending on the mass of the lkp observed .

1602.00656

i

bulk iron selenide ( fese ) is an unconventional superconductor with a relatively modest transition temperature @xmath4 k at ambient pressures @xcite ; however , its @xmath5 can be increased by upwards of a factor of ten when a monolayer of fese is deposited on srtio@xmath6 ( sto ) @xcite or batio@xmath6 ( bto ) substrates @xcite . this discovery has attracted considerable scientific interest @xcite as it provides not only a new route to high - temperature ( high-@xmath5 ) superconductivity but also a new lens through which unconventional superconductivity can be studied . several proposals have been advanced for the microscopic origin of this enhancement and the most widely discussed scenarios are broadly divided into two categories . the first category involves charge transfer between the substrate and the film , which dopes the monolayer with excess electrons . this may result in modifications of the electronic structure , which in turn enhances an unconventional pairing mechanism @xcite or suppresses competing phases @xcite . in addition to this , the charge transfer shifts the holelike bands centered at @xmath7 below the fermi level @xcite , creating an electronic structure similar to the intercalated fese systems @xcite . this electronic structure challenges the fermi - surface - nesting driven , purely electronic pairing mechanism common to the iron - based superconductors @xcite . the second category of proposals for fese / sto encompasses interface - related effects , where a more direct role is played by the substrate . the main proposals here include the suppression of a competing phase via strain or modifications of the electron - phonon ( @xmath1-@xmath2 ) interaction in the fese layer @xcite , or the introduction of one across the interface @xcite . in this paper we focus on the last scenario , which is motivated by several key experimental observations . the first is that the intercalated fese systems @xcite and fese / sto thin films post - treated with k @xcite or na @xcite adatoms all have maximum @xmath5 values @xmath8 k. this is despite the fact that all of these systems have a similar electronic structure to fese monolayers on sto . this indicates that any common unconventional pairing mechanism in these systems is insufficient to account for the observed high-@xmath9 k in monolayer fese / sto and fese / bto and an additional contribution to pairing is likely needed @xcite . the second ( and more important ) observation is that of replica bands in the electronic structure of superconducting fese / sto @xcite . these are interpreted as shake - off states arise from a coupling between the fese 3@xmath10 electrons and an optical o bond stretching phonon branch in the oxide substrate . the crucial observation here is the size and shape of these replica bands being complete copies of the main electron band shows that the @xmath1-@xmath2 coupling constant must be strongly peaked in the forward scattering direction ( small @xmath11 ) . because of this momentum structure , the cross - interface coupling is strongly intraband in nature and can contribute to pairing in most channels , even those commonly associated with repulsive pairing mechanisms relevant for the iron - based superconductors @xcite . these observations make the cross - interface coupling a likely candidate for the additional pairing needed to produce the observed @xmath5 in fese / sto @xcite . as this is a special issue on _ superconductivity in the two - dimensional ( 2d ) limit _ it is worth stressing that the forward focus of the cross - interface @xmath1-@xmath2 interaction can be understood as a consequence of dimensionality of the fese thin films and the anisotropic dielectric properties of the interface . a more complete discussion of this aspect can be found in ref . @xcite . here , we summarize the main points . the fese films sit a distance @xmath12 above the tio terminated sto substrate @xcite . the motion of the oxygen atoms in the direction perpendicular to the fese film induce a local dipole moment with an effective charge @xmath13 at the surface of the substrate . as a result , the optical o modes create an electric dipole potential on the fese electrons . in the continuum limit , this perturbation will dynamically scatter the fese electrons from states with in - plane momentum @xmath14 to @xmath15 with a matrix element @xmath16 here , @xmath11 is the in - plane momentum transfer , @xmath17 sets the range of the interaction in momentum space , and @xmath18 ( @xmath19 ) is the dielectric constant parallel ( perpendicular ) to the interface . in fese / sto ( and also fese / bto ) one expects @xmath20 @xcite , since the fese film can provide additional metallic screening parallel to the interface . in this limit , @xmath21 is small , resulting in an interaction that is peaked at @xmath22 . previously , some of the present authors showed that a strong forward - focused interaction not only reproduces the replica band structure but also acts as a remarkably effective pairing mediator with a superconducting @xmath23 in the weak coupling limit @xcite . as such , the cross - interface @xmath1-@xmath2 coupling implied by the replica bands can provide a substantial contribution to @xmath5 and this can work in conjunction with an unconventional pairing mechanism . this outlook is supported by recent projector quantum monte carlo results @xcite and multiband bcs results involving the incipient hole bands at the @xmath24-point @xcite . it is therefore important to understand and confirm the exact role played by the cross - interface coupling . motivated by this , we build upon our previous work @xcite and present several aspects of a 2d system of electrons coupled to an optical phonon branch by forward focused interaction . our aim is to draw a more complete picture of the consequences of such interaction and to provide further spectroscopic signatures that can be used to confirm its presence . we note that while our focus is on the fese / sto system , similar forward scattering may occur in other low - dimensional correlated systems @xcite . we hope that our results will provide additional means to confirm or rule out this possibility . the paper is organized as follows . section [ sec : formalism ] provides the details of the model and migdal - eliashberg formalism used throughout the paper . section [ sec : migdal ] discusses the validity of this approach in fese / sto , which has been questioned recently @xcite . our major results are presented in section [ sec : results ] , beginning in section [ sec : akw ] , where we review our prior results for the formation of the replica bands and present new details . in section [ sec : gap ] we then examine the properties of the superconducting state and the anisotropy of the superconducting order parameter . finally , in sections [ sec : dos ] and [ sec : qpi ] we present results for electronic density of states and quasiparticle interference patterns , respectively . finally , section [ sec : conclusions ] provides additional discussion and concluding remarks .

a number of proposals have been advanced for the mechanism of this enhancement . motivated by this , we explore the consequences of such an interaction on the superconducting state and electronic structure of a two - dimensional system using migdal - eliashberg theory . we also discuss the applicability of migdal - eliashberg theory for a situation where the- interaction is peaked at small momentum transfer and in the fese / sto system . = 4 _ keywords _ : superconductivity , forward scattering , eliashberg theory , fese films

mono- and multilayer fese thin films grown on srtio and bitio substrates exhibit a greatly enhanced superconductivity over that found in bulk fese . a number of proposals have been advanced for the mechanism of this enhancement . one possibility is the introduction of a cross - interface electron - phonon (- ) interaction between the fese electrons and oxygen phonons in the substrates that is peaked in the forward scattering ( small direction due to the two - dimensional nature of the interface system . motivated by this , we explore the consequences of such an interaction on the superconducting state and electronic structure of a two - dimensional system using migdal - eliashberg theory . this interaction produces not only deviations from the expectations of conventional phonon - mediated pairing but also replica structures in the spectral function and density of states , as probed by angle - resolved photoemission spectroscopy , scanning tunneling microscopy / spectroscopy , and quasi - particle interference imaging . we also discuss the applicability of migdal - eliashberg theory for a situation where the- interaction is peaked at small momentum transfer and in the fese / sto system . = 4 _ keywords _ : superconductivity , forward scattering , eliashberg theory , fese films

1602.00656

r

we begin by presenting details of the spectral properties of our model , which illustrates the formation of the replica bands . this section will also serve to briefly review some of our results from ref [ fig : akw ] shows @xmath105 for @xmath113 and @xmath114 . results are shown for @xmath106 k @xmath115 k , and the superconducting gap is apparent in the main band crossing @xmath80 . two replica bands are also present , with each offset by approximately @xmath74 and @xmath116 , respectively , from the main band . here , the forward - focused @xmath1-@xmath2 interaction produces replicas that are complete copies of the main band ; each replica terminates at @xmath117 , and has the characteristic back bending associated with the bogliubov quasiparticle dispersion . the results shown in fig . [ fig : akw ] are consistent with arpes data of lee _ et al . _ this points to the @xmath22 nature of the coupling in fese / sto @xcite . if the @xmath1-@xmath2 interaction is broadened ( increasing @xmath21 ) then the replica band is significantly smeared in momentum space , as shown in the lower row of fig . [ fig : akwlmd ] . for @xmath118 the replica nature of the shake - off band is maintained . for @xmath119 , however , the shake - off band is significantly broadened and no longer follows the same curvature of the main band . this confirms that @xmath21 must be small in order to reproduce the experimentally observed clear and complete copies of the main band . the total strength of the interaction can also be extracted from the data by examining the relative spectral weight of the two bands . we define the ratio @xmath120 as the ratio of the maximum intensity in the replica band relative to the main band . the top row of fig . [ fig : akwlmd ] shows the spectral function at @xmath121 for several values of the dimensionless coupling , which allows us to extract this ratio from our data as a function of @xmath63 . the results are summarized in the insets of that figure . a conservative estimate of @xmath122 was obtained from the experimental data in ref . we can compare this to our results , where we find extract @xmath123 for @xmath124 and @xmath125 for @xmath107 . these values confirm that the cross - interface coupling in fese / sto is in the perturbative regime . the interface effects leading to the strong forward scattering peak in the @xmath1-@xmath2 interaction do not require a shallow electron band as realized in fese / sto . it is therefore interesting to examine how this interaction will manifest itself in a system where the main band crosses the phonon energy . in fig . [ fig : bandmin ] we explored such a scenario by adjusting the chemical potential of our model such that the band minimum moves from above the phonon energy ( left side ) to below the phonon energy ( right side ) . results are shown for @xmath124 ( top row ) , @xmath107 ( middle row ) , and @xmath119 ( bottom row ) . in all cases , the replica bands remain located below the main band , however , as the main band begins to cross the phonon energy scale , we see the formation of the traditional kink features commonly seen in the high-@xmath5 cuprates @xcite . interestingly , the kink structure of the main band is also copied completely in the replica band when @xmath21 is sufficiently small . we now exam the superconducting state mediated by the forward - focused @xmath1-@xmath2 interaction . our aim here is not to advocate for a purely phonon mediated pairing interaction in fese / sto at this time . rather , we wish to examine the effects of an @xmath1-@xmath2 interaction with a strong forward scattering peak in order to understand the properties of the superconducting state formed by such an interaction . we will discuss how our results fit into the larger context of the fese / sto discussion in section [ sec : conclusions ] . the superconducting gap function at the @xmath126 matsubara frequency and on the fermi surface @xmath127 is plotted in fig . [ fig : gap](a ) as a function of temperature for several values of @xmath21 . only the maximal value on the fermi surface is plotted here , since the gap function has @xmath128-wave symmetry and is quite isotropic for this set of parameters . here , results are shown for a series of increasing @xmath21 values , while the total coupling is fixed at @xmath108 . for the broadest interaction ( @xmath119 ) we obtain a relatively modest @xmath129 k , which is larger than the @xmath130 k one would estimate from the weak coupling bcs result . as the interaction becomes more focused around @xmath22 , @xmath5 increases rapidly , with @xmath131 k for @xmath124 ( see inset ) . this result demonstrates the high-@xmath5 s that can be produced by a strong forward scattering @xmath1-@xmath2 interaction and are consistent with our prior results @xcite , as well as those obtained from simplified bcs treatments @xcite . we obtain @xmath132 ratios of @xmath133 , @xmath134 , @xmath135 , and @xmath136 for @xmath119 , @xmath137 , @xmath138 , and @xmath139 , respectively , indicating that the deviation from the weak coupling bcs value increases as the interaction becomes increasingly peaked . ( a ) the temperature dependence of the superconducting gap at @xmath117 as a function of temperature for increasingly forward - focused interactions . different symbols indicate different values of @xmath21 used , as indicated by the same legend of ( b ) . ( b ) the gap value at low temperature ( @xmath140 k ) vs. the total coupling strength . the dash - dotted line shows zero temperature gap value expected from the perfect forward scattering . the dashed line mark the value of the @xmath63 used in ( a ) . ] the magnitude of the superconducting gap at @xmath141 k as a function of @xmath63 is plotted in fig . [ fig : gap](b ) for several values of @xmath21 . for a perfect forward scattering ( @xmath142 ) in the weak coupling limit , the analytic expression of the zero temperature gap on the fermi surface is @xmath143 while @xmath144 @xcite . for a strong forward scattering @xmath124 we see a linear dependence on @xmath63 at weak coupling , in agreement with the result @xmath23 for the same limit . as the value of @xmath21 is increased , however , there is a crossover to a more exponential - like dependence on @xmath63 , which reflects the change from a @xmath145 behavior in the strong forward scattering limit to a @xmath146 behavior for a more uniform interaction . ( a ) the momentum dependence of the superconducting gap function at the first matsubara frequency . the results are plotted along the high symmetry directions @xmath147 @xmath148 ( left ) and @xmath147 @xmath149 ( right ) . ( b ) the spectral function obtained for @xmath124 at @xmath150 ( solid black ) and @xmath151 k ( dashed red ) . results are shown for @xmath152 , @xmath153 , and @xmath154 when read from the bottom to the top of panel ( b ) . ] another interesting aspect is the momentum structure of @xmath155 , which is shown in fig . [ fig : deltak ] . for small @xmath21 the superconducting gap has maximum values on the fermi surface but it is rapidly suppressed for @xmath14 away from @xmath117 . this is in contrast to the case of a momentum independent interaction , where @xmath156 is independent of momentum . as @xmath21 increases ( with @xmath63 fixed ) , the total magnitude of the gap decreases and broadens in momentum space ; however , the maximum remains on the fermi surface . this behavior can be easily understood in the limit of perfect forward scattering , where the vertex reduces to @xmath157 with @xmath158 @xcite . in the weak coupling limit ( @xmath159 , @xmath160 , @xmath161 ) , the gap equation then reduces to @xmath162 this modified gap equation shows that @xmath156 depends most sensitively on the electronic structure at @xmath14 in the limit of strong forward scattering . hence the value of the gap at @xmath163 has decoupled from the values at the other momenta . as discussed in our previous work @xcite , this momentum decoupling " @xcite is the ultimate cause of the large @xmath5 values produced by this type of interaction . it is also the origin of the momentum structure shown in fig . [ fig : deltak ] , as one can immediately see that @xmath164 will be suppressed as @xmath31 deviates from the fermi surface . this is confirmed by the numerical calculations with finite width @xmath21 of the interaction shown in fig . [ fig : deltak](a ) , which also show that this effect becomes less pronounced as the width of the interaction is made more uniform . the momentum structure of @xmath164 implies that only the dispersion of states near @xmath80 will be affected by the transition to the superconducting state . this is illustrated in fig . [ fig : deltak](b ) , where we show the spectral function @xmath165 at @xmath152 , @xmath153 , and @xmath154 in the normal ( @xmath65 k , dashed red ) and superconducting ( @xmath150 k , solid black ) states . the peaks of the main and replica bands at @xmath117 shift with the opening of the superconducting gap . in contrast , the two spectral functions away from @xmath117 are hardly affected in the superconducting state , since the gap function decays to zero very fast away from the fermi surface . thus , the lack of shift at the band minimum is a characteristic of a superconducting state mediated by forward scattering bosons . the absence of this shift at the band minimum may be discernible from the case of a uniform gap if the band is shallow relative to the size of the gap [ @xmath166 . this condition would be met in fese / sto , if the observed @xmath167 mev gap @xcite is momentum independent throughout the whole first brillioun zone . ( solid line ) and local dos @xmath168 ( dashed line ) for chemical potential ( a ) @xmath169 mev and ( b ) @xmath170 mev . the insets show the corresponding fermi surfaces and the definition of the angle around the fermi surface . ] at @xmath140 k along the path in the @xmath171 ( solid line ) and @xmath172 directions ( dashed line ) for chemical potentials ( a ) @xmath169 mev and ( b ) @xmath170 mev . the insets show the ratio of the maximal gap in the @xmath171 and @xmath172 directions . the colour of lines indicates different values of @xmath21 as indicated the insets . in all cases @xmath173 . ] another consequence of the momentum decoupling in the gap equation is that a significant anisotropy in @xmath174 can occur , which is determined by the anisotropy of the fermi velocity or local dos in @xmath14-space @xcite . to illustrate this point , we calculated the gap function for our model with @xmath175 mev such that @xmath80 lies in close proximity to the van hove singularity in the band structure . in this case , the local dos at fermi level , defined as @xmath176 , is extremely anisotropic , as shown in fig . [ fig : vfndos](a ) . ( @xmath177 defines the angle around the fermi surface measured from the positive @xmath178-axis and @xmath179 is the momentum in the direction tangential to the fermi surface . ) for comparison , @xmath168 and @xmath180 for @xmath170 mev are shown in fig . [ fig : vfndos](b ) , where each has a much weaker variation around the fermi surface . the corresponding gap functions @xmath181 at @xmath182 k along the @xmath171 ( solid lines ) and @xmath172 ( dashed lines ) directions are plotted in fig . [ fig : gap0kpath ] . results are shown for several values of @xmath21 , as indicated by the colour of the lines . the insets of fig . [ fig : gap0kpath ] show the ratio of the gap maximum along the @xmath171 ( @xmath183 ) and @xmath172 ( @xmath184 ) directions , which defines a measure of the gap anisotropy . in the @xmath169 mev case , we see a non - trivial evolution of the gap anisotropy as a function of @xmath21 . for large @xmath21 ( red ) , i.e. closer to uniform scattering , @xmath164 is somewhat anisotropic with the maximum value along ( @xmath185 ) being @xmath186 times the maximum along the diagonal . these values are inversely proportional to the fermi velocity , with @xmath187 , which can be inferred from the gap equation in the perfect forward scattering limit . as the value of @xmath21 initially decreases , the gap anisotropy becomes more pronounced until a maximum is reached for @xmath188 . this reflects the momentum decoupling effect seen in ref . further decreases in @xmath21 , however , result in a more uniform gap . this can be traced to an increase in the gap magnitude along the zone diagonal relative to the gap along @xmath171 . we speculate that the decreasing anisotropy in this region is related to an increase in the phase stiffness of the condensate when @xmath21 is very small and larger total gap values are obtained . these results are in contrast to those obtained when @xmath39 mev and the anisotropy in the band structure is much less pronounced . in this case , the resulting gap function is relatively isotropic with at most a @xmath189 variation occurring when @xmath107 . in both cases the gap has an @xmath128-wave symmetry , as can be expected for an attractive interaction . figs . [ fig : vfndos ] and [ fig : gap0kpath ] demonstrate that a strong forward scattering can produce an anisotropic gap if the variations in the fermi velocity are significant . in such a case the gap magnitude is inversely related to the fermi velocity . early arpes measurements on fese / sto found that the superconducting gap was fairly isotropic @xcite ; however , a more recent arpes study has observed a @xmath190 variation in @xmath156 around the electron pockets @xcite . this is larger than we infer from our single - band model , but our calculation neglects the nearly degenerate electron pockets , their relative orbital character , and any hybridization effects between them , and the anisotropy from an unconventional pairing mechanism that may be working in conjunction with the forward scattering . it would be interesting to carry out our calculation for a more realistic band structure that captures these aspects . the last topic that we wish to discuss in this section is the relevance for forward scattering to pairing channels that are traditionally considered in the context of purely electronic , repulsive interactions . for any momentum dependent interaction , one can define a projection of the coupling in the @xmath191-pairing channel @xcite @xmath192 where @xmath193 for an @xmath128-wave gap , @xmath194 for an @xmath195-wave gap , @xmath196/{2}$ ] for a @xmath197 gap , and so forth . if @xmath198 then the coupling is attractive in that channel . for a single - band system with strong forward scattering one can convince oneself that @xmath199 is positive for many @xmath191 since @xmath200 and @xmath201 have a better chance to have the same sign if @xmath14 is close to @xmath202 when @xmath203 is large ( this is somewhat sensitive to shape and size of the fermi surface ) while @xmath204 is the largest . as a result , strong forward scattering on its own will realize an @xmath128-wave gap but has non - zero contributions in other pairing channels . therefore , if a dominant pairing interaction arising from repulsive interactions is present , then the forward scattering @xmath1-@xmath2 interaction can contribute to the resulting unconventional superconducting state in most instances . these considerations also show that if the @xmath128-wave channel is blocked by a repulsive interaction in a singleband system , then the forward scattering will produce a gap symmetry in the channel with the next leading value of @xmath205 . this was pointed out in ref . @xcite , where it was discussed in the context of forward scattering in the cuprates using a simplified eliashberg treatment . we demonstrate this here for our model by introducing the morel - anderson coulomb pseudopotential @xmath206 , which suppresses the @xmath128-wave pairing tendency . [ fig : gapfwvdwv ] shows the resulting gap function for two different choices in parameters and @xmath207 . in this case the @xmath128-wave channel is effectively blocked by @xmath208 and a @xmath10-wave or @xmath209-wave gap is realized , depending on our parameter choice . we stress that these solutions were not imposed during our self - consistent calculations . rather , they were found naturally during the iterative procedure . the reader should also note that the @xmath5 is not strongly suppressed by the coulomb pseudopotential @xcite . left : @xmath209-wave gap @xmath210 for @xmath211 . right : @xmath10-wave gap @xmath210 for @xmath212 . @xmath213 , @xmath214 for @xmath211 , and @xmath215 for @xmath212 are used in the calculation . the green line indicates the fermi surface . ] in a boson - mediated superconductor , the electron - boson interaction produces fine - structure in the single - particle density of states ( dos ) @xmath216 . the energy at which these structures appear is determined by boson energy shifted by the maximum value of the superconducting gap @xmath217 @xcite . in addition , these structures can appear either as shoulders or as local minima in @xmath216 , depending on the gap symmetry and momentum dependence of the interaction @xcite . as such , the renormalized electronic structure carries valuable information regarding the pairing mediator . motivated by this , we calculated @xmath218 for our model in the case of a strongly forward focused interaction . the result is shown in fig . [ fig : dos ] , where the model parameters are @xmath219 mev , @xmath124 , and @xmath220 . these results were obtained on an @xmath221 @xmath222-grid and at a temperature of @xmath150 k , well below @xmath5 . the dos shows clear coherence peaks associated with the fully gapped @xmath128-wave state , which are broadened by a @xmath223 mev contribution that was added to the imaginary part of @xmath224 . the dos also has several additional structures arising from the replica bands . the insets of fig . [ fig : dos ] zoom in on the relevant energy ranges . in this case , the structures are different from those expected for a conventional @xmath1-@xmath2 mediated superconductor with an @xmath128-wave gap . in the conventional case , the boson renormalizations form shoulders in @xmath216 , where the dos is enhanced ( suppressed ) for energies below ( above ) @xmath225 , resulting in a characteristic minima in @xmath226 @xcite . in the forward scattering case , however , we see step - like features located at approximately @xmath74 above and below @xmath80 , which correspond to the onset of the spectral weight of the replica bands . this results in a local maxima in @xmath226 at the energy @xmath74 , occurring for both for the unoccupied and occupied dos . this difference provides another structure in the electronic structure that might be used for identifying replica bands in real materials . the density of states @xmath216 for @xmath124 , @xmath220 , and @xmath219 mev , calculated at @xmath150 k. a small @xmath227 mev contribution was also added to the imaginary part of the single - particle self - energy in order to broaden the spectra at this @xmath14-resolution . the two insets on the left zoom in on the spectra in the regions where the boson - induced features are found and the inset on the right shows @xmath228.,scaledwidth=45.0% ] fourier transform scanning tunneling spectroscopy , also commonly known as quasi - particle interference ( qpi ) , has become a popular method for studying the electronic structure and gap symmetry of unconventional superconductors @xcite . this technique exploits the fact that the incoming and outgoing wavefunction of an electron scattered from an impurity will interfere with each other to form ripples in the charge density . the power spectrum of the resulting density modulations measured at a bias voltage @xmath229 will have peaks in its intensity at wave vectors @xmath230 , which are related to spanning vectors across the constant energy contours of the band @xmath231 . by tracking the dispersion of the @xmath230 peaks , one can infer information about the underlying electronic band structure . one of the advantages of this technique over arpes is that it can access unoccupied states @xcite . this technique can therefore probe both the occupied and unoccupied replica bands produced by a strong forward scattering mode . motivated by this , we calculated the qpi spectrum for our model . our qpi calculations are carried out using the standard @xmath232-matrix formalism for a single - band superconductor , as outlined in a number of references @xcite . in the presence of an impurity , the fourier transform ( ft ) of the local electron density ( ft - ldos ) is partitioned as @xmath233 , where @xmath234 is the ft - ldos for the homogeneous system and @xmath235 is the ft of the induced density modulations due to the impurity . the latter part is given by @xmath236 , where @xmath237.\end{aligned}\ ] ] here , @xmath238 is the green s function in the presence of the impurity ; @xmath239 is the @xmath232-matrix ; and @xmath240 is the bare green s function in the absence of the impurity . for our purposes in this section , @xmath240 includes the self - energy due to the @xmath1-@xmath2 interaction . the assumption here is that the impurities and @xmath1-@xmath2 interaction do not significantly influence one another . for simplicity , we treat the impurity as a weak non - magnetic point - like potential scatter located at the origin . in this limit the @xmath232-matrix is momentum independent and is given by @xmath241^{-1},\ ] ] where @xmath242 and @xmath243 characterizes the strength of the impurity potential . for our calculations we took @xmath244 mev ; however , our results are not too sensitive to this value . our qpi results are summarized in figs . [ fig : qpi ] and [ fig : qpi_dispersion ] . the spectral function for our bare " electronic structure , including the effects of the @xmath1-@xmath2 interaction , is shown in fig . [ fig : qpi](a ) for reference . the relevant model parameters are given in the figure caption . constant energy cuts of the spectral function are shown figs . [ fig : qpi](b1)(b4 ) for energies located inside the occupied replica band [ @xmath245 mev , panel ( b1 ) ] , inside the occupied states of the main band [ @xmath246 mev , panel ( b2 ) ] , inside the unoccupied states of the main band [ @xmath247 mev , panel ( b3 ) ] , and inside the unoccupied replica band [ @xmath248 mev , panel ( b4 ) ] . in fig . [ fig : qpi](b1)(b3 ) one can see a clear ring - like feature corresponding to the single replica or main band that is intersected at these energies ; however , in fig . [ fig : qpi](b4 ) , a double ring structure is observed where the inner ring corresponds to the replica band and the outer ring corresponds to the main band . this electronic structure is reflected in the corresponding qpi spectra , shown in fig . [ fig : qpi](c1)(c4 ) , respectively . the maps in figs . [ fig : qpi](c1)(c3 ) have a clear ring - like structure with a radius @xmath249 , where @xmath250 is a vector spanning the constant energy contours . these features resemble what one would expect for a simple single band system @xcite . at @xmath251 mev , however , the qpi pattern develops a double ring structure , as one would might expect from the topology of the main and replica bands shown in fig . [ fig : qpi](b4 ) . based on the geometry of the features we can assign the outer qpi peak to intraband scattering within the main band and inner qpi peak to interband scattering between the unoccupied states of the replica and main bands . we also see a very weak feature due to intraband scattering within the replica band , however , it is very difficult to resolve in this image . the intensity of these features also follows the hierarchy of spectral weight associated with the type of band . the relative intensity of these features are also shown in fig . [ fig : qpi_dispersion ] . these results establish that the replica bands can be observed in the qpi spectra and therefore ft - sts could in principle study these features , particularly on the unoccupied side of @xmath80 . in this case , the qpi peaks due to the replica bands will appear similar to regular bands at a given bias voltage albeit with a reduced intensity ; however , the dispersion and spectral weight of these features will be quite different . to illustrate this , we plot the qpi intensity along the @xmath252 line as a function of energy in order to track the dispersion of the qpi peaks . [ fig : qpi_dispersion](a1 ) presents this information as a false colour image while fig . [ fig : qpi_dispersion](a2 ) presents it as a contour plot in order to highlight the features with weaker intensity . if a qpi peak is due to intraband scattering in the main band , then it will disperse towards @xmath22 as the bias voltage is tuned towards the top or bottom of the band @xcite . this can be clearly seen in fig . [ fig : qpi_dispersion](a1 ) from the most intense feature . in contrast , the dispersion of a peak due to inter or intraband scattering to a replica band will be different due to the extinction of the replica band s spectral weight at @xmath117 . this is apparent in fig . [ fig : qpi_dispersion](a1 ) and fig . [ fig : qpi_dispersion](a2 ) , where the intensities of the interband scattering feature at positive energies and the intraband scattering feature at negative energies sudden disappears at the energy where the replica band disappears . this is another unique spectral fingerprint of a replica band . while there have been several qpi studies conducted on the fese / sto system @xcite , to the best of our knowledge no indications of the replica bands have been observed . one study by huang _ et al . _ ( ref . @xcite ) found evidence for an electron - like and located 75 mev above @xmath80 ; however , the measurements of the tunneling decay length indicated that this band was centered at the @xmath24-point rather than the @xmath44-point . this rules out the possibility that this feature is due to the replica expected for the electron pockets at the @xmath44-point . however , we also note that nearly all of the qpi studies completed to date have focused on energy windows of less than 80 mev of the fermi level @xcite . this is outside the region where the replica band are expected , based on the phonon energy scale inferred by arpes @xcite . it would therefore be interesting to extend these studies to higher bias voltages in order to determine if the features shown in fig . [ fig : qpi_dispersion ] can be observed . this will be a challenging task , however , as our calculations have shown that the replica qpi peaks are much weaker in intensity than the main qpi peaks .

one possibility is the introduction of a cross - interface electron - phonon (- ) interaction between the fese electrons and oxygen phonons in the substrates that is peaked in the forward scattering ( small direction due to the two - dimensional nature of the interface system . this interaction produces not only deviations from the expectations of conventional phonon - mediated pairing but also replica structures in the spectral function and density of states , as probed by angle - resolved photoemission spectroscopy , scanning tunneling microscopy / spectroscopy , and quasi - particle interference imaging .

mono- and multilayer fese thin films grown on srtio and bitio substrates exhibit a greatly enhanced superconductivity over that found in bulk fese . a number of proposals have been advanced for the mechanism of this enhancement . one possibility is the introduction of a cross - interface electron - phonon (- ) interaction between the fese electrons and oxygen phonons in the substrates that is peaked in the forward scattering ( small direction due to the two - dimensional nature of the interface system . motivated by this , we explore the consequences of such an interaction on the superconducting state and electronic structure of a two - dimensional system using migdal - eliashberg theory . this interaction produces not only deviations from the expectations of conventional phonon - mediated pairing but also replica structures in the spectral function and density of states , as probed by angle - resolved photoemission spectroscopy , scanning tunneling microscopy / spectroscopy , and quasi - particle interference imaging . we also discuss the applicability of migdal - eliashberg theory for a situation where the- interaction is peaked at small momentum transfer and in the fese / sto system . = 4 _ keywords _ : superconductivity , forward scattering , eliashberg theory , fese films

math-ph0702005

i

@xmath0 `` numerical ranges and @xmath0 '' numerical radii @xcite naturally relate to optimization problems on the unitary orbit of a given matrix . a particularly interesting class of applications concerns quantum systems as shown in more detail in the accompanying paper @xcite . this is because quantum dynamics and quantum control of closed hamiltonian systems are governed by the unitary group of the underlying hilbert space and its subgroups . for instance , in quantum information and quantum computation , where spin-@xmath9 two - level systems are exploited as elementary units called quantum bits or qubits for short the full dynamics of @xmath5 qubits take place on the unitary group @xmath10 . this includes two types of coherent time evolutions , ( i ) _ within _ each individual qubit independently as well as ( ii ) _ between _ coupled qubits . the former is brought about by so - called _ local actions_. hence , we refer to the corresponding subgroup as the subgroup of local time evolution @xmath11 . it takes the form of an @xmath5-fold tensor product of @xmath6 with itself . clearly , matrices ( states ) that are themselves @xmath5-fold tensor - products remain in this product form under conjugation with elements of @xmath11 . therefore , quantum optimization problems which can be expressed via local actions motivate in a most natural way the study of a subset of the classical @xmath0 " numerical range , namely the _ local @xmath0 " numerical range_. it is but a special instance of the more general structure which we introduce here as the _ relative @xmath0 " numerical range _ , where the full unitary group is restricted to some arbitrary compact connected subgroup . to be mathematically precise , let @xmath2 denote the compact and connected lie group of all unitary matrices of size @xmath12 , i.e. @xmath13 if and only if @xmath14 with @xmath15 , where @xmath16 stands for the conjugate transpose . moreover , let @xmath17 be the subgroup of all special unitary matrices , i.e. @xmath18 if and only if @xmath13 with @xmath19 . finally , let @xmath20 be the @xmath5-fold tensor product of @xmath6 , which consists of all @xmath5-fold kronecker products of the from @xmath21 for all @xmath22 . following terminology from quantum information as mentioned above we refer to @xmath11 as the subgroup of _ local _ unitary transformations . now , for arbitrary complex matrices @xmath23 the _ local @xmath0 " numerical range _ of @xmath24 is defined as @xmath25 obviously , @xmath26 is a subset of the classical @xmath0 " numerical range of @xmath24 , denoted @xmath27 . however , its geometry is significantly more intricate than in the classical case and has yet not been studied in any systematic way , cf . analysing its basic properties leads naturally to the following slightly more general object @xmath28which we call the _ relative @xmath0 " numerical range _ of @xmath24 . here , @xmath29 may be any compact and connected subgroup of @xmath2 . clearly , @xmath1 is invariant under unitary similarities of @xmath24 and @xmath0 by elements of @xmath29 . moreover , with @xmath1 being a continuous image of @xmath29 , it is compact and connected . however , in contrast to the classical @xmath0 " numerical range , cf . @xcite , counterexamples show that @xmath1 is neither star - shaped nor simply connected . in general , the actual size and shape of @xmath1 are mostly unknown . the purpose of the present paper is to initiate the study of the relative @xmath0 `` numerical range and in particular its geometry . starting points for our investigations are well - known results on the classical @xmath0 '' numerical range . therefore , we have summarized the fundamental geometric properties of @xmath27 at the beginning of section [ sec:2 ] . subsequently , the above mentioned counterexamples and straightforward consequences of ( [ def : relnumrange ] ) are collected in subsection [ subsec:2.1 ] . the main result , a generalisation on rotationally symmetric @xmath0-umerical ranges , is presented in subsection [ subsec:2.2 ] . particularly , the original work by li and tsing @xcite is recovered as a immediate corollary . in section [ sec:3 ] we return to local @xmath0 `` numerical ranges . here , the central conclusion is that rotationally symmetric local @xmath0 '' numerical ranges are essentially circular discs . finally , we illustrate the previous results by determining all complex @xmath30-matrices , the local @xmath0 " numerical range of which is a circular disc centered at the origin of the complex plane . these computations lead to a conjecture on unitray similarity to block - shift form of such matrices . some concluding remarks on numerical issuse and perspectives for future work can be found in section [ sec:4 ] .

motivated by applications in quantum information and quantum control , a new type of `` numerical range , the relative '' numerical range denoted , is introduced . furthermore , we concentrate on the subgroup , i.e. the-fold tensor product of , which is of particular interest in applications . in this case , sufficient conditions are derived for being a circular disc centered at origin of the complex plane .

motivated by applications in quantum information and quantum control , a new type of `` numerical range , the relative '' numerical range denoted , is introduced . it arises upon replacing the unitary group in the definition of the classical " numerical range by any of its compact and connected subgroups . the geometric properties of the relative `` numerical range are analysed in detail . counterexamples prove its geometry is more intricate than in the classical case : e.g. is neither star - shaped nor simply - connected . yet , a well - known result on the rotational symmetry of the classical '' numerical range extends to , as shown by a new approach based on lie theory . furthermore , we concentrate on the subgroup , i.e. the-fold tensor product of , which is of particular interest in applications . in this case , sufficient conditions are derived for being a circular disc centered at origin of the complex plane . finally , the previous results are illustrated in detail for .

1105.0484

r

the model is defined on a 1d lattice . at any time @xmath0 , a lattice site @xmath1 has @xmath2 particles of type @xmath3 and @xmath4 particles of type @xmath5 . we start with an empty lattice with @xmath6 sites at @xmath7 . at each instant , a site @xmath1 is chosen at random and one of the following moves ( illustrated in fig . [ model_schematic ] ) occurs in an infinitesimal time interval @xmath8 : 1 . injection : if the site picked is site 1 , then an a particle is injected into it from the left boundary with probability @xmath9 : @xmath10 2 . interconversion : with probability @xmath11 , one of the a particles residing on the selected site converts to type b : if @xmath12 , then @xmath13 and @xmath14 . with probability @xmath15 one of the b particles residing on the site converts to type a : if @xmath16 then @xmath17 and @xmath18 . 3 . chipping : with probability @xmath19 ( @xmath20 ) , one of the a particles chips off the site and hops to the right ( left ) neighbouring site , thereby decreasing the mass of a on the site by 1 and increasing the mass of a on the neighbouring site by 1 ; if @xmath12 then @xmath13 and @xmath21 . with probability @xmath22 ( @xmath23 ) , one of the b particles chips off the site and hops to the right ( left ) : if @xmath16 then @xmath17 , @xmath24 4 . stack movement : with probability @xmath25 ( or @xmath26 ) , the entire mass ( i.e. all a and b particles together ) present at the site hops to the right ( left ) neighbouring site : @xmath27 , @xmath28 , @xmath29 , @xmath30 . at the last site an a ( b ) particle can hop out of the system at a rate @xmath31 , i.e. with the same hopping rate as in the bulk . once particles hop rightwards from the last site @xmath6 , they can not return to the system . thus , site @xmath32 acts as a sink . [ [ section-8 ] ] in general , the drive i.e. the asymmetry in the rates of the three hopping processes hopping of stacks , hopping of a particles after chipping and hopping of b particles after chipping , can be different . however , for simplicity , we will take the asymmetry to be the same for all three processes , i.e. @xmath33 . then we can parametrize the rates as follows : @xmath34 , @xmath35 ; @xmath36 , @xmath37 ; @xmath38 , @xmath39 . here , @xmath40 is the measure of the asymmetry in hopping and takes on values between 0 and 1 . [ [ section-9 ] ] the moves ( i ) to ( iv ) above define a general model in which particles can move via both stack movement and chipping . however , as indicated in section [ sec : intro ] , in this paper we will analyse the model in the absence of stack movement i.e. in the limit @xmath41 . [ [ section-10 ] ] several features of our model , including boundary effects , mass movement and coalescence , and two - species coupling have been studied separately in a number of different contexts . macroscopic aggregates are known to form in models such as the the zero range process ( zrp ) @xcite and the aggregation - chipping model @xcite . in these models , the closed system in steady state can enter a condensate phase in which a finite fraction of the total mass resides on a single site . a quasi - stationary state characterised by growth of total mass in the system occurs in aggregation models such as the takayasu model @xcite in which particles are injected at every site . the in - out model @xcite , which extends the takayasu model to allow for evaporation of unit masses , exhibits a phase transition from a growing state to a steady state . such a phase transition is also seen in our model . however , the phases in our model are not spatially uniform as injection occurs only at the boundary . [ [ section-11 ] ] open boundaries with injection can induce interesting features such as boundary - driven phase transitions in the asymmetric simple exclusion process ( asep ) @xcite . in the zrp with open boundaries @xcite , steady state , in the sense of constant average mass , is not reached for strong boundary injection ; indefinitely growing aggregates may form on one or both boundaries , while bulk sites attain steady state or show slower growth , depending on the injection , hopping rates , and asymmetry . our model , in which injection takes place at the boundary , also shows growing phases ; somewhat counter intuitively , a steady state with constant mass is reached close to the boundary , while there is unbounded growth of the mass in the bulk . [ [ section-12 ] ] coupling between different species of particle may or may not involve interconversion . for example , in the two - species zrp @xcite , condensates of one or both species may form above critical densities but the number of particles of each species in the system does not change . new effects are seen when interconversion ( or more generally , non - conservation of particle number ) occurs . multi - species models that allow for inter - conversion have been studied earlier in the context of transport in single @xcite and multiple @xcite channels@xcite . these models differ from the present work in that they restrict the occupancy to at most one particle per site in each channel . generically in an open boundary channel , if the number of particles is not conserved in the bulk ( e.g. if switching between channels or deposition and evaporation occurs ) , then for low switching rates , the system may develop a localised shock separating low density and high density regions in one of the channels @xcite . our model too shows co - existence of two phases of one species ( a steady phase and a growing phase ) in different spatial regions separated by a domain wall with a tunable location . our main results may be summarised as follows : + the model is parametrized by the rates @xmath42 and the asymmetry parameter @xmath40 , where @xmath43 corresponds to symmetric and @xmath44 to fully asymmetric rightward hopping . in different regions of parameter space , different kinds of behaviour are seen : 1 . for some values of parameters , the system exists in a steady phase . occupation probabilities of a and b at a site @xmath1 , i.e. the probability that the site has at least one a ( b ) particle are defined as @xmath45 where @xmath46 is the probability of finding @xmath47 a particles and @xmath48 b particles on site @xmath1 between time @xmath0 and @xmath49 . in the steady phase , @xmath50 and @xmath51 at each site , reach a time independent value _ less than 1_. the total mass in the system ( and on each site ) also reaches a finite time - independent value . 2 . for other values of parameters , the system exists in a quasi - stationary state characterised by stationary ( time - independent ) currents but _ non - stationary i.e. indefinitely growing total mass_. this happens even in a finite system . we will refer to unbounded growth of mass as _ formation of pile - ups_. more precisely , if the average a ( b ) mass at a site grows indefinitely , we refer to this as an a ( b ) pile - up at the site . at the site with an a ( b ) pile - up , the mean occupancy @xmath52 approaches @xmath53 at long times ( see sec . [ sec : first_site ] ) . this may be treated as a functional definition of a pile - up . a pile - up is to be distinguished from a condensate of the sort found in the zero range process ( zrp ) @xcite : a condensate at a site contains a finite fraction of the total number of particles in the system but the condensate mass does not grow in time . 3 . in the growing phase , a system may have pile - ups of a , of b or of both species . for the situation with injection of only a particles , as studied in this paper , an a pile - up can be found only on site 1 ( except in the special case @xmath54 , @xmath55 ) , i.e. it is a boundary phenomenon . b pile - ups , on the other hand , are found in the bulk . in a phase with b pile - ups , an interesting situation can occur where the lattice has a _ region in steady state ( with finite mean mass ) co - existing with a region of b pile - ups ( where the mean mass grows indefinitely)_. for fully asymmetric hopping , the region close to the left boundary is in steady state while pile - ups occur in the entire region to the right ( shown schematically in fig [ schematic_asym ] ) . for the symmetric or partially asymmetric case , there are two regions in steady state close to either boundary , with a region of b pile - ups between these ( fig . [ schematic_sym ] ) . in the rest of the paper , we will adopt the following terminology . if the average mass of both a and b reaches a finite time - independent value , we will refer to the system as being in a steady phase . if one region of the system attains constant average mass and another region shows unbounded growth , we will refer to the two regions as a region in steady state and a region with pile - ups respectively . the system as a whole will be referred to as being in a growing phase . [ [ section-13 ] ] steady and growing phases can also be distinguished by the spatial profile of the currents . let @xmath56 , @xmath57 and @xmath58 denote respectively the net a particle current , the b particle current and the total particle current in the @xmath1th bond of the lattice i.e. from site @xmath1 to @xmath59 . figs . [ j(x)steady ] and [ j(x)growing ] show schematically how , for @xmath44 , these three currents vary across the lattice in a steady phase and a growing phase ( with b pile - ups ) respectively . in the steady phase , although @xmath60 and @xmath61 vary with the distance from the origin @xmath62 , they do so in such a way that the total particle current @xmath63 remains constant across the lattice . in contrast , in the growing phase , the _ total particle current @xmath63 also varies with @xmath62 _ in the pile - up region . in fact , @xmath64 must be greater than @xmath65 for a pile - up to exist at site @xmath1 , implying that @xmath63 decreases with @xmath1 ( or @xmath62 ) in a pile - up region . ) , the occupation probability profiles @xmath66 and @xmath67 ( dashed lines ) are flat , being @xmath68 and @xmath69 respectively . when @xmath70 , @xmath71 , there is a net interconversion from a to b at each site , pushing @xmath72 down from the value @xmath66 and pushing up @xmath73 from the value @xmath67 . here @xmath72 and @xmath73 ( solid lines ) are occupation probabilities with interconversion.,scaledwidth=40.0% ] [ [ section-14 ] ] in order to explain the spatial structure of the various phases , it is useful to understand what causes the spatial variation in @xmath60 and @xmath61 or equivalently , @xmath72 and @xmath73 . for simplicity , let us consider purely rightward hopping ( @xmath44 ) in a system of size @xmath6 . in the absence of interconversion , the particle current @xmath60 is the same in each bond , and so is @xmath61 . thus , @xmath72 and @xmath73 are constant across the lattice , being @xmath68 and @xmath69 respectively ( dotted lines in fig . [ s(x ) ] ) . interconversion changes @xmath60 and @xmath61 and consequently @xmath72 and @xmath73 ( solid lines in fig . [ s(x ) ] ) in the following way . the particle current into site 1 ( @xmath74 ) is entirely of type a. at site 1 , some of the a particles convert to type b , resulting in a small probability that site 1 also has b particles . hence , @xmath75 is different in composition , having a small b component as well . at site 2 , there is still a much larger concentration of a particles than b particles , and hence a net conversion of a to b particles . thus , the composition of @xmath76 shifts further towards b. this process continues until we reach a site at which there is _ no net conversion_. beyond this site @xmath60 and @xmath61 do not change with @xmath62 . if interconversions are faster than hopping ( i.e. @xmath77 ) , then at a given site , the relative amounts of a and b can alter significantly through interconversion before hopping occurs . in this limit , @xmath60 and @xmath61 change sharply over a few sites and reach their asymptotic values very close to the left boundary . in the other limit ( @xmath78 ) , @xmath60 and @xmath61 vary slowly over a large part of the lattice . in particular , if @xmath79 and @xmath80 are not @xmath81 but @xmath82 , then the spatial variation in @xmath60 and @xmath61 becomes a bulk rather than boundary effect . [ [ section-15 ] ] the right boundary is an absorbing boundary . the degree of asymmetry in the hopping determines how far into the lattice the effect of the absorbing boundary condition propagates . for fully asymmetric dynamics ( @xmath44 ) , the right boundary has no effect on any other site while for @xmath40 slightly less than 1 , the effect extends only into a very small region of the lattice close to the boundary . for @xmath43 , the information about the right boundary propagates into the entire lattice . thus , the asymmetry in hopping rates and the rate of interconversion relative to the rate of hopping together determine how @xmath60 and @xmath61 or @xmath72 and @xmath73 vary across the lattice .

it is found that , depending on the rates of various processes and the asymmetry in the hopping , the system may exist either in a steady phase , in which the average mass at each site attains a time - independent value , or in a `` growing '' phase , in which the total mass grows indefinitely in time , even in a finite system . in particular , we find phases in which some spatial regions of the system have a constant average mass , while other regions show unbounded growth .

motivated by the phenomenology of transport through the golgi apparatus of cells , we study a multi - species model with boundary injection of one species of particle , interconversion between the different species of particle , and driven diffusive movement of particles through the system by chipping of a single particle from a site . the model is analysed in one dimension using equations for particle currents . it is found that , depending on the rates of various processes and the asymmetry in the hopping , the system may exist either in a steady phase , in which the average mass at each site attains a time - independent value , or in a `` growing '' phase , in which the total mass grows indefinitely in time , even in a finite system . the growing phases have interesting spatial structure . in particular , we find phases in which some spatial regions of the system have a constant average mass , while other regions show unbounded growth .

1105.0484

c

[ [ section-46 ] ] in this paper , motivated by the phenomenology of traffic in the golgi apparatus of the cell , we have studied a stochastic two - species model with boundary injection of type a , interconversion between types a and b , and transport of both species through the lattice ( in general , in a driven diffusive way ) by chipping of one particle at a time . we found that depending on the rates of various processes , the system may either eventually attain steady state or show unbounded growth of mass at all times . pile - ups ( as defined in the text ) may be composed of a particles or b particles or both . unlike in translationally invariant systems , the phases in our model have interesting spatial structure . generically , in growing phases , a part of the lattice attains steady state while other regions show unbounded growth of mass ( pile - ups ) . [ [ section-47 ] ] below , we comment on some possible extensions of the model : 1 . if stack movement also occurs ( as in the more general model defined in section [ sec : model ] ) , there are _ no growing phases _ and the average mass in the system always attains a constant finite value . this may be argued as follows . if @xmath300 and @xmath301 are the in and out currents at a site , then the average mass @xmath302 at the site grows as @xmath303 . in the ` chipping only ' case , @xmath304 ( assuming only one type of particle ) . if @xmath305 , then in and out currents can not balance , and @xmath302 grows indefinitely . on the other hand , with stack movement , @xmath301 which is given by @xmath306 , can always balance @xmath300 , resulting in zero growth rate or constant mass . however , if the rate of stack movement is mass dependent i.e. @xmath307 , then @xmath301 which is now @xmath308 will be bounded for @xmath309 . in this case , pile - ups can occur and the behaviour of the system would be expected to be similar to that of the ` chipping only ' model . one extension of this model to higher dimensions is trivial . if injection takes place at a surface perpendicular to one of the spatial directions , and we assume periodic boundary conditions in other directions , the model is still effectively one dimensional as there are no @xmath310 currents between sites in the transverse direction . generalizations to higher dimensions with other boundary conditions can be more complex . this model can also be extended quite easily to include injection of b particles at the left boundary , at a rate @xmath311 . now , depending on the value of the ratio @xmath312 , the system either has net interconversion from a to b ( and behaviour similar to what has been discussed in the paper ) or net interconversion from b to a ( resulting in a pile - ups in the bulk etc . ) or no net interconversion , i.e. no effective coupling between the two species . at the right boundary , introducing exit rates that are different from the chipping rates can also change the behaviour of the system . however , this change is only a boundary effect unless the exit rate is @xmath82 times the chipping rate . if the exit rate is small in the sense defined above , then @xmath72 and @xmath73 vary with @xmath62 differently from eqs . . however , growing phases with b pile - ups in the bulk are still found . [ [ section-48 ] ] finally , we comment on the possible relevance to the biological system . the model system we have studied is a simple one , but it shares the following qualitative features with the golgi apparatus . first , there is a gradation of sizes of stacks from the source to the sink . in particular , small stacks are found close to the source while large , though growing , aggregates occur in regions farther away . secondly , there is a gradation of ` chemical ' species across the system , with different spatial regions having aggregates that may be predominantly of type b and/or type c etc . these aggregates , however , show unbounded growth , which is not realistic in the context of the golgi , which consists of large but bounded and discrete structures . as discussed above , unbounded growth is eliminated once we allow for movement of whole stacks , as in the more general model defined in sec [ sec : model ] , and discussed in this section . [ [ section-49 ] ] in the present model , we have assumed that mass transfer occurs either by chipping of a single particle or by movement of the whole stack . other transport processes could involve the fragmentation and movement of chunks of intermediate sizes . the study of these different mass transport processes in systems with boundary injection is an interesting direction for future study .

motivated by the phenomenology of transport through the golgi apparatus of cells , we study a multi - species model with boundary injection of one species of particle , interconversion between the different species of particle , and driven diffusive movement of particles through the system by chipping of a single particle from a site . the growing phases have interesting spatial structure .

motivated by the phenomenology of transport through the golgi apparatus of cells , we study a multi - species model with boundary injection of one species of particle , interconversion between the different species of particle , and driven diffusive movement of particles through the system by chipping of a single particle from a site . the model is analysed in one dimension using equations for particle currents . it is found that , depending on the rates of various processes and the asymmetry in the hopping , the system may exist either in a steady phase , in which the average mass at each site attains a time - independent value , or in a `` growing '' phase , in which the total mass grows indefinitely in time , even in a finite system . the growing phases have interesting spatial structure . in particular , we find phases in which some spatial regions of the system have a constant average mass , while other regions show unbounded growth .

1011.0996

i

there has been recent progress in understanding the phase diagram of higher - dimensional asymptotically flat vacuum black holes . the purpose of this work is to extend some of the techniques used to the case of asymptotically anti - de sitter ( ads ) black holes . let us first review the asymptotically flat case . while the four - dimensional kerr black hole is unique and ( expected to be ) stable , the higher - dimensional picture is much richer @xcite . in @xmath7 , the discovery of the black ring by emparan and reall @xcite showed that it can have the same conserved charges as the myers - perry ( mp ) black hole @xcite . this non - uniqueness discovery triggered the research in higher dimensional black holes and a variety of explicit rotating solutions have been recently found : black saturns @xcite , concentric rings @xcite , orthogonal rings @xcite , and generalisations thereof . consider solutions rotating on a single plane which are in thermal equilibrium ( i.e. in the case that there are disconnected components of the event horizon , these have the same temperature and angular velocity ) . one interesting fact is that in the zero temperature limit the new solutions _ and _ the mp black hole coincide in the same nakedly singular solution @xcite . in @xmath0 , this limit does not exist , and the mp black hole has an unbounded angular momentum for a given mass . in a certain sense , the singular limit is ` resolved ' . however , does the mp black hole still connect to the new solutions ? in @xmath0 , the black ring and the other solutions have not been constructed exactly , but are expected to exist . in fact , approximate methods for solving the einstein equations in the ultraspinning limit ( large angular momentum with respect to the mass scale ) indicate that they do exist @xcite . the answer seems to be that the mp black hole connects to the other solutions through yet more families of black holes . these families bifurcate from the mp branch at the ( stationary ) onset of the so called ` ultraspinning instabilities ' . the first step in understanding this connection was given by emparan and myers @xcite , who argued that the singly - spinning ( i.e. rotating on a single plane ) mp black hole should be unstable if rotating sufficiently rapidly . the reasoning is that if the angular momentum per unit mass is large enough , mp black holes start behaving like black branes , since their horizons become disk - like along the rotation plane in this ultraspinning limit . but it has been shown by gregory and laflamme @xcite that black branes are unstable and therefore one concludes that mp black holes should be unstable for a sufficiently large ( but finite ) angular momentum per unit mass . emparan and myers further pointed out that at the onset of such an instability , there should exist a stationary perturbation that preserves the rotational symmetries of the background . this perturbation would then signal the existence of a new family of black holes with spherical horizon topology . this is analogous to what happens in the black brane case : the threshold mode of the gregory - laflamme instability is the perturbative signal for a family of non - uniform branes @xcite . @xcite conjectured that the new families bifurcating from the mp branch , when continued along the phase diagram , would connect continuously to the black ring branch , the black saturn branch , and so on . therefore , the connection of non - uniqueness with instabilities provides a partial understanding of the proliferation of higher dimensional black hole phases . recently , these conjectures were put on a firmer footing when it was shown numerically that the singly - spinning mp black hole does indeed possess such threshold modes @xcite . furthermore , these perturbations exhibit an underlying harmonic structure and induce deformations on the shape of the horizon which are consistent with the proposal that the new families will connect to the black ring , to the black saturn , etc . @xcite also conjectured that these classical instabilities can only occur when the black hole possesses at least two distinct local thermodynamic instabilities , as we shall review later . this is a necessary but not sufficient condition . the reason is that local thermodynamic instabilities are associated to the lowest harmonics , and thus with the asymptotic charges , the mass and the angular momentum . higher harmonics , which can not change the asymptotic charges and are associated to the bifurcation to new families , should only become unstable for rotations higher than the thermodynamic modes . this conjecture allows for any number of independent angular momenta , and has already been verified in the instability of @xmath0 cohomogeneity-1 mp solutions ( equal independent spins in odd @xmath8 ) @xcite . this sector of mp black holes has a regular extremal limit and the angular momentum is bounded from above , yet the conjecture of ref . @xcite indicates that an instability is possible . indeed linear perturbations growing exponentially with time were found , which is an important check since the previous work could only determine the stationary threshold modes . in this paper , we will extend the results in refs . @xcite to the asymptotically ads case . the properties of asymptotically ads spacetimes have been greatly explored due to the ads / cft correspondence , which equates quantum gravity ( string theory ) in an asymptotically ads spacetime to a conformal field theory ( cft ) living on the boundary of that spacetime @xcite . in particular , the phase diagram of black holes in ads is in direct correspondence to the phases of the dual cft at finite temperature . therefore , even if many higher - dimensional black hole solutions present classical instabilities , or do not dominate thermodinamically the gravitational partition function , they still provide a valuable insight into the cft phases . black rings and black saturns in ads have been constructed in certain approximations @xcite , and the conjectures of ref . @xcite regarding the connections between singly - spinning black hole families were extended to the asymptotically ads case also in ref . notice that singly - spinning mp - ads black holes @xcite ( and indeed any asymptotically ads stationary black hole @xcite ) present a bps - type upper bound on their angular momentum , @xmath9 ( with @xmath10 being the mass and @xmath11 the cosmological length ) , while there is no such bound in the asymptotically flat case . however , the instabilities / bifurcations are still expected as we increase the rotation up to that bound @xcite ( see fig . [ fig : phases ] ) . in this paper we will numerically determine the dependence of the stationary threshold modes on the cosmological constant . the procedure is an extension to @xmath12 of the @xmath13 kerr - ads analysis @xcite , where no classical instability was found ; the latter was itself an extension of the schwarzschild - ads case @xcite . we confirm the conjecture of ref . @xcite , which gives a necessary but not sufficient condition for the onset of the ultraspinning instability . in this paper we generalise the previous formulation so that it can be applied to the asymptotically ads case . we find that all bifurcations occur when the mp - ads black hole is unstable under superradiance @xcite , which implies that the new families of black holes will inherit this instability . before proceeding , let us mention that asymptotically flat singly - spinning mp black holes also suffer from an instability that breaks their axisymmetry @xcite . this occurs even in @xmath7 , and for @xmath12 it sets in for lower rotations than the ultraspinning instability that we study here . however , the threshold mode is not associated to new stationary black holes . it would be interesting to find whether this non - axisymmetric instability also extends to asymptotically ads black holes and to understand how it relates to the ads superradiant instability . this paper is organised as follows . in section [ sec : ultraspin ] , we review the properties of singly - spinning mp - ads black holes and discuss the ultraspinning instability . in section [ sec : perturbationproblem ] , we detail the linear perturbations problem that is solved numerically . we conclude in section [ sec : results ] , with the discussion of the results .

myers - perry black holes with a single spin in have been shown to be unstable if rotating sufficiently rapidly . we extend the numerical analysis which allowed for that result to the asymptotically ads case . we determine numerically the stationary perturbations that mark the onset of the instabilities for the modes that preserve the rotational symmetries of the background . each of these perturbations has been conjectured to represent a bifurcation point to a new phase of stationary ads black holes , and this is consistent with our results .

myers - perry black holes with a single spin in have been shown to be unstable if rotating sufficiently rapidly . we extend the numerical analysis which allowed for that result to the asymptotically ads case . we determine numerically the stationary perturbations that mark the onset of the instabilities for the modes that preserve the rotational symmetries of the background . the parameter space of solutions is thoroughly analysed , and the onset of the instabilities is obtained as a function of the cosmological constant . each of these perturbations has been conjectured to represent a bifurcation point to a new phase of stationary ads black holes , and this is consistent with our results . * ultraspinning instability of anti - de sitter black holes * + * scar j. c. dias * , * pau figueras * , + * ricardo monteiro * , * jorge e. santos * _ damtp , centre for mathematical sciences , university of cambridge , + wilberforce road , cambridge cb3 0wa , united kingdom _ + _ the niels bohr international academy , the niels bohr institute , + blegdamsvej 17 , dk-2100 copenhagen , denmark _ + _ department of physics , ucsb , santa barbara , ca 93106 , usa _ +

1608.03673

i

near earth objects ( neos ) are small solar system bodies whose orbits bring them close to the earth s orbit . neos lie at the intersection of science , space exploration , and civil defense . because neos are constantly being replenished from sources elsewhere in the solar system , they act as compositional and dynamical tracers and allow us to probe environmental conditions throughout the solar system and the history of our planetary system . neos are the parent bodies of meteorites , one of our key sources of detailed knowledge about the solar system s development , and neo studies provide the needed context for this work . the space exploration of neos is carried out both through robotic spacecraft such as near @xcite ; hayabusa @xcite ; change 2 @xcite ; hayabusa 2 @xcite ; and osiris - rex @xcite ; as well as remote sensing observations using iras , spitzer , wise / neowise , akari , and other assets ( as reviewed in @xcite ) . energetically , some neos are easier to reach with spacecraft than the earth s moon @xcite , and neos offer a large number of targets with a range of physical properties and histories . neos present advanced astronautical challenges , and president obama announced in 2010 that missions to asteroids would form the cornerstone of nasa s exploration for the next decade or more ; the new asteroid retrieval mission @xcite is part of those activities . finally , neos are a civil defense matter : the impact threat from neos is real , as demonstrated again recently in chelyabinsk , russia , in february , 2013 @xcite . understanding the number and properties of neos affects our planning strategies , international cooperation , and overall risk assessment . the spitzer space telescope is a powerful neo characterization system . neos typically have daytime temperatures around 300 k. hence , their thermal emission at 4.5 microns is almost always significantly larger than their reflected light at that wavelength . we can therefore employ a thermal model to derive neo properties , with the primary result being derived diameters and albedos @xcite . measuring the size distribution and albedos and compositions for a large fraction of all known neos allows us to understand the scientific , exploration , and civil defense - related properties of the neo population . spitzer s sensitivity at 4.5 microns is unparalleled , allowing us to observe many hundreds of neos over the course of the 20 month cycle 11 period . we present here a new warm spitzer exploration science program entitled neosurvey : an exploration science survey of near earth object properties ( pid11002 ; pi : trilling ) . in this paper we present the design of our program and results for the first 80 neos observed in this program ; results for the complete sample will appear in a forthcoming paper . we also introduce nearearthobjects.nau.edu , a publicly - accessible web page where all data and results from this program are posted , typically within a week of the data being released by the spitzer science center . in the 710 hours assigned to this program we use spitzer to observe 597 neos ; the vast majority of these are not accessible with any other facility . for each observed target , we use a thermal model to derive the diameter and albedo . this sample , when combined with existing data from our previous exploreneos work ( spitzer cycle 6 + 7 exploration science program ) , together with results from neowise and akari , includes nearly 20% of all neos known at the inception of this project . the majority of the infrared measurements of neos in this combined catalog with @xmath1 bodies smaller than around 175 meters diameter will come from this new program .

near earth objects ( neos ) are small solar system bodies whose orbits bring them close to the earth s orbit . we are carrying out a warm spitzer cycle 11 exploration science program entitled neosurvey a fast and efficient flux - limited survey of 597 known neos in which we derive diameter and albedo for each target . all data and derived diameters and albedos from this entire program are being posted on a publicly accessible webpage at nearearthobjects.nau.edu .

near earth objects ( neos ) are small solar system bodies whose orbits bring them close to the earth s orbit . we are carrying out a warm spitzer cycle 11 exploration science program entitled neosurvey a fast and efficient flux - limited survey of 597 known neos in which we derive diameter and albedo for each target . the vast majority of our targets are too faint to be observed by neowise , though a small sample has been or will be observed by both observatories , which allows for a cross - check of our mutual results . our primary goal is to create a large and uniform catalog of neo properties . we present here the first results from this new program : fluxes and derived diameters and albedos for 80 neos , together with a description of the overall program and approach , including several updates to our thermal model . the largest source of error in our diameter and albedo solutions , which derive from our single band thermal emission measurements , is uncertainty in , the beaming parameter used in our thermal modeling ; for albedos , improvements in solar system absolute magnitudes would also help significantly . all data and derived diameters and albedos from this entire program are being posted on a publicly accessible webpage at nearearthobjects.nau.edu .

astro-ph0611226

i

theory suggests that supernovae and/or winds from massive stars existing in clusters confined to the disk of the galaxy produce bubbles in the interstellar medium which expand , becoming superbubbles , and burst out of the galactic disk producing collimated outflows into the galactic halo ( norman & ikeuchi 1989 ; tenorio - tagle & bodenheimer 1988 ) . the superbubbles , which create cavities in the atomic hydrogen gas in the disk of the galaxy , contain a plasma of hot gas , high energy photons , and cosmic rays ( crs ) . when a bubble s wall bursts at high latitudes the structure is termed a `` chimney '' since the cavity and its walls act as a conduit for the outflow of this plasma towards the halo of the galaxy ( see e.g. de avillez & berry 2001 ) . in addition , the magnetic field that is oriented parallel to the disk of the galaxy is `` frozen '' into the plasma and is thus `` pulled '' upwards with the shell material as the bubble expands . consequently , it is predicted that these conduits should have magnetic field lines that run tangential to the shell ( norman & ikeuchi 1989 ; basu , johnstone & martin 1999 , hereafter bjm99 ) . an unusual , cone shaped void observed in neutral hydrogen ( normandeau , taylor & dewdney 1996 , hereafter ntd96 ) , which has the star cluster ocl 352 at its base , is one of the few observationally identified galactic chimney candidates and has come to be known as the `` w4 chimney '' . it was proposed that the region has been evacuated of by the winds of 9 o - type stars that are part of the open cluster ocl 352 . in this case the stellar wind scenario is favoured over the supernovae scenario since the cluster seems too young to have had any supernovae occur and the energy output of the winds appears to be sufficient to account for the void ( ntd96 ) . estimates of the age of ocl 352 range from 1.32.5 myr ( dennison , topasna & simonetti 1997 , hereafter dts97 , and references therein ) to 3.74.3 myr ( ntd96 ) . we adopt a distance to the region of 2.35 kpc . the `` chimney '' region is located above ocl 352 and is a distinct component from the ionized `` w4 loop '' , which is located below ocl 352 ( normandeau , taylor & dewdney 1997 ) . we consider only the structure that is above the star cluster and above the ridge of ionized gas that defines the upper latitude structure of the w4 hii region . the hi images ( see ntd96 and figures [ fig : hi-43.40_general ] and [ fig : hi-43.40_faint ] ) make it clear that the regions above and below the cluster , i.e. above and below the upper ionized ridge of w4 , are different in nature : the upper region has been mostly cleared of hi , hence the possibility that it is a chimney or a superbubble . the lower region has not been cleared , at least not at the same velocities . the interpretation of terebey et al . ( 2003 ) and bjm99 that the superbubble structure includes the w4 loop is in contrast to this picture . while it is likely that both the w4 loop and the structure above w4 are powered by the same stars , they do not form one dynamical entity . the use of the term `` chimney '' provides a metaphor only for the part of the structure above w4 since a chimney not only has walls but it also has a fire at its base . in this case the fire is the ocl 352 cluster . to avoid unwieldy nomenclature , rather than referring to the structure as the w4 superbubble / chimney , we dub it g134.4 + 3.85 . the new name , however , should not be understood as implying that g134.4 + 3.85 has a different origin from w4 . indeed we will argue that both objects are thermal emission regions excited by the open cluster ocl 352 . in the radio rgime , at galactic latitudes of less than + 4 , the structure is reminiscent of norman & ikeuchi s ( 1989 ) conventional chimney model , i.e. a broken shell allowing crs and uv photons to escape to higher latitudes . the contrasting analysis of dts97 , using narrow - band data , is that w4 is an `` apparently closed superbubble '' . however the dts97 data suffer from substantial vignetting at the field edges which could lead the eye to see a bubble shape where none exists . this makes corroboration from other datasets desirable . additionally , the dts97 data do not include velocity information , which means that the observed emission could be from unrelated sources along the line of sight . bjm99 considered both the dynamics ( kompaneets modelling ) and the ionization of the superbubble based on the data from dts97 . of particular interest here is the conclusion of bjm99 that an open geometry in images and a closed one in data showing ionized gas are not mutually exclusive . the superbubble s shell could be sufficiently thin at high latitudes that , while it closes the shell and prevents streaming of gas towards higher latitudes , it does not hold back the ionizing radiation which then obliterates the at higher latitudes . this scenario is in fact likely according to these authors . in this paper we present new observations of radio continuum and hi emission , extending coverage from @xmath2 , the limits of earlier data , to @xmath3 . we analyze the spectral line emission as well as the 1420 mhz and 408 mhz radio continuum emission from this region for evidence supporting either the chimney or the superbubble picture . for the 1420 mhz continuum data , full polarization information is available . the data acquisition and processing are described in [ sec : data ] . image mosaics and false colour morphological analysis are presented in [ sec : mosaics ] . the emission is addressed in [ sec : hi ] . the polarization data are discussed in [ sec : polar ] . the inter - relationship between emission components is discussed in [ sec : inter ] and the magnetic field of the region is explored , using our polarization data , in [ sec : best ] . our analysis creates a picture of a _ fragmented _ superbubble , g134.4 + 3.85 , above w4 that may be in the process of evolving into a chimney possibly due to magnetic effects . while we use two separate names we believe that both `` objects '' are the outcome of the ionizing flux from ocl 352 , and are therefore in some sense just one object . in [ sec : discuss ] we discuss this picture , superbubble formation scenarios , and the superbubble s connection to the galactic halo . the paper is summarized in [ sec : conclu ] .

new observations at high latitudes above the region w4 show that the structure formerly identified as a chimney candidate , an opening to the galactic halo , is instead a superbubble in the process of fragmenting and possibly evolving into a chimney . we explore the connection between w4 and the galactic halo , considering whether sufficient radiation can escape from the fragmenting superbubble to ionize the kpc - scale loop discovered by reynolds , sterling & haffner .

new observations at high latitudes above the region w4 show that the structure formerly identified as a chimney candidate , an opening to the galactic halo , is instead a superbubble in the process of fragmenting and possibly evolving into a chimney . data at high galactic latitudes ( ) above the w3/w4 star forming region at 1420 and 408 mhz stokes i ( total power ) and 1420 mhz stokes q and u ( linear polarization ) reveal an egg - shaped structure with morphological correlations between our data and the data of dennison , topasna , & simonetti . polarized intensity images show depolarization extending from w4 up the walls of the superbubble , providing strong evidence that the radio continuum is generated by thermal emission coincident with the emission regions . we conclude that the parts of the region hitherto known as w4 and the newly revealed thermal emission are all ionized by the open cluster ocl 352 . assuming a distance of 2.35 kpc , the ovoid structure is 164 pc wide and extends 246 pc above the mid - plane of the galaxy . the shell s emission decreases in total - intensity and polarized intensity in various locations , appearing to have a break at its top and another on one side . using a geometric analysis of the depolarization in the shell s walls , we estimate that a magnetic field line - of - sight component of 3 to 5 exists in the shell . we explore the connection between w4 and the galactic halo , considering whether sufficient radiation can escape from the fragmenting superbubble to ionize the kpc - scale loop discovered by reynolds , sterling & haffner .

astro-ph0611226

r

mosaics showing the spectral line emission at velocities of interest are shown in figures [ fig : hi-43.40_general ] , [ fig : hi-43.40_faint ] , [ fig : hi-40 ] , and [ fig : hi-48 ] . the mosaics of continuum emission at 408 mhz and 1420 mhz , stokes i , q and u are presented in figures [ fig:408 ] through [ fig : qu ] . the grating rings that remain visible in the hi and polarization data are due to the high intensity sources w3 and 3c 58 . the 1420 mhz data were convolved to match the lower resolution ( @xmath43.7 ) of the 408 mhz data . the polarization data were convolved to a resolution of 5 to improve the signal to noise ratio and the stokes q and u images were combined to produce a polarized intensity image ( @xmath12 ) and a polarization angle map ( @xmath13 ) ( see figure [ fig : pipang ] ) . measurements of stokes i intensities and pi for 56 regions of interest are tabulated in west ( 2003 ) . [ [ sec : hi ] ] figure [ fig : hi-43.40_general ] shows the data at @xmath14 . the eastern wall of the superbubble is clearly visible up to + 5.5 , at which point it curves slightly inward and disappears . the western wall is only well defined up to + 3.4 . in the new data set presented here , there is no evidence of a cap at high latitudes in the . at lower latitudes , the cavity spans 5 channels and lsr velocities 38.46 to 45.05 . we consider the region defined by @xmath15 , @xmath16 , the latitudes associated with the shell described by dts97 . we assume that the cap would have a velocity width of 5 channels ( 8 ) , the velocity width of the cavity . averaging the signal over 5 channels , we could have detected a cap of column density @xmath17 @xmath18 . using 5 channels reduces @xmath19 from the value of the rms noise in a single channel , which is 3.3 k or @xmath20 @xmath18 . thus if such a cap had been detected its column density would be at the 6@xmath19 level . the observed column density in the top of the ionized bubble is @xmath21 @xmath18 . by comparison , the column density of electrons in the dts97 shell is @xmath22 @xmath23 . for this latter estimate we converted emission measure into column density using an average of dts97 s measurements of 4 points in the upper shell , t = @xmath24 k , their emission measure conversion of 1r = 2.8 pc @xmath25 , and their shell thickness estimate of 10 to 20 pc . if there was neutral material associated with this shell at a density comparable to that of the ionized material , we would not have been able to detect it . there is a small filament of pointing upward , away from the plane ( figure [ fig : hi-43.40_faint ] ) . this low level feature is present in four channels of the mosaic , from 41.76 to 46.70 . a line through this linear feature passes through ocl 352 . we will argue in [ sec : chimney ] that this is material within the superbubble which remains neutral , protected from the ionizing radiation by shadowing . this faint arc is well below the latitude of the cap claimed by dts97 and therefore below the upper boundary of the best fit kompaneets model found by bjm99 . furthermore , the upper tip of the vertical filament is above the ionized cap suggested by the dts97 data . it is noticeable that the ocl 352 cluster is at the base of the cone , as was described by ntd96 , whereas the kompaneets model by bjm99 , which was fit primarily to the h@xmath26 image , shows a bubble extending to lower latitudes , to the base of the ionized gas loop which forms the lower half of w4 . this conical shape is not unique - something similar is seen at the base of the aquila supershell ( maciejewski et al . the w4 cone extends approximately 200 pc upward from the ocl 352 cluster , based on the well - defined upper longitude wall . this is comparable to the cone at the base of the aquila supershell which extends roughly 175 pc for an assumed distance of 3.3 kpc . the most surprising result from the modeling by bjm99 is the implication of a very small scale height ( @xmath27 ) , namely 25 pc . this value was obtained by matching the aspect ratio of the superbubble as seen in h@xmath26 using the kompaneets model and assuming a distance of 2.35 kpc . using the data from the 26-m telescope , which extends further up in latitude , almost to + 10 , and fitting an exponential to the decay in column density , a scale height of 140 @xmath28 40 pc is found for the in the vicinity of the g134.4 + 3.85 ( c.f . figure [ fig : nvsz ] ) . a variety of different velocity intervals were used to test the robustness of this result , as well as different data sets ( 26-m data , cgps pilot project data , and cgps data ) , and all yield a scale height of approximately 140 pc , which is significantly larger than the 25 pc required by the model of bjm99 . this value compares well with the values of 135 pc quoted by lockman , hobbs & shull ( 1986 ) . apart from the contradiction with the prediction by bjm99 , this result is not particularly surprising : scale heights for the neutral medium are in the 100 - 200 pc range . clearly , however , although the fit of the kompaneets model to the shape of the w4 superbubble is very good , it does not address all of the physical processes occurring in this vicinity . in particular , magnetic fields may have contributed to the collimation ( komljenovic et al . 1999 , de avillez & breitschwerdt 2005 ( see [ sec : time ] ) ) . it should be noted that the scale height evaluated here used data from all longitudes covered by the available 26-m data , from 124.4to 144.4 with varying coverage in latitude . however , if only longitudes greater than those corresponding to g134.4 + 3.85 are used , the profile is greatly different for latitudes below + 6 , particularly between + 1.5 and + 4.0 where the high longitude data show a plateau instead of a decrease . the difficulty lies in deciding which profile is representative of the medium into which the superbubble expanded . the effect of including g134.4 + 3.85 itself in the longitude range is minor compared to the effect of what appears to be a partial shell at lower longitudes which may be associated with 3c 58 . these difficulties generate the uncertainty of @xmath28 40 pc associated with the 140 pc scale height used in this paper . gray et al . ( 1999 ) presented polarization data from the low latitudes ( @xmath29 ) of this region . the high electron density combined with the magnetic field in the w3/w4/w5 region act as a `` faraday screen '' , causing the polarized , background galactic synchrotron radiation passing through the plasma to be rotated by the process of faraday rotation . these effects are observationally recognized as depolarized regions that follow the contours of the regions . depolarization occurs when the polarization angle varies by a significant amount between vectors contributing to a single measurement . the polarization angle can differ between adjacent lines of sight sampled by a single telescope beam ( beamwidth depolarization ) or vary along the path length ( depth depolarization ) . a third depolarization mechanism , bandwidth depolarization , becomes important if the rotation measure ( rm ) is very high at the observing wavelength , and so the angle may change by a large amount across the observing band . bandwidth depolarization is not significant in this study as typical rms in the region are on the order of @xmath30 and to produce significant depolarization over the 35 mhz observing band of these observations , a rm of @xmath41400 would be required ( brown 2002 ) . in fig . [ fig : qu ] and fig . [ fig : pipang ] we see that the depolarization extends without interruption from w4 up the `` walls '' of g134.4 + 3.85 . this is seen in stokes q and u and in polarized intensity . the continuity of depolarization from w4 to the walls of the superbubble provides strong evidence that the superbubble is connected to the hii region ; this is not a chance superposition . a temperature spectral - index map ( west 2003 ) also suggests that w4 and g134.4 + 3.85 are a single coherent structure . an unusual wishbone - shaped feature is visible in both stokes q and stokes u as well as in polarized intensity and polarization angle maps . this feature has no counterpart in stokes i , total - intensity . the feature appears above g134.4 + 3.85 with approximate center coordinates ( 134.9 , + 7.1667 ) ( see fig . [ fig : qu ] and fig . [ fig : pipang ] ) . the morphology of the object suggests a shell - like structure . a local steepening of the spectral index is observed south of the wishbone ( west 2003 ) . a bright , comma - shaped knot of strong polarized intensity with approximate center coordinates of ( 134.5 , + 2.58 ) is particularly prominent in polarized intensity ( fig . [ fig : pipang ] ) but invisible in total - intensity . it is @xmath40.5 wide and @xmath40.2 high and has a peak polarized intensity of 0.46 k. the object appears near the base of the prominent v - shaped filaments which are visible in both and 60 @xmath31 m iras dust emission . however , there is no clear morphological evidence of an association . the simbad database was searched for catalogue objects which might be coincident with the comma - shaped knot on the plane of the sky . a prominent object in this region is an o8 star , bd+62 424 with coordinates 134.53 , + 2.46 . there have been two , distinctly different heliocentric radial velocity measurements for this star : abt , levy , & gandet ( 1972 ) measured a value of 42.5 ( 40.2 lsr ) while fehrenbach et al . ( 1996 ) measured a value of 9 ( 6.7 lsr ) . the measurement by abt et al . is consistent with the chimney velocities as observed in the spectral line . however , the radial velocity measurement of fehrenbach et al . ( 1996 ) yields a kinematic distance of @xmath4800 pc ( brand & blitz 1993 ) implying that this star is a foreground object . the high polarized intensity of this knot suggests that it may be closer than the w4 region as it suffers less depolarization than the surrounding region .

data at high galactic latitudes ( ) above the w3/w4 star forming region at 1420 and 408 mhz stokes i ( total power ) and 1420 mhz stokes q and u ( linear polarization ) reveal an egg - shaped structure with morphological correlations between our data and the data of dennison , topasna , & simonetti . we conclude that the parts of the region hitherto known as w4 and the newly revealed thermal emission are all ionized by the open cluster ocl 352 . assuming a distance of 2.35 kpc , the ovoid structure is 164 pc wide and extends 246 pc above the mid - plane of the galaxy .

new observations at high latitudes above the region w4 show that the structure formerly identified as a chimney candidate , an opening to the galactic halo , is instead a superbubble in the process of fragmenting and possibly evolving into a chimney . data at high galactic latitudes ( ) above the w3/w4 star forming region at 1420 and 408 mhz stokes i ( total power ) and 1420 mhz stokes q and u ( linear polarization ) reveal an egg - shaped structure with morphological correlations between our data and the data of dennison , topasna , & simonetti . polarized intensity images show depolarization extending from w4 up the walls of the superbubble , providing strong evidence that the radio continuum is generated by thermal emission coincident with the emission regions . we conclude that the parts of the region hitherto known as w4 and the newly revealed thermal emission are all ionized by the open cluster ocl 352 . assuming a distance of 2.35 kpc , the ovoid structure is 164 pc wide and extends 246 pc above the mid - plane of the galaxy . the shell s emission decreases in total - intensity and polarized intensity in various locations , appearing to have a break at its top and another on one side . using a geometric analysis of the depolarization in the shell s walls , we estimate that a magnetic field line - of - sight component of 3 to 5 exists in the shell . we explore the connection between w4 and the galactic halo , considering whether sufficient radiation can escape from the fragmenting superbubble to ionize the kpc - scale loop discovered by reynolds , sterling & haffner .

astro-ph0608188

i

with the measurement of visible linear polarization of field stars , followed by developments of near and far infrared ( respectively nir and fir ) and submillimetric polarimetry , it is now possible to trace magnetic field structures from the scale of the milky way to that of star forming regions and cores . in the diffuse interstellar medium ( ism ) , the general assumption that elongated dust grains usually have their smallest axis aligned in a direction comparable to that of the local magnetic field has lead to a toroidal representation of the galactic magnetic field . a similar topology of the magnetic field can also sometimes be observed in other galaxies ( e.g. @xcite ) . on the smaller scales of molecular clouds , a similar relation exists between grain alignment and magnetic field directions ( see @xcite for an exciting review on the subject ) and many topologies of the magnetic field are suspected to exist . among others , helicoidal , toroidal , poloidal and hourglass configurations have been proposed to interpret observed polarization patterns , taking care of the physical conditions in these environments ( e.g. , orion a , m17 ) . however , one of the most important limitations of linear polarimetry is that we only get a two - dimensional projected average representation of the magnetic field topology because of the integration on the plane of the sky of the contribution to the polarized emission due to each aligned grain , or its dichroic absorption for visible / nir observations . this leads to a degeneracy problem since many three dimensional ( 3d ) topologies of the field can produce identical polarization patterns . a method to get rid of this degeneracy problem is the use of models . on the scale of relatively nearby filamentary molecular clouds and cores , this method has been used and allows in some cases to select one field topology among many possible ones ( e.g. , @xcite , @xcite ) . in addition to models , other diagnostics of magnetic fields can be used to lift the degeneracy due to the plane - of - sky integration . when column densities are high enough , observations of the zeeman effect can yield the line - of - sight component of the magnetic field strength ( e.g. @xcite ) . finally , by determining the ion - to - neutral molecular line - width ratio in non turbulent regions with a linear flow , it is possible to determine the angle between the field direction and the line of sight ( @xcite , @xcite , @xcite ) . by combining all three methods together , we get the 3d field topology ( e.g. , @xcite for m17 , @xcite for orion a ) . the observation of zeeman splitting of spectral lines requires bright dense cores , but even in other regions , it is possible to get the 3d geometry of the field even if the field strength is unknown . these methods can inform us about how magnetic fields can contribute to cloud dynamics , but our ultimate goal is to understand the competition between gravitational , thermal , magnetic , and turbulent forces . more specifically , magnetic fields and turbulence are both competing to slow down the star formation process , otherwise stars would form much faster than observations show . combining polarization modeling techniques ( e.g. , @xcite ) and predictions for magnetized simulations of turbulence ( e.g. , @xcite , @xcite ) , one can hope to be able to determine the relative contributions of magnetic fields and turbulence . to reach this goal , and to understand how magnetic fields thread the dark filaments , and to put observational constraints on modeling we propose to make comparisons of magnetic fields as seen in and around individual objects . this approach , namely a multi - scale analysis of the magnetic field , has begun to be done via comparisons of visible , nir , fir and/or submm polarization data in the omc1 ( @xcite ) , omc3 ( @xcite ) and gf 9 regions ( @xcite ) . in these works , aspects of the galactic magnetic field extending on tens of degrees are compared with aspects of the clouds probed in the densest regions of the clouds with resolutions @xmath2 , but there is generally a lack of information between these two scales . here we present observations at an intermediate scale , as much as the presence of field stars allows it , to have a clearer view of the topology of the field at the interface ism / filamentary molecular clouds . from a general point of view , this approach should provide new insights on the way magnetic fields and clouds are dynamically coupled and shaped . in this paper we address this problem for the gf 9 filamentary molecular cloud region . a forthcoming paper will address the more complex situation for the orion a region . a description of data available about gf 9 is given in section [ gf9region ] . observations and observational results are presented in section [ obsres ] . an analysis and a discussion follow in section [ discuss ] , and our conclusions are given in section [ conclu ] .

new visible polarization data combined with existing ir and fir polarization data are used to study how the magnetic field threading the filamentary molecular cloud gf 9 connects to larger structures in its general environment . the visible polarization is smooth and has a well - defined orientation . hence , in spite of the fact that the spatial resolution is not the same in the visible / nir and in the fir data , all the data put together indicate that the field direction changes with the spatial scale . finally , the chandrasekhar and fermi method is used to evaluate the magnetic field strength , indicating that the core region is approximately magnetically critical .

new visible polarization data combined with existing ir and fir polarization data are used to study how the magnetic field threading the filamentary molecular cloud gf 9 connects to larger structures in its general environment . we find that when both visible and nir polarization data are plotted as a function of extinction , there is no evidence for a plateau or a saturation effect in the polarization at 1.3 as seen in dark clouds in taurus . this lack of saturation effect suggests that even in the denser parts of gf 9 we are still probing the magnetic field . the visible polarization is smooth and has a well - defined orientation . the ir data are also well defined but with a different direction , and the fir data in the core region are well defined and with yet another direction , but are randomly distributed in the filament region . on the scale of a few times the mean radial dimension of the molecular cloud , it is as if the magnetic field were ` blind ' to the spatial distribution of the filaments while on smaller scales within the cloud , in the core region near the iras point source psc 20503 + 6006 , polarimetry shows a rotation of the magnetic field lines in these denser phases . hence , in spite of the fact that the spatial resolution is not the same in the visible / nir and in the fir data , all the data put together indicate that the field direction changes with the spatial scale . finally , the chandrasekhar and fermi method is used to evaluate the magnetic field strength , indicating that the core region is approximately magnetically critical . a global interpretation of the results is that in the core region an original poloidal field could have been twisted by a rotating elongated ( coreenvelope ) structure . there is no evidence for turbulence and ambipolar diffusion does not seem to be effective at the present time .

astro-ph0608188

c

as can be seen in figure [ polmap ] and in the histogram of position angles in figure [ anghisto ] , the polarization pattern in the vicinity of gf 9 is relatively well oriented on the plane of the sky with a mean direction of @xmath31 and a standard deviation @xmath50 . since the filament has an incurved concentric shape reminiscent of supernova remnants ( @xcite ) , one can ask if a possible object at the origin of this shape could be located somewhere in the region delimited by the black circle traced in figure [ skymap ] . a possible candidate seems to be the post agb star glmp 1012 ( see figure [ skymap ] ) but given its distance estimate @xmath51 3 kpc ( @xcite ) compared with those of gf 9 , even by considering @xmath52 km s@xmath53 winds , it is difficult to defend the view that this source can be responsible for the shape of the filaments . however since the problem is tridimensional , a source at the origin of such a shape could also be located outside of the domain defined by this circle . maybe such a source exists but has not been detected , or the apparent concentric shape of the dense ism is only a projection effect and other mechanisms , such as turbulent fluctuations in the ism or density waves , are at the origin of its formation . a quick look in the catalogs reveals no potential candidate in a circle a few degrees in diameter around the position r.a.(2000 ) = 20@xmath54 and dec.(2000 ) @xmath55 . if now one compares the direction of the inferred magnetic field with the orientation of the filamentary structures on the plane of the sky , it seems that the magnetic field has approximately the same orientation over an arc circle which covers about 135@xmath56 , from a position angle ( p.a . ) = 270@xmath56 to 45@xmath56 as measured from the center of the circle in figure [ skymap ] . when looking at both maps from east to west in figure [ skymap ] and 2 , a slow rotation of the direction of the field is present , the average directions near the core and near the filament regions differ by about 10@xmath56 ( see table [ means ] ) , significantly under the variation in p.a . of the filament over the whole region . moreover from east to west , there is a great dispersion in the orientation of the filamentary structures , thus it is hard with this two dimensional representation to see a direct impact of the field on the apparent shape of the filaments . this is in agreement with the fact that in other regions there is no prefered projected angle on the plane of the sky between the directions of the ambient magnetic field and the orientation of the filamentary structures ( e.g. @xcite , @xcite ) . see also @xcite for a discussion on this subject . comparisons of the orientation of the magnetic field according to the visible , ir and fir data around and in the core and the filament regions can be done by looking at the maps in figures [ mapcore ] and [ mapfila ] respectively . in the core region , when going from visible to ir , to fir data , one can see an anticlockwise rotation of the p.a . by about 63@xmath56 in total . for each of these two regions , the means and dispersions of the degree of polarization and of the p.a . of the visible , ir and fir data are compiled in table [ means ] . the p.a . for the fir data corresponds to the observed polarization , rotated by 90@xmath56 to give the direction of the magnetic field . in figures [ mapcore ] and [ mapfila ] , only fir data for which the p.a . is approximately the same when using the klc instrumental polarization and the c - off instrumental polarization ( clemens 1999 ) are shown . the degree of polarization of the fir data is not considered in the present analysis . table [ means ] also includes similar information for the whole gf 9 region and for the local galactic scale , to be discussed below . _ comparison of visible and ir data _ first , visible and ir data do not probe the same regions on the plane of the sky . visible data probe the more diffuse parts around prestellar cores while the ir data probe the denser phases where protostellar cores are present . secondly we note that in the core region the ir vectors have approximately the same orientation which implies that the ir polarization is not intrinsic to each star but produced by dichroic absorption by aligned grains . this statistical argument , however , does not apply in the filament region where only one ir measurement with sufficient signal - to - noise ratio is available . thirdly , in both cases the resolution used with each technique is comparable . fourthly , the simple fact that the ` ir ' magnetic field has not the same orientation than the ` visible ' one implies that if the grains observed with these two techniques have identical properties , and if their dichroic absorption properties are the same at both ir and visible wavelengths , then the net polarization produced by aligned grains located in the densest parts of the cloud dominates the net polarization produced by aligned grains located in the foreground diffuse ism . all these facts , in addition to the dependence of @xmath22 with @xmath25 mentionned in section [ pversusav ] , suggest that there is a real rotation of the magnetic field lines in the core region when moving across the plane of the sky . _ comparison of ir and fir data _ firstly , ir and fir data probe the same regions on the plane of the sky in both the core and the filament regions . secondly we note that in the core region the fir vectors are very well aligned but not with the same p.a . than the ir vectors . ir data result from a magnetic field oriented at p.a . @xmath57 while fir data suggest a magnetic field oriented at p.a . thirdly , the resolution with these two techniques is not the same . the fir data resolution is @xmath59 , many times the ` pencil ' beam resolution of the ir and visible data . finally , fir observations probe the radiation emitted by grains mainly located in the densest parts of the cloud while ir observations probe grains located between the stars and the observer . when looking at figure [ mapcore ] , we see that ir and fir data cover a common area @xmath60 in size . thus if these two observational techniques probe the same column densities but at two different resolutions , one should be able to explain the rotation of the magnetic field lines as seen at these two wavelengths . a first hypothesis is that a given magnetic field morphology leads to several orientations according to the resolution at which it is observed ( see @xcite , but also @xcite ) . however , here we see that ir data are spatially distributed through fir data , thus by using a simple principle of juxtaposition it seems impossible to reproduce the mean orientation of fir vectors seen through @xmath59 beams by combining several ir vectors with very small cross sections . on the other hand , since the mean position angle of the stars observed in the visible is not the same than the one for stars observed in the ir , these ir - observed stars should not be foreground to the clouds , but rather embedded in or background to the clouds . in what follows we review possible explanations for the shift in position angles . \(1 ) the stars observed in the ir could be located inside the gf 9 core . if this was the case , the impact of their presence on their immediate environment should be observed . iras observations of these stars show that their luminosities satisfy @xmath61 ( see section [ gf9region ] ) , which would argue against them being class 0 sources , i.e. , very young . therefore , we reject the hypothesis that these ir stars are all embedded in the gf 9 core . \(2 ) the stars observed in the ir could be background to the gf 9 core region . this is suggested by their position in the @xmath62 diagram shown in figure [ pav ] . two possibilities can be invoked to explain the difference in position angles : + ( a ) a first and may be naive approach is assume that grains along the line of sight to the gf 9 core are all at the same temperature , and that both the ir and fir observational techniques probe all grains with the same efficiency . if this is right , the mean position angles observed at both wavelengths should be similar , except for the known 90@xmath63 difference between them . in this scenario , the difference in position angles is explained by a second cloud or filamentary structure located behind the gf 9 core , and in which dust grains would be aligned differently . + ( b ) a second and probably more realistic scenario is to emphasize differences related to the intrinsic nature of both observational techniques . based on point ( 1 ) mentioned above , the assumption of a dust temperature gradient for an externally heated cloud seems reasonable . in this case , the fir measurements should be more sensitive to `` cold '' dust grains aligned in the densest regions of the core than to `` hot '' dust grains aligned in the envelope and in the diffuse ism . on the other hand , ir observations should probe all the grains along the line of sight , independently of their temperature . thus grains aligned differently in the envelope than in the denser core should both contribute to the ir polarization position angle , explaining the offset in position angles . while scenario ( 2b ) does not reject the possibilty of a second cloud or filament evoked in ( 2a ) , it has the benefit to propose a simple and consistent explanation . thus we prefer scenario ( 2b ) , in which the intermediate position angles of ir vectors shown in figure [ mapcore ] may result from a vectorial addition of both fir and visible vectors covering this region and its vicinity . _ comparisons of the magnetic fields orientations with the cores elongations _ we compare in table [ offsets ] the orientations of five protostellar cores spread into the filaments with the magnetic field orientations . orientations of the cores l1082a , b and c were determined with the @xmath64 lines of nh@xmath16 while orientations of the lm cores are based on the visible dss data for l1082c and visible extinction for lm351 . ] at first sight we see that , except for l1082b , these dark condensations have a tendency to be elongated along the filaments as was noticed by @xcite ( see figures [ skymap ] and [ polmap ] ) . names , positions and p.a . of these cores are shown in table [ offsets ] in columns 1 through 4 respectively . for objects lm351 and l1082c , located in the core region , and for objects lm349 and lm350 , located in the filament region , the offset , @xmath65 , on the plane of the sky between the p.a . of each protostellar core and the mean magnetic field orientation probed with visible data is shown in column 5 . the same is done with the ir and fir measurements in columns 6 and 7 respectively . these offsets were not estimated for l1082b since the magnetic field direction is undersampled around this object . on larger scales , the magnetic field is mostly along the minor axis of the cores , as can be seen in figure [ polmap ] . however , on smaller scales , if we accept that ir measurements can probe the magnetic field in dense regions as it is suggested by the variations of @xmath22 with @xmath66 shown in figure [ pav ] , we see that a rotation of the field is apparent in the core region . on this smaller spatial scale the field is well aligned in the core region in a direction mainly parallel to the cores major axes . turbulence models such as those developed by @xcite show that matter may flow onto cores along filaments with the field being stretched along the filaments . in such a case , the field would tend to be along the major axis of the elongated low - density structures connected with higher density cores . however , such models show that the polarization pattern probing dust in the low density structures would be chaotic rather than smooth and well aligned . moreover , @xcite showed recently that a velocity gradient of 2.3 km s@xmath53 pc@xmath53 is present along the major axis of the core gf9 - 2 but none along its minor axis . therefore , if we assume that sources named lm351 , l1082c and gf 9 - 2 are associated to a common spatial volume traced with different tracers , and if we assume that the velocity gradient along the major axis of gf 9 - 2 is due to rotation of the core , this picture suggests that an original poloidal field has been twisted on small scales by the rotation of the core into a toroidal field . this would be consistent with a magnetic support model . on the other hand , this effect does not seem to be present in the filament region where the magnetic field probed with ir data is mainly parallel to the small axes of the cores detected in this area , in approximately the same direction than the magnetic field seen at greater scales . but on the other hand if fir measurements are reliable , the chaotic fir polarization pattern suggests that turbulence plays an active role in the filament region . finally comparison of both regions suggests a magnetic field interacting differently , and maybe less with its surrounding medium in the filament than it does in the core region , in agreement with the evolutionary stage of these two regions . additional ir data would be necessary to confirm this point , and the quality of fir measurements should of course be confirmed in both regions . the mean orientation of the ambient magnetic field can also be compared to the local galactic magnetic field orientation . figure [ mapgal ] shows a polarization map in galactic coordinates based on measurements compiled by @xcite with data for which @xmath67 . the region presents a complicated picture because we are looking down a spiral arm and possibly because of the influence of the cygnus star - forming complex . in their works @xcite and @xcite have used a large set of polarization data and studied the inferred magnetic field geometry in this part of the galaxy . at first sight , the simple picture of a toroidal magnetic field implies that the magnetic field lines should point in the direction toward @xmath68 . in their statistical study @xcite show that this trend is effectively real and are also able to detect the curvature of the local spiral arm . as mentionned by @xcite , since gf 9 is at a relatively close distance it is probably threaded by the magnetic field in the local spiral arm . jones compares the orientation of the mean ir vector in the core region with the visible vectors on a greater scale , and shows that this vector points in the direction of the ` vanishing point ' approximately located at @xmath68 . we can see this vector denoted by ` ir ' in figure [ mapgal ] . we also show the mean visible vector ` v ' in this map . it does not point in the same direction than the ` ir ' vector but it is approximately parallel to its nearest neighbours . all these facts suggest that it is preferable to use data probing the diffuse parts of the ism in the environments of molecular clouds to compare ambient to the cloud and galactic magnetic field s orientations . in order to estimate if the core region observed in cs by @xcite is magnetically supercritical or magnetically subcritical , we use the @xcite method to estimate the magnetic field strength . the magnetic field strength in the plane - of - sky is estimated with the expression : @xmath69 where @xmath70 is the polarization p.a . dispersion in degrees , @xmath71 is the molecular hydrogen density in molecules @xmath13 , @xmath72 is the fwhm line width in km s@xmath53 , and @xmath73 is the velocity dispersion ( see @xcite ) . we use only the ir data for the core region since we have no way of estimating the turbulent velocity dispersion for the larger area corresponding to the visible data . the value @xmath74 is taken from table [ means ] using the jones ir data . this value is provided by a relatively small set of six measurements for which the mean of the uncertainties is @xmath75 . if instead of a direct average , we use a weighted average for estimating the dispersion in p.a . , we get @xmath76 . finally , working with the p.a . directly instead of the vectors , the dispersions are @xmath77 and @xmath78 , weighted and unweighted respectively . all these values are close to each other and reflect the fact that there is little dispersion in p.a . in the cloud . therefore , we believe that despite the small number of measurements , we nevertheless have a representative value for the dispersion . the various parameters that we used for the cs core region and our results are shown in table [ strengths ] . once @xmath79 is derived , we estimate @xmath80 , the observed mass to flux ratio @xmath81 normalized to its critical value . this observed normalized mass to flux ratio is subject to geometrical bias , as explained by @xcite . in the case of estimating the total field from the plane - of - sky component of the field , two of the three components are known and the correction factor for @xmath80 is then @xmath82 , which corresponds to @xmath83 given in table [ strengths ] . this correction is statistical in nature since we do not know the appropriate angle for any individual object . in fact , there may not be a line of sight component to the field . using @xmath84 for the dispersion in p.a . is the quadratic sum of the dispersion @xmath85 and the mean uncertainty @xmath75 ] to take into account the uncertainties in the measurements would decrease the magnitude of @xmath79 and increase the magnitude of @xmath80 and @xmath87 by about 50% . for comparison , the dispersion in p.a . for the visible data around the core region is @xmath88 ( table [ means ] ) . with this value ( even though we are outside the area for which the cs line - widths have been measured ) , the values of @xmath80 and @xmath83 are larger by about 110% . these values are probably too large because the visible data cover a much larger area than just the core region . also , a bias exists in the chandrasekhar - fermi method that tends to cause estimated field strentghs to be too large and thus to underestimate values of @xmath80 ( e.g. @xcite ) . what is the effect of the distance @xmath89 on these results ? the column density @xmath90 is used to get the gas mass , so @xmath91 , where @xmath92 is the radius of the cloud , assumed to be spherical . the density @xmath93 . since @xmath94 , @xmath95 , @xmath96 and @xmath97 . if the distance is 200 pc instead of 440 pc as assumed for the values given in table [ strengths ] , @xmath98 would be closer to unity by about @xmath99 . is there additional possible evidence for a subcritical core ? @xcite identified two other tests to distinguish between ambipolar diffusion and turbulence as supporting mechanisms for star formation . if ambipolar diffusion is acting , one would expect an hourglass configuration for the magnetic field . but the distribution of the ir polarization vectors ( see fig [ mapcore ] ) suggests a smooth field , or even a slight curvature in the opposite direction than expected for an hourglass shape . a third test identified by @xcite , if ambipolar diffusion is acting one expects @xmath100 with @xmath101 approaching 1/2 for larger densitites ( @xmath102 @xmath13 ) . the values derived here are more or less compatible with this relation ( see figure 1 in @xcite ) . in addition , the comparison of the magnetic field orientations with the elongations of the cores seen in table [ offsets ] is not in general compatible with ambipolar diffusion , since in that case the cores would be perpendicular to the direction of the magnetic field . taking all the above arguments into account , our data suggest that the gf 9 core region is approximately magnetically critical . ambipolar diffusion does not appear to be supported . also , turbulence would produce a randomness in the polarization vectors which is not observed . the picture presented in section [ tosmall ] of an original poloidal field which is transformed into a toroidal field by rotation appears most plausible .

we find that when both visible and nir polarization data are plotted as a function of extinction , there is no evidence for a plateau or a saturation effect in the polarization at 1.3 as seen in dark clouds in taurus . the ir data are also well defined but with a different direction , and the fir data in the core region are well defined and with yet another direction , but are randomly distributed in the filament region . on the scale of a few times the mean radial dimension of the molecular cloud , it is as if the magnetic field were ` blind ' to the spatial distribution of the filaments while on smaller scales within the cloud , in the core region near the iras point source psc 20503 + 6006 , polarimetry shows a rotation of the magnetic field lines in these denser phases .

new visible polarization data combined with existing ir and fir polarization data are used to study how the magnetic field threading the filamentary molecular cloud gf 9 connects to larger structures in its general environment . we find that when both visible and nir polarization data are plotted as a function of extinction , there is no evidence for a plateau or a saturation effect in the polarization at 1.3 as seen in dark clouds in taurus . this lack of saturation effect suggests that even in the denser parts of gf 9 we are still probing the magnetic field . the visible polarization is smooth and has a well - defined orientation . the ir data are also well defined but with a different direction , and the fir data in the core region are well defined and with yet another direction , but are randomly distributed in the filament region . on the scale of a few times the mean radial dimension of the molecular cloud , it is as if the magnetic field were ` blind ' to the spatial distribution of the filaments while on smaller scales within the cloud , in the core region near the iras point source psc 20503 + 6006 , polarimetry shows a rotation of the magnetic field lines in these denser phases . hence , in spite of the fact that the spatial resolution is not the same in the visible / nir and in the fir data , all the data put together indicate that the field direction changes with the spatial scale . finally , the chandrasekhar and fermi method is used to evaluate the magnetic field strength , indicating that the core region is approximately magnetically critical . a global interpretation of the results is that in the core region an original poloidal field could have been twisted by a rotating elongated ( coreenvelope ) structure . there is no evidence for turbulence and ambipolar diffusion does not seem to be effective at the present time .

astro-ph0608188

c

visible linear polarization data taken at the mont - mgantic observatory on 78 stars in the vicinity of the dark filamentary cloud gf 9 were presented and compared with available nir and fir polarization data covering part of the same region . our main conclusions are : there is no evidence for saturation of polarization as a function of extinction for both the visible and nir data , suggesting that even in the denser regions the same grain properties and grain alignment mechanisms apply , and that the magnetic field is still being probed adequately there . all these facts put together suggest that _ in gf 9 the magnetic field changes direction with the spatial scale . _ the field differs by @xmath103 in the gf 9 core compared to the surrounding region . ambipolar diffusion does not appear to be supported given the current evidence . the effects expected from turbulence are definitely missing . a global interpretation of the results is that an original poloidal field could have been twisted into a toroidal configuration by a rotating elongated structure during its collapse . future work should check if the trend in polarization position angles to rotate counterclockwise with increasing wavelength still continues in the submm . also , as the lack of saturation of polarization as a function of extinction suggests , if dust grains are magnetically aligned there should be no polarization hole in the submm in the core and the filament regions . as an additional benefit , submm polarization would afford a higher spatial resolution than the fir data discussed here . we thank the conseil de recherche en sciences naturelles et en gnie du canada for supporting this research . the authors thank j. s. greaves for providing information about observations of gf 9 with scubapol at the jcmt , as well as b. malenfant and g. turcotte for their helpful and friendly support during observations at mont - mgantic observatory . we also thank an anonymous referee for his constructive comments and helpful suggestions . this work made extensive use of the simbad database at the canadian astronomy data center , which is operated by the dominion astrophysical observatory for the national research council s herzberg institute of astrophysics . andr , ph . ; ward - thompson , d. and barsony , m. 2000 , protostars and planets iv , p59 arce , h. g. ; goodman , a. a. ; bastien , p. ; manset , n. and sumner , m. 1998 , apj 499 , l93 barnard , e. e. 1927 , atlas of selected regions in the milky way , carnegie institute of washington bastien , p. and mnard , f. 1990 , apj 364 , 232 benson , p. j. @xmath33 myers , p. c. 1989 , apjss , 71 , 89 chandrasekhar , s. and fermi , e. 1953 , apj 118 , 113 ciardi , d. r. ; woodward , c. e. ; clemens , d. p. ; harker , d. e. and rudy , r. j. 2000 , aj 120 , 393 ciardi , d. r. ; woodward , c. e. ; clemens , d. p. ; harker , d. e. and rudy , r. j. 1998 , aj 116 , 349 clemens , d. ; kraemer , k. and ciardi , d. 1999 , workshop on iso plarisaton observations , eds . r.j . laureijs @xmath33 r. siebenmorgen . esa - sp 435 , p.7 crutcher , r. m. 2004 , astrophysics and space science , v. 292 , issue 1 , p. 225 crutcher , r. m. 1999 , apj 520 , 706 crutcher , r. m. ; nutter , d. j. ; ward - thompson , d. and kirk , j. m. 2004 , apj 600 , 279 dobashi , k. ; uehara , h. ; kandori , r. ; sakurai , t. ; kaiden , m. ; umemoto , t. and sato , fumio 2005 , pasj 57 , sp1 , 1 dobashi , k. ; bernard , j. p. ; yonekura , y. and fukui , y. 1994 , apjss 95 , 419 fiege , d. j. and pudritz , r. e. 2000 , apj 544 , 830 froebrich , d. 2005 , apjs 156 , issue 2 , pp . 169 - 177 furuya , r. s. ; kitamura , y ; wootten , a. ; claussen , m. j. and kawabe , r. 2003 , apjss , 144 , 71 furuya , r. s. ; kitamura , y ; shinnaga , h. 2005 , poster presented at protostars and planets v , no 8087 goodman , a. a. ; benson , p. j. ; fuller , g. a. and myers , p. c. 1993 , apj 406 , 528 goodman , a. a. ; jones , t. j. ; lada , e. a. and myers , p. c. 1995 , apj 448 , 748 gsten , r. 1994 , in _ the cold universe _ , eds . th . montmerle et al . ( editions frontires : gif - sur - yvette ) , p.169 heiles , c. ; goodman , a. a. ; mckee , c. f. and zweibel , e. g. 2000 , protostars and planets iv , p279 heiles , c. 2000 , aj 199 , 923 heiles , c. 1996 , apj 462 , 316 heitsch , f. ; zweibel , e. g. ; mac low , m - m . ; li , p. ; norman , m. l. , 2001 , apj 561 , 800 heyer , m. h. ; vrba , f. j. ; snell , r. l. ; schloerb , f. p. , strom , s. e. , goldsmith , p. f. & strom , k. m. 1987 , apj 321 , 855 hilton , j. @xmath33 lahulla , j.f . 1995 , aass 113 , 325 houde , m. ; bastien , p. ; dotson , j. l. ; dowell , c. d. ; hildebrand , r. h. ; peng , r. ; phillips , t. g. ; vaillancourt , j. e. and yoshida , h. 2002 , apj 569 , 803 houde , m. ; bastien , p. ; peng , r. ; phillips , t. g. and yoshida , h. 2000a , apj 536 , 857 houde , m. ; peng , r. ; phillips , t. g. ; bastien , p. and yoshida , h. 2000b , apj 537 , 245 houde , m. ; phillips , thomas g. ; bastien , p. ; peng , r. and yoshida , h. 2001 , apj 547 , 311 houde , m. ; dowell , c. d. ; hildebrand , r. h. ; dotson , j. l. ; vaillancourt , j. e. ; phillips , t. g. ; peng , r. and bastien , p. 2004 , apj 604 , 717 jones , t. j. 2003 , aj , 125 , 3208 lazarian , a. 2003 , jqsrt 79 - 80 , 881 - 902 lee , c. w. @xmath33 myers , p. c. 1999 , apjss 123 , 233 lynds , b. d. 1962 , apjs 7 , 1 manset , n. and bastien , p. 1995 , pasp 107 , 483 matthews , b. c. ; wilson , d. w. and fiege , j. d. 2001 , apj 562 , 400 myers , p. c. , fuller , g. a. , goodman , a. a. , @xmath33 benson , p. j. 1991a , apj , 376 , 561 myers , p. c. and goodman , a. a. 1991b , apj 373 , 509 padoan , p. ; goodman , a. a. ; draine , b. t. ; juvela , m. ; nordlund , . and rgnvaldsson , . e. 2001 , apj 559 , 1005 preite - martinez , a. 1988 , a@xmath33a 76 , 317 scarrott , s. m. ; rolph , c. d. ; @xmath33 semple , d. p. 1990 , in galactic and interstellar magnetic fields , iau symposium 140 , edited by r. beck and p. p. kronberg ( kluwer , dordrecht ) , p. 245 serkowski , k. , mathewson , d. l. , @xmath33 ford , v. l. 1975 , apj vol . 196 , p. 261 - 290 . schleuning , d. a. 1998 , apj 493 , 811 schneider , s. @xmath33 elmegreen , b. g. 1979 , apjss 41 , 87 valle , j. p. ; greaves , j. s. and fiege , j. d.2003 , apj 588 , 910 viotti , n. r. 1969 , mem . soc . astron . italiana , 40 , 75 walawender , j. m. , zweibel , e. g. @xmath33 heiles , c. 2001 , baas , 198 , 41.05 wiesemeyer , h. 1998 , asp conf . series , vol . , 189 wiesemeyer , h. 1997 . the spectral signature of accretion in low mass protostars . phd dissertation , university of bonn lrrrrrrrrcc no&91&20:47:23.5&+60:12:59.5&[email protected]&[email protected]&1.61&1 + 0424600447 & 40 & 20:47:25.8 & + 60:17:41.2&[email protected]&[email protected]&1.34&1 + no&120&20:47:34.0&+59:51:54.4&[email protected]&[email protected]&2.09&1 + 0424601275&46&20:47:35.4&+60:03:35.1&[email protected]&[email protected]&1.89&0 + no&92&20:47:47.6&+60:01:02.2&[email protected]&[email protected]&2.14&1 + 0424601151&57&20:47:48.0&+60:06:49.4&[email protected]&[email protected]&1.78&1 + 0424600411&31&20:47:50.2&+60:14:40.6&[email protected]&[email protected]&1.39&1 + 0396300254&48&20:48:01.0&+59:57:01.1&[email protected]&[email protected]&1.89&1 + no&98&20:48:01.1&+60:00:47.1&[email protected]&[email protected]&2.13&0 + 0424600967 & 47&20:48:08.4&+60:00:24.6 & [email protected]&[email protected]&1.66&1 + 0424600359 & 39&20:48:11.5 & + 60:18:52.2&[email protected]&[email protected]&1.14&1 + 0424601339 & 36&20:48:17.9 & + 60:06:26.9 & [email protected]&[email protected]&2.22&1 + 0424600585 & 18&20:48:20.5 & + 60:01:15.2 & [email protected] & [email protected]&1.66&1 + 0424600629 & 17&20:48:25.5 & + 60:10:11.9 & [email protected] & [email protected]&1.97&0 + 0424600469 & 11 & 20:48:27.7 & + 60:32:54.5 & [email protected] & [email protected]&0.64&1 + 0424601143&13 & 20:48:30.0 & + 60:24:59.4 & [email protected] & [email protected]&0.98&1 + 0424601171 & 16&20:48:32.5 & + 60:15:08.4 & [email protected] & [email protected]&1.43&1 + 0424600521 & 10 & 20:48:40.8 & + 60:32:15.1 & [email protected] & [email protected]&0.66&1 + 0424600727 & 35&20:48:44.2 & + 60:09:52.9 & see table [ vardata]&&2.17 & + 0424601053 & 34&20:48:46.5 & + 60:09:42.4 & [email protected]&[email protected]&2.17&1 + 0424600659&54&20:48:47.1&+60:12:49.4&[email protected]&[email protected]&1.73&1 + 0424600961&37&20:48:47.3&+60:01:45.4 & [email protected]&[email protected]&1.24&1 + 0424601093&53&20:48:51.3&+60:13:46.1&[email protected]&[email protected]&1.69&1 + 0424600621 & 15 & 20:48:51.4&+60:15:27.6 & [email protected] & [email protected]&1.38&1 + 0424600109 & 14 & 20:49:03.7 & + 60:18:57.7 & [email protected] & [email protected]&1.27&1 + 0424601169&52&20:49:07.1&+60:05:05.0&[email protected]&[email protected]&1.17&1 + 0424600721&55&20:49:09.6&+60:18:43.4&[email protected]&[email protected]&1.56&1 + 0424600857 & 9 & 20:49:13.6 & + 60:30:03.6 & @xmath1050.11 & [email protected]&0.75&1 + no&90&20:49:14.1&+60:12:44.5&[email protected]&[email protected]&2.19&1 + 0424600123 & 8&20:49:14.4 & + 60:29:21.0 & 2.70@xmath104 0.12 & [email protected]&0.80&1 + 0424601087 & 38&20:49:15.7&+60:16:26.1 & [email protected]&[email protected]&1.97&1 + 0424600963&51&20:49:18.6&+60:05:50.6&[email protected]&[email protected]&1.17&1 + 0424600281&56&20:49:18.7&+60:20:20.9&[email protected]&[email protected]&1.42&1 + 0396300376 & 19&20:49:33.3 & + 59:56:54.5 & [email protected] & [email protected]&0.82&1 + 0424600981 & 7 & 20:49:33.7 & + 60:27:11.5 & [email protected] & [email protected]&0.85&1 + 0396300020 & 20&20:49:41.5 & + 59:56:15.7 & [email protected] & [email protected]&0.82&1 + 0424601133 & 21&20:49:44.1 & + 60:03:12.3 & [email protected] & [email protected]&0.84&1 + 0424601015 & 6 & 20:50:04.3 & + 60:24:04.9&[email protected] & [email protected]&1.35&1 + 0424601131 & 42&20:50:25.7&+60:24:15.8 & [email protected]&[email protected]&1.56&1 + 0424601183&50&20:50:25.8&+60:10:52.6&[email protected]&[email protected]&1.04&1 + 0424601341 & 33&20:50:31.9&+60:13:00.4 & [email protected]&[email protected]&1.49&1 + 0424601127 & 44&20:50:36.8&+60:26:15.6 & [email protected]&[email protected]&1.06&1 + 0424601041 & 32&20:50:37.2 & + 60:15:38.6 & [email protected]&[email protected]&1.84&0 + no&86&20:50:45.3&+60:20:01.4&see table [ vardata]&&2.36 & + 0424600477 & 41&20:50:46.3&+60:23:26.3&[email protected]&[email protected]&1.39&1 + 0396300338 & 22&20:50:48.3 & + 59:58:22.0 & [email protected] & [email protected]&0.77&1 + 0396300620 & 23&20:50:56.2 & + 59:59:30.6 & [email protected] & [email protected]&0.73&1 + 0424600655&29&20:51:07.8&+60:11:24.2&[email protected]&[email protected]&1.34&1 + 0424601145&27&20:51:11.2&+60:06:26.2&[email protected]&[email protected]&1.06&1 + 0424601213&28&20:51:12.6&+60:08:53.9&[email protected]&[email protected]&1.16&1 + 0424601111 & 4&20:51:12.8 & + 60:25:15.5 & [email protected] & [email protected]&1.33&1 + 0424600103 & 5 & 20:51:16.2 & + 60:33:19.9 & [email protected]&[email protected]&1.14&1 + no&70&20:51:32.3&+60:41:41.3&[email protected]&[email protected]&1.02&1 + 0424701143 & 43&20:51:33.6&+60:25:05.5&[email protected]&[email protected]&1.44&1 + 0424701033&45&20:51:34.7&+60:14:03.5 & [email protected]&[email protected]&2.07&1 + 0424701049&30&20:51:43.7&+60:11:50.0&[email protected]&[email protected]&1.59&0 + 0396300164 & 24&20:51:49.2 & + 59:54:15.5 & [email protected] & [email protected]&1.01&0 + 0424701155&26&20:51:51.7&+60:05:31.0&[email protected]&[email protected]&1.13&1 + 0424701211 & 3 & 20:51:53.4 & + 60:25:18.5&[email protected] & [email protected]&1.36&1 + no&85&20:51:55.4&+60:19:00.0&[email protected]&[email protected]&2.29&0 + 0424701127 & 2 & 20:51:57.1 & + 60:22:44.6&[email protected] & [email protected]&1.87&0 + no&71&20:52:01.8&+60:38:13.2&[email protected]&[email protected]&1.13&1 + 0424701215 & 1 & 20:52:02.7&+60:22:27.9&[email protected] & [email protected]&1.87&0 + 0424701115&25&20:52:04.5&+60:03:55.6&[email protected]&[email protected]&1.11&1 + 0424701085&72&20:52:23.2&+60:32:48.4&[email protected]&[email protected]&1.36&1 + no&75&20:53:25.7&+60:16:32.6&[email protected]&[email protected]&3.29&1 + no&68&20:53:42.0&+60:24:07.8&[email protected]&[email protected]&2.39&1 + no&66&20:53:52.0&+60:26:37.7&[email protected]&[email protected]&2.52&1 + no&59&20:53:52.8&+60:35:44.6&[email protected]&[email protected]&1.45&1 + no&74&20:53:55.6&60:15:51.6&[email protected]&[email protected]&3.20&0 + no&69&20:53:55.7&+60:22:55.9&[email protected]&[email protected]&2.72&1 + no&69bis&20:53:59.0&+60:22:50.0&[email protected]&[email protected]&2.72&1 + no&61&20:54:01.3&+60:39:55.3&[email protected]&[email protected]&1.15&1 + no&77&20:54:27.8&+60:11:16.5&[email protected]&[email protected]&1.93&1 + no&65&20:54:28.8&+60:26:53.5&[email protected]&[email protected]&2.32&1 + 0424700062&62&20:54:31.3&+60:32:40.7&[email protected]&[email protected]&1.90&1 + no&64&20:54:53.0&+60:29:35.7&[email protected]&[email protected]&2.28&0 + 0424700686&73&20:56:15.6&+60:17:41.9&[email protected]&[email protected]&1.94&1 + lrrrr 35&[email protected]&[email protected]&2,452,054.64583 + 35&[email protected]&@xmath1068.7&2,452,141.72222 + 86&[email protected]&[email protected]&2,452,830.75347 + 86&[email protected]&[email protected]&2,452,835.78125 + lrrrr c1&[email protected]&@xmath107&2.34 + c2&[email protected]&@xmath108&2.34 + c3&[email protected]&@xmath109&2.60 + c4&[email protected]&@xmath110&2.34 + c5&[email protected]&@xmath111&2.60 + c6&[email protected]&@xmath112&2.34 + f2&[email protected]&@xmath113&2.19 + lrrrr @xmath114 ( @xmath115)&@xmath116 & @xmath117 & @xmath118 & @xmath119 + @xmath120 ( @xmath121 ) & @xmath122&@xmath123&@xmath124&@xmath125 + @xmath126 ( @xmath115)&@xmath127&@xmath128 & & + @xmath129 ( @xmath121 ) & @xmath130&@xmath131 & & + @xmath132 ( @xmath115 ) & ... & ... & & + @xmath133 ( @xmath121 ) & @xmath134&random & & + lrrrrrrrr lm349&20 49 6.9&60 11 48&47&@xmath135&@xmath136&random&f + lm350&20 49 46.5&60 15 40&49&@xmath137&@xmath138&random&f + lm351&20 51 28.0&60 18 33&43&@xmath139&@xmath140&@xmath141&c + lm352&20 53 49.9&60 11 27 & ... & ... & ... & ... & ... + l1082c&20 51 27.4&60 19 00&7&@xmath142&@xmath143&@xmath144&c + l1082a&20 53 29.6&60 14 41 & ... & ... & ... & ... & ... + l1082b&20 53 50.3&60 09 47&48 & ? & & ... + ll @xmath145 ( h@xmath9 @xmath13 ) & 15000 @xmath104 3000 + @xmath90 ( h@xmath9 @xmath146 ) & 9.9 @xmath147 + @xmath148 & 0.16 + @xmath149 @xmath150 & @xmath151 + @xmath152 & @xmath153 + @xmath154 ( @xmath155 ) & 0.88@xmath104 0.20 + @xmath70 @xmath156 & @xmath157 + @xmath79 ( @xmath158 ) & 170@xmath10456 + @xmath80 & @xmath159 0.44 + @xmath83 & 0.35 +

this lack of saturation effect suggests that even in the denser parts of gf 9 we are still probing the magnetic field . a global interpretation of the results is that in the core region an original poloidal field could have been twisted by a rotating elongated ( coreenvelope ) structure . there is no evidence for turbulence and ambipolar diffusion does not seem to be effective at the present time .

new visible polarization data combined with existing ir and fir polarization data are used to study how the magnetic field threading the filamentary molecular cloud gf 9 connects to larger structures in its general environment . we find that when both visible and nir polarization data are plotted as a function of extinction , there is no evidence for a plateau or a saturation effect in the polarization at 1.3 as seen in dark clouds in taurus . this lack of saturation effect suggests that even in the denser parts of gf 9 we are still probing the magnetic field . the visible polarization is smooth and has a well - defined orientation . the ir data are also well defined but with a different direction , and the fir data in the core region are well defined and with yet another direction , but are randomly distributed in the filament region . on the scale of a few times the mean radial dimension of the molecular cloud , it is as if the magnetic field were ` blind ' to the spatial distribution of the filaments while on smaller scales within the cloud , in the core region near the iras point source psc 20503 + 6006 , polarimetry shows a rotation of the magnetic field lines in these denser phases . hence , in spite of the fact that the spatial resolution is not the same in the visible / nir and in the fir data , all the data put together indicate that the field direction changes with the spatial scale . finally , the chandrasekhar and fermi method is used to evaluate the magnetic field strength , indicating that the core region is approximately magnetically critical . a global interpretation of the results is that in the core region an original poloidal field could have been twisted by a rotating elongated ( coreenvelope ) structure . there is no evidence for turbulence and ambipolar diffusion does not seem to be effective at the present time .

1308.5238

i

our @xmath97 , nmr and nd data clearly demonstrate that @xmath239 exhibits a collinear afm ground state below @xmath4 = 9.8(2 ) k. the @xmath52al - nmr spectrum exhibits a symmetric broadening below 10 k which indicates the presence of a long - range afm ordered ground state for this compound . furthermore , the line width of the nmr spectrum which is proportional to the order parameter shows a continuous increase below 10 k , as expected for second order phase transition . the presence of spontaneous magnetization below 10 k is confirmed directly by the observation of a @xmath57co nmr signal under zero magnetic field in the magnetically ordered state . using the internal field at the co sites in the magnetically ordered state and the hyperfine coupling constant estimated from the @xmath126-@xmath0 analysis , an ordered moment at the @xmath1-site co@xmath12 ion is estimated to be 2.4(1 ) @xmath14/co . the sharp peak of @xmath195 at around 10 k further confirms a second - order phase transition to a long - range magnetically ordered state at the same temperature . the results from the nd measurements are not only consistent with the nmr results but also indicate a collinear long - range afm - ordered ground state for this compound with an ordered moment of 1.9(5 ) @xmath14/co , consistent with the estimate from nmr . the magnetic entropy @xmath107 at @xmath4 is considerably smaller than its value at high temperature , which indicates that strong afm correlations occur above @xmath4 . the emergence of afm correlations was manifested by the increase of @xmath213 below 100 k , by the presence of broad magnetic peaks observed below 50 k in the nd measurements , and by the broad peak in @xmath0(@xmath38 ) at @xmath28 15 k. there are two factors which govern the magnetic properties of this system , @xmath240 frustration and site inversion . we successfully prepared a polycrystalline sample of @xmath239 with a low inversion parameter @xmath39 = 0.057(20 ) . site disorder creates increased randomness of exchange interactions in the already frustrated compound.@xcite the suppression of the value of magnetic entropy at high temperatures from the value expected for @xmath13 = 3/2 suggests that the effective spin of the co at the @xmath1-site is smaller than 3/2 , which could be a manifestation of both spin frustration and co - al site inversion effects . the presence of dynamic short - range magnetic ordering observed in neutron scattering experiments below @xmath209 50 k can be caused mainly by the site inversion effects . as pointed out previously , although a spin - liquid ground state has been proposed from magnetic susceptibility measurements for @xmath239 with low values of @xmath39,@xcite our nmr and nd measurements conclusively proved the existence of a long - range afm - ordered state below 10 k. since site inversion plays a crucial role in determining the magnetic properties of this spinel compound , it will also be interesting to perform systematic nmr and nd measurements on highly disordered ( high @xmath39 ) @xmath239 samples to investigate how the system changes from the afm state to a spin glass state . we thank dr . vladimir tsurkan for providing us the heat capacity data of the nonmagnetic reference compound @xmath241 in ref . . this research was supported by the u.s . department of energy , office of basic energy sciences , division of materials sciences and engineering . ames laboratory is operated for the u.s . department of energy by iowa state university under contract no . de - ac02 - 07ch11358 . 9 w. l. roth , j. phys . ( paris ) * 25 * , 507 ( 1964 ) . d. bergman , j. alicea , e. gull , s. trebst , and l. balents , nature phys . * 3 * , 487 ( 2007 ) . o. zaharko , n. b. christensen , a. cervellino , v. tsurkan , a. maljuk , u. stuhr , c. niedermayer , f. yokaichiya , d. n. argyriou , m. boehm , and a. loidl , phys . b * 84 * , 094403 ( 2011 ) . n. tristan , j. hemberger , a. krimmel , h .- a . krug von nidda , v. tsurkan , and a. loidl , phys . b * 72 * , 174404 ( 2005 ) . a. p. ramirez , annu . * 24 * , 453 ( 1994 ) . t. suzuki , h. nagai , m. nohara , and h. takagi , j. phys . : condens . matter * 19 * , 145265 ( 2007 ) . o. zaharko , a. cervellino , v. tsurkan , n. b. christensen , and a. loidl , phys . b * 81 * , 064416 ( 2010 ) . g. j. macdougall , d. gout , j. l. zarestky , g. ehlers , a. podlesnyak , m. a. mcguire , d. mandrus , and s. e. nagler , proceedings of the national academy of sciences * 38 * , 15693 ( 2011 ) . n. tristan , v. zestrea , g. behr , r. klingeler , b. bchner , h .- a . krug von nidda , a. loidl , and v. tsurkan , phys . b * 77 * , 094412 ( 2008 ) . k. hanashima , y. kodama , d. akahoshi , c. kanadani , and t. saito , j. phys . . jpn . * 82 * , 024702 ( 2013 ) . j. rodrguez - carvajal , physica b * 192 * , 55 ( 1993 ) ; see also www.illeu / sites / fullprof/. a. maljuk , v. tsurkan , v. zestrea , o. zaharko , a. cerellino , a. loidl , and d. n. argyriou , j. cryst . growth * 311 * , 3997 ( 2009 ) . m. hagiwara , s. kimura , n. nishihagi , t. suzuki , m. nohara , h. takagi , and k. kindo , j. low temp . phys . * 159 * , 11 ( 2010 ) . d. meschede , f. steglich , w. felsch , h. maletta , and w. zinn , phys . lett . * 44 * , 102 ( 1980 ) . l. r. walker and r. e. walstedt , phys . lett . * 38 * , 514 ( 1977 ) . k. miyatani , k. kohn , s. iida , and h. kamimura , j. phys . . jpn . * 20 * , 471 ( 1965 ) . edited by l. j. de jongh ( klewer , dordrecht , 1989 ) . t. fukai , y. furukawa , s. wada , and k. miyatani , j. phys . . jpn . * 65 * , 4067 ( 1996 ) . t. tsuda , a. hirai , and h. abe , phys . 26a * , 463 ( 1968 ) . y. furukawa , s. wada , t. kajitani , and s. hosoya , j. phys . 68 * , 346 ( 1999 ) . a. abragam , j. horowitz , and m. h. l. pryce , proc . ( london ) , ser . a * 230 * , 169 ( 1955 ) . a. narath , _ hyperfine interactions _ edited by a. j. freeman and r. b. frankel ( academic press , new york , 1967 ) . a. j. freeman and r. e. watson , _ magnetism _ edited by g. t. rado and h. shul ( academic press , new york , 1965 ) vol . 2 . a. narath , phys . rev . * 162 * , 320 ( 1967 ) . t. moriya , j. phys . * 18 * , 516 ( 1963 ) . a. v. mahajan , r. sala , e. lee , f. borsa , s. kondo , and d. c. johnston , phys . b * 57 * , 8890 ( 1998 ) . w. l. roth , j. phys . chem . solids * 25 * , 1 ( 1964 ) a. krimmel , v. tsurkan , d. sheptyakov , and a. loidl , physica b * 378 - 380 * , 583 ( 2006 ) . a. nakatsuka y. ikeda , y. yamasaki , n. nakayama and t. mizota , solid state commun . * 128 * , 85 ( 2003 ) .

nuclear magnetic resonance ( nmr ) , neutron diffraction ( nd ) , x - ray diffraction , magnetic susceptibility and specific heat measurements on the frustrated-site spinel coalo compound reveal a collinear antiferromagnetic ordering below = 9.8(2 ) k. a high quality powder sample characterized by x - ray diffraction that indicates a relatively low co - al inversion parameter in ( coal)[alcoo , shows a broad maximum around 15 k in and a sharp peak at in heat capacity . antiferromagnetic spin fluctuations and correlations in the paramagnetic state are revealed from the , nmr and nd measurements , which are due to spin frustration and site inversion effects in the system .

nuclear magnetic resonance ( nmr ) , neutron diffraction ( nd ) , x - ray diffraction , magnetic susceptibility and specific heat measurements on the frustrated-site spinel coalo compound reveal a collinear antiferromagnetic ordering below = 9.8(2 ) k. a high quality powder sample characterized by x - ray diffraction that indicates a relatively low co - al inversion parameter in ( coal)[alcoo , shows a broad maximum around 15 k in and a sharp peak at in heat capacity . the average ordered magnetic moment of co ( = 3/2 ) ions at the-site is estimated to be 2.4(1 ) from nmr and 1.9(5 ) from nd which are smaller than the expected value of 3 for and = 2 . antiferromagnetic spin fluctuations and correlations in the paramagnetic state are revealed from the , nmr and nd measurements , which are due to spin frustration and site inversion effects in the system . the nd data also show short - range dynamic magnetic ordering that persists to a temperature that is almost twice .

1212.5172

c

in order to assess the suitability of nanodiamonds as photonic ldos probes and as building blocks for hybrid photonic systems , we have investigated the brightness , decay rate , and quantum efficiency of single nv centers in nanodiamonds of 25 nm , and of 100 nm median size . for both size ranges a wide distribution in brightnesses and rates is found , consistent with reports by earlier workers . we conclude that the wide distribution of rates is due to a distribution in radiative rates , nonradiative rates and quantum efficiencies . this conclusion contradicts earlier work , that interpreted the wide distribution of decay rates as mainly due to a photonic effect that causes a distribution in radiative decay rates via the ldos . instead , our measurements show that even nv centers in large nanocrystals show a wide range of quantum efficiencies when probed in a controlled ldos experiment . for nv centers in 100 nm nanocrystals we find quantum efficiencies distributed between 10% and 90% , while for the smaller nv centers the quantum efficiency for fluorescence is likely a factor of two smaller on average . for applications in nanophotonic experiments using single nv centers , a highly problematic property is that quantum efficiency does not correlate with brightness , due to the fact that both the radiative and nonradiative rate are distributed . in other words , screening nanodiamonds to pick the best one to probe ldos or for incorporation in a photonic device can not rely on a simple metric such as spectrum or brightness . instead , we argue that future work in the hybrid assembly of nanodiamonds in plasmonics and photonic crystals to realize accelerated spontaneous emission decay always requires an experimental protocol in which nanodiamonds are first individually calibrated in terms of quantum efficiency . while we have shown a method for such calibration , this is a highly tedious procedure that is not easily implementable and requires dedicated near - field manipulation equipment . in this work , we have not speculated on the origin of the apparent low quantum efficiency of single nv centers in nanodiamonds . we close with two remarks on the origin of the low apparent quantum efficiency . firstly , we have treated the nv center as a quasi two - level system . our experiments thus address the question what the apparent quantum efficiency is when attempting to use an nv center as a two - level ldos probe . from the nv center spectrum it is clear that the spectrum is very wide with a large vibrational broadening spectrum . moreover it is well known that the nv@xmath68 center is not a two level system . instead , the nv@xmath68 has different spin sublevels , and may experience spin - flip intersystem crossing between allowed spin transition manifolds . the rates for these transitions were recently characterized in detail for nv centers in bulk diamond in ref . a further complication is that the nv@xmath68 defect may infrequently transition to an uncharged nv center that also luminesces , yet at different rate and efficiency . the many rates involved in these transitions can further vary between nv centers due to , e.g. , variations in crystal strain . a full treatment of the response of nv centers to ldos changes would hence have to treat the full rate equations in which radiative transition rates are , and intersystem crossing rates are not , affected by ldos . an important step beyond our work will be to perform the measurements we have described here but employing the spin selective techniques reported by robledo @xcite to establish what the nonradiative and radiative rates are for each transition separately , instead of lumping rates into effective two - level parameters . while the ldos changes we have applied using a mirror are broadband ldos changes that modify radiative transitions roughly equally across the emission spectrum , ldos changes that have strong spectral features could be used advantageously to enhance or suppress the importance of intersystem crossing . having established that further work is required to separate the quantum efficiencies reported here into parameters per transition in a more complete level scheme , we turn to possible reasons for the below - unity values of quantum efficiency that we find . the lower brightness of the smaller nv centers , as well as their lack of response to ldos changes suggest that the surface , i.e. , surface contamination with carbon , or surface defects may play a role in providing quenching sites . indeed , it has already been suggested for very small ( 5 nm ) nanodiamonds that nv centers may suffer quenching due to graphite shells on the diamonds . while the nanodiamonds we used have been employed by several groups in spontaneous emission control experiments in untreated form , exactly as in our experiments , additional surface treatments such as by prolonger immersion in boiling sulphuric acid , or cleaning in kningswasser have been proposed by several workers . whether or not such treatments actually affect quantum efficiency is as yet unclear , as is whether quenching can be completely suppressed . we propose that the quantum efficiency calibration method that we demonstrated will be an indispensable tool to evaluate such cleaning methods , as well as to screen other color centers in diamond for advantageous fluorescence properties . we thank s. schietinger for communications regarding sample preparation methods , m. frimmer for experimental help and discussions , and c. osorio for suggestions to improve the manuscript . this work is part of the research program of the `` foundation for fundamental research on matter ( fom ) '' , which is financially supported by the `` the netherlands organization for scientific research ( nwo ) '' . afk gratefully acknowledges a nwo - vidi grant for financial support .

we report an experimental quantification of the brightness , radiative decay rate , nonradiative decay rate and quantum efficiency of single nv centers in diamond nanocrystals . we report that nv centers in 25 nm nanocrystals are essentially insensitive to local density of states ( ldos ) variations that we induce at a dielectric interface by using liquids to vary the refractive index , and propose that quantum efficiencies in such nanocrystals are widely distributed between 0% and 20% . for single nv centers in larger 100 nm nanocrystals ,

nv centers in diamond are generally recognized as highly promising as indefinitely stable highly efficient single - photon sources . we report an experimental quantification of the brightness , radiative decay rate , nonradiative decay rate and quantum efficiency of single nv centers in diamond nanocrystals . our experiments show that the commonly observed large spread in fluorescence decay rates of nv centers in nanodiamond is inconsistent with the common explanation of large nanophotonic mode - density variations in the ultra - small high - index crystals at near - unity quantum efficiency . we report that nv centers in 25 nm nanocrystals are essentially insensitive to local density of states ( ldos ) variations that we induce at a dielectric interface by using liquids to vary the refractive index , and propose that quantum efficiencies in such nanocrystals are widely distributed between 0% and 20% . for single nv centers in larger 100 nm nanocrystals , we show that decay rate changes can be reversibly induced by nanomechanically approaching a mirror to change the ldos . using this scanning mirror method , for the first time we report calibrated quantum efficiencies of nv centers , and show that different but nominally identical nanocrystals have widely distributed quantum efficiencies between 10% and 90% . our measurements imply that nanocrystals that are to be assembled into hybrid photonic structures for cavity qed should first be individually screened to assess fluorescence properties in detail .

1204.0063

i

the nature of the interaction between an accreting super - massive black hole ( smbh ) and its host galaxy remains a challenging problem in the study of galaxy evolution . numerical simulations reveal that gas can be drawn inward toward the nucleus by gravitational torques arising from a series of gravitational instabilities @xcite . this gas typically forms a dusty structure at small radii with a characteristic length scale of @xmath41 - 10 parsecs which in some cases has been imaged directly @xcite . phenomenologically , this structure can be modelled as a torus @xcite , but there is an ongoing theoretical effort to provide a detailed , self - consistent explanation of its configuration and what supports it . if a sufficiently strong poloidal magnetic field is present at the parsec scale , one possible explanation is that the dusty gas is launched as a hydromagnetic wind @xcite . heating of the ism from stellar feedback might support the dusty gas in a puffy disk @xcite . the disk might be simultaneously supported by infrared radiation pressure @xcite , or the infrared radiation pressure may generate a failed wind @xcite . regardless of what supports the torus , gas continues to be drawn in to the black hole accretion disk at small radii ( @xmath5 cm ) , where it powers an active galactic nucleus ( agn ) . the radiation emitted from smbh accretion disks influences the dynamics of the torus itself , along with the dynamics of the host galaxy . this feedback may act through a number of channels that include radiative heating ( e.g. * ? ? ? * ) , jets @xcite , and winds driven by radiation pressure on resonant ultraviolet lines @xcite and dust @xcite . our challenge is to understand the combined effect of all these modes of interaction . improving our understanding of this connection will be crucial for answering questions about the growth of smbhs , observations of agn , and the star formation histories in galaxies . recent observations have begun to reveal the violent impact that agn may have on their host galaxies . observations of obscured quasars such as sdss j1356 + 1026 have revealed outflows extending out to tens of kiloparsecs from the galactic nucleus @xcite . the estimated mechanical luminosity of these outflows ( @xmath6 ergs s@xmath7 ) is too large to be explained by the inferred star formation activity . other obscured quasars possess more massive outflows , with mass - loss rates of hundreds of solar masses per year @xcite . meanwhile , observations of local ultra - luminous infrared galaxies ( ulirgs ) have led to the discovery of outflows with velocities that are correlated with the agn bolometric luminosity @xcite . these outflows also have mass - loss rates equal to several times the star formation rate and in some cases exceeding 1000 solar masses per year , depleting the gas on timescales as short as @xmath8 years . adding to our picture are studies of post - starburst galaxies , exhibiting outflows with median velocity of approximately 1000 km s@xmath7 , suggesting that past agn activity played a role in launching the gas @xcite . these observations are complemented by numerical simulations of agn feedback @xcite that account for deposition of both energy and momentum from the accretion radiation , including a combination of heating by x - rays and photoionizations , radiation pressure at the kiloparsec scale , and winds driven from within a radius of less than 100 parsecs . taken together , these effects can help to explain both the @xmath9 - @xmath10 relation @xcite and the existence of galactic outflows observed at speeds of thousands of km s@xmath7 . the results , particularly those of @xcite , also suggest that line - driven winds may be insufficient to drive observed outflows , and that a large amount of momentum ( @xmath11 ) may need to be deposited via absorption by dust grains during the period when the smbh is optically thick to both ultraviolet and far - infrared radiation , the time when most black hole growth is believed to occur @xcite . a large uncertainty in the numerical calculations referenced above is the amount of radiative momentum deposited within the central unresolved radius . the velocity and mass - loss rate of the resulting wind depend sensitively on this coupling . moreover , in those studies the momentum was deposited in a spherically symmetric manner . in reality , multidimensional effects , such as the tendency for radiation to escape out the rarefied , polar regions of the gas distribution , will be crucial . these effects have been considered by several previous studies . @xcite computed the radiation forces exerted on a torus modelled as a constant density cylindrical shell , and @xcite extended that work to account for a more self - consistent rearrangement of the gas under the influence of the radiation . a radiation - hydrodynamics study that linked the effects of compton scattering and broad absorption line winds at the parsec scale with inflow processes on galactic ( kiloparsec ) scales in two spatial dimensions was undertaken by @xcite , and this was extended in order to capture the radiative transfer through dusty gas in @xcite . our study extends this work further by performing three dimensional monte carlo radiative transfer calculations for dusty gas , including both smooth and clumpy gas distributions , and by integrating the force on columns of gas in order to quantify the mass outflow rate from agn radiating at high luminosity . the momentum flux in radiation from a smbh accretion disk with luminosity @xmath12 is @xmath1 . generally @xmath12 will not exceed @xmath13 , the eddington luminosity set by the electron scattering ( thomson ) opacity . dust will contribute to the opacity seen by the radiation at large radii , but only at distances greater than the radius @xmath14 at which its temperature drops below the sublimation temperature @xmath15 . although the sublimation temperature varies for each grain depending on its composition and its size , we choose to adopt the simplification of assigning a uniform sublimation temperature to all the dust in our calculations . the sublimation radius may be estimated as @xmath16 when the gas distribution surrounding the smbh is not isotropic , @xmath14 may vary with angle . within this radius , electron scattering dominates the opacity , and the usual eddington limit applies . once the intrinsic photons from the accretion disk encounter dust in the surrounding gas , they are absorbed and the energy is re - emitted at infrared wavelengths . if the gas is also optically thick to the infrared , then the re - emitted radiation will continue to be absorbed and re - emitted in a random - walk pattern until it exits the optically thick region . along the way , momentum will be imparted by the photons to the gas multiple times . in this scenario it is possible for the radiation to transfer momentum to the gas at a rate that exceeds @xmath17 . for a spherically symmetric problem , this `` boost '' factor to the infrared radiation force is exactly the infrared optical depth of the gas , which can be shown as follows : in steady - state , when radiative equilibrium holds and the luminosity as a function of radius is constant , we may compute the radiation force per volume @xmath18 as @xmath19 the total outward force exerted by the radiation is @xmath20 where @xmath21 is the radial optical depth for the infrared photons . in a gas rich galactic nucleus with a column density of @xmath22 @xmath23 , a mean mass per particle of 1.5 times the proton mass , and an infrared dust opacity of 10 @xmath24 per gram of gas , an initial guess for the optical depth would be approximately 250 . there are two primary effects that will reduce the actual radiation force from such a high value . the first is the lack of spherical symmetry : a torus obscures only a fraction of the solid angle surrounding the accretion disk , and the presence of clumps and voids in the torus can increase the photon mean free path for certain sightlines . the second effect is dust sublimation : dust will be absent from the innermost regions of the nucleus that contribute a substantial fraction to the gas column density , and the force integral can be well - approximated by setting its lower limit to @xmath14 . to get a sense of the sort of momentum deposition rates that have been observed , consider the case of mrk 231 . this system features an outflow of neutral gas with velocities in the range 360 - 900 km s@xmath7 and a mass - loss rate estimated at 420 solar masses per year @xcite . the momentum flux in the outflow , estimated by multiplying the mass loss rate by the velocity , is between 2.6 to 6.5 times @xmath1 where @xmath12 is measured to be @xmath25 ergs s@xmath7 . the kinetic luminosity of the outflow , on the other hand , is estimated at @xmath26 ergs s@xmath7 , less than 1% of the bolometric agn luminosity . modeling the force from radiation pressure , and predicting by what factor it exceeds @xmath1 , becomes a difficult problem to tackle analytically in the absence of spherical symmetry , the presence of clumps , and with an accounting for dust sublimation . for these reasons , we turn here to three - dimensional radiative transfer calculations using the wavelength - dependent monte carlo radiative transfer code sedona @xcite . given that the radiative diffusion time in these systems is shorter than the dynamical times , we restrict ourselves to steady - state configurations that do not include an explicit coupling to hydrodynamics . in section [ methodologysection ] , we describe how we parametrize the gas configurations surrounding the black hole and how we treat the key physical processes in the radiative transfer . in section [ results ] , we present our results for a series of calculations in which we vary the opening angle of the torus , the amount of gas present , and the accretion disk luminosity . we also examine how our dynamical conclusions are affected by accounting for a clumpy rather than smooth distribution of dust and gas . finally , in section [ conclusion ] we present our conclusions .

observational and theoretical arguments suggest that the momentum carried in mass outflows from agn can reach several times , corresponding to outflow rates of hundreds of solar masses per year . radiation pressure on resonant absorption lines alone may not be sufficient to provide this momentum deposition , and the transfer of reprocessed ir radiation in dusty nuclear gas has been postulated to provide the extra enhancement . the efficacy of this mechanism , however , will be sensitive to multi - dimensional effects such as the tendency for the reprocessed radiation to preferentially escape along sightlines of lower column density . we use monte carlo radiative transfer calculations to determine the radiation force on dusty gas residing within approximately 30 parsecs from an accreting super - massive black hole . we calculate the net rate of momentum deposition in the surrounding gas and estimate the mass - loss rate in the resulting outflow as a function of solid angle for different black hole luminosities , sightline - averaged column densities , clumping parameters , and opening angles of the dusty gas . these results help to explain the origin of high velocity molecular and atomic outflows in local ulirgs , and can inform numerical simulations of galaxy evolution including agn feedback .

observational and theoretical arguments suggest that the momentum carried in mass outflows from agn can reach several times , corresponding to outflow rates of hundreds of solar masses per year . radiation pressure on resonant absorption lines alone may not be sufficient to provide this momentum deposition , and the transfer of reprocessed ir radiation in dusty nuclear gas has been postulated to provide the extra enhancement . the efficacy of this mechanism , however , will be sensitive to multi - dimensional effects such as the tendency for the reprocessed radiation to preferentially escape along sightlines of lower column density . we use monte carlo radiative transfer calculations to determine the radiation force on dusty gas residing within approximately 30 parsecs from an accreting super - massive black hole . we calculate the net rate of momentum deposition in the surrounding gas and estimate the mass - loss rate in the resulting outflow as a function of solid angle for different black hole luminosities , sightline - averaged column densities , clumping parameters , and opening angles of the dusty gas . we find that these dust - driven winds carry momentum fluxes of 1 - 5 times and correspond to mass - loss rates of 10 - 100 per year for a black hole radiating at or near its eddington limit . these results help to explain the origin of high velocity molecular and atomic outflows in local ulirgs , and can inform numerical simulations of galaxy evolution including agn feedback .

1701.04892

r

table 1 lists the basic results for all of the models , namely the final times reached , the final spatial resolution employed , and the maximum number of virtual planets ( @xmath103 ) that formed and existed simultaneously , usually close to the final number of vps . the final times reached ranged from 244 yrs to 978 yrs . for comparison , the initial orbital period of the disk at the inner edge ( 4 au ) was 8.0 yr , whereas the initial orbital period at the outer edge ( 20 au ) was 91 yrs . the key point is that all the models were evolved far enough in time that there was no evidence for any further significant growth of non - axisymmetry , i.e. , no need to further refine the spatial grid . some models still required the creation of additional vps , but this was balanced by the loss of vps that hit either the inner or outer grid boundaries , indicating that a semblance of a steady state configuration had been reached . because the boss & myhill ( 1992 ) code employed has not been parallelized , each model was computed continuously on a single , dedicated cluster core . most models were run for as long as 2.3 yrs on the dtm flash cluster , while others were run for as long as 7 months on the considerably faster carnegie memex cluster at stanford university . figure 4 summarizes the results from table 1 as follows . models where the initial spatial resolution of @xmath60 and @xmath63 sufficed for the entire evolution without violating the jeans or toomre constraints experienced little growth of non - axisymmetry ( red dots ) , while those that needed to be refined to @xmath78 with @xmath63 experienced moderate growth ( green dots ) , and those that ended with @xmath78 and @xmath79 experienced significant growth of spiral arms ( blue dots ) . the remaining models continued to violate the jeans or toomre criteria , even with @xmath78 and @xmath79 , necessitating the creations of vps at the location of the violations . the black symbols in figure 4 represent the maximum number of vps created for those models , ranging from a black circle for a single vp , to a bar for two vps , to a three - pointed star for three vps , etc . figure 4 demonstrates that the assumed initial conditions are just as important for determining the success of a possible disk gravitational instability in forming self - gravitating clumps as is the choice of the @xmath0 cooling parameter . all of the models with @xmath101 fragmented and formed from 4 to 10 vps , regardless of the cooling rates investigated , from @xmath0 = 1 to @xmath0 = 100 . this somewhat surprising result means that if a disk is initially extremely gravitationally unstable , self - gravitating clumps can form rapidly without being stifled by compressional heating during their assembly . however , the time at which the first vp formed depended strongly on the value of @xmath0 , with the first vp in models 1.3 - 1 and 1.3 - 3 forming after 104 yrs and 118 yrs , respectively , compared to forming only after 190 yrs and 212 yrs , respectively , for models 1.3 - 50 and 1.3 - 100 . clearly even for an initially highly unstable disk , the cooling rate affects the time evolution of the fragmentation process . at the same time , the models starting with @xmath104 show that such an initially gravitationally stable disk can not become non - axisymmetric enough to undergo fragmentation , even for @xmath105 . as noted previously , this result is largely a result of the constraint that the disk temperatures can not drop below their initial values , in spite of vigorous cooling , and can only become more gravitationally unstable by increasing the disk surface density in a limited region of the disk , e.g. , by forming a ring . for initial toomre @xmath10 values in between these two extremes , the general result is a smooth progression toward more of a tendency toward fragmentation at a fixed value of @xmath0 ( e.g. , for @xmath0 = 3 and 10 as @xmath2 is lowered ) . however , the transition from stable to unstable with regard to forming vps is not necessarily completely monotonically dependent on @xmath2 ( i.e. , for @xmath0 = 1 and 100 , where as @xmath2 is decreased , successive models can fragment and then resist fragmentation , before eventually fragmenting again ) . this result demonstrates the stochastic nature of gravitationally unstable disks , where the spiral arms that form repeatedly and interact with each other may or may not happen to combine in a constructive wave sense and form a clump dense enough to require the creation of a vp . given this ambiguity , the critical value for fragmentation appears to be @xmath106 for @xmath107 , @xmath108 for @xmath109 , and @xmath110 for @xmath111 , roughly speaking . figure 5 presents the final midplane density distributions for the four models at the extremes of the parameter space investigated , namely models 1.3 - 1 , 1.3 - 100 , 2.7 - 1 , and 2.7 - 100 . the two models with @xmath2 = 1.3 both clearly formed numerous spiral arms and clumps , regardless of whether @xmath0 = 1 or 100 , though in the latter case the spiral arms are broader and nowhere near as sharply defined . neither of the two models with @xmath2 = 2.7 formed any significant non - axisymmetric features , and the model with @xmath0 = 100 looks the most similar to the initial disk model ( figure 3a ) , in spite of having evolved for 414 yrs . figure 6 displays the corresponding midplane temperature distributions for these same four end - member models . the slower cooling rate in model 1.3 - 100 ( figure 6b ) compared to that of 1.3 - 1 results in well - defined , moderately warm spiral arms throughout the disk , whereas the rapid cooling assumed in model 1.3 - 1 ( figure 6a ) allows the disk to cool back down to its initial temperature throughout most of the disk . for the high @xmath2 models , figure 6c shows that model 2.7 - 1 maintains a disk temperature essentially unchanged from its initial conditions , as a result of the rapid cooling , whereas in figure 6d , model 2.7 - 100 shows several distinct rings of somewhat hotter gas than the initial temperature distribution . figure 7 shows the location of the nine vps still active in model 1.3 - 1 at the end of the evolution ( 224 yrs ) , the same time as the midplane density contours shown in figure 5a . it is evident that the nine vps are not aligned with the numerous spiral arm features seen in figure 5a , as is to be expected , given that the vps begin their existence with an initial mass of the order of a fraction of a jupiter mass , and as such are not subject to the tendency for gas drag to force small ( e.g. , cm - size ) particles to remain in the vicinity of spiral arms ( e.g. , boss 2013 , 2015 ) . the time evolution of the ensemble of vps formed in the eight models with @xmath2 = 1.3 is presented in figure 8 , sampled roughly every 40,000 time steps . starting with masses only a small fraction of a jupiter mass , the vps accrete mass at the blh rate and soon reach masses as high as 5 @xmath8 . the vps tend to be created in the sweet spot between 6 au and 10 au , where the disk is cool enough and massive enough to support the growth of strong spiral arms . once formed there , the vps can migrate through disk interactions ( e.g. , boss 2013 ) both inwards and outwards , with significant numbers hitting either the inner or outer disk boundaries and thereafter being removed from the calculations . finally , figure 9 compares the vps formed in the @xmath2 = 1.3 models with the presently known distribution in mass and semi - major axis of exoplanets between 4 au and 20 au . while not intended to be a rigorous exoplanet population synthesis on a par with those presented in section 2.5 , figure 9 hints that the disk instability mechanism may be able to crudely match the exoplanet demographics for gas giants with semi - major axes of 4 au to 6 au , and if so , this approach would predict an as yet mostly undetected significant population of jupiter - mass gas giants orbiting at distances of about 6 au to 16 au . refining the implications of these disk instability models for explaining the known exoplanet demographics , and for predicting what more might be discovered by future exoplanet surveys ( e.g. , by microlensing and direct imaging searches with the nasa wfirst mission ) is a promising subject for further work .

the controversy extends to population synthesis models of exoplanet demographics and to hydrodynamical models of the fragmentation process . we show that the choice of is equal in importance to the value assumed : high disks can be stable for small , when the initial disk temperature is taken as a lower bound , while low disks can fragment for high . these results imply that the evolution of disks toward low must be taken into account in assessing disk fragmentation possibilities , at least in the inner disk , i.e. , inside about 20 au . the models suggest that if low disks can form , there should be an as yet largely undetected population of gas giants orbiting g dwarfs between about 6 au and 16 au .

observational evidence exists for the formation of gas giant planets on wide orbits around young stars by disk gravitational instability , but the roles of disk instability and core accretion for forming gas giants on shorter period orbits are less clear . the controversy extends to population synthesis models of exoplanet demographics and to hydrodynamical models of the fragmentation process . the latter refers largely to the handling of radiative transfer in three dimensional ( 3d ) hydrodynamical models , which controls heating and cooling processes in gravitationally unstable disks , and hence dense clump formation . a suite of models using the cooling approximation is presented here . the initial disks have masses of 0.091 and extend from 4 to 20 au around a 1 protostar . the initial minimum toomre values range from 1.3 to 2.7 , while ranges from 1 to 100 . we show that the choice of is equal in importance to the value assumed : high disks can be stable for small , when the initial disk temperature is taken as a lower bound , while low disks can fragment for high . these results imply that the evolution of disks toward low must be taken into account in assessing disk fragmentation possibilities , at least in the inner disk , i.e. , inside about 20 au . the models suggest that if low disks can form , there should be an as yet largely undetected population of gas giants orbiting g dwarfs between about 6 au and 16 au .

astro-ph9911045

i

diffraction limited mid - infrared observations of a sample of seven ulirgs obtained on the keck 10 m telescopes have shown : 1 - extremely compact structures , corresponding to emission on spatial scales of @xmath24100@xmath21200 pc , are seen in six of the seven systems observed . the mid - infrared emission in these galaxies generally emerges from a single region of diameter @xmath24 1 kpc , and in most cases from regions @xmath24200 pc in diameter . 2 - the upper limit on the diameter of the 12.5@xmath0 m source in markarian 231 , 0.13@xmath2 , is too small to be consistent with the observed 60@xmath0 m flux density emerging from a region this size , and demonstrates that in this agn the source size increases with increasing wavelength ( decreasing dust temperature ) . 3 - in iras 05189 - 2524 and iras 08572 + 3915 there is strong circumstantial evidence that the size of the infrared source increases with wavelength between 12.5 and 60 @xmath0 m , suggesting that these too are predominantly agn powered ulirgs . 4 - in the other objects observed , the angular size limits for the compact mid - infrared sources are not yet adequate to distinguish between agn and starburst luminosity sources , although the small sizes are consistent with a central luminosity source heating the surrounding dust as in agn models in all the sources except iras 17208 - 0014 . 5 - if star formation powers the luminosity in the very compact infrared sources seen in these systems , the star formation rates averaged over a few hundred parsecs is comparable to that seen in the brightest @xmath610 pc sized clusters in nearby starbursts , and exceeds by factors of up to 100 , the global star formation rates in nearby starburst galaxies .

we find extremely compact structures , with spatial scales of ( diameter ) in six of the seven ulirgs observed . we have utilized the compact mid - infrared structures as a diagnostic of whether an agn or a compact ( 100 300 pc ) starburst is the primary power source in these ulirgs . in markarian 231 , the upper limit on the diameter of the 12.5 m source , 0.13 , shows that the size of the infrared source must increase with increasing wavelength , consistent with agn models . in iras 05189 - 2524 and iras 08572 + 3915 there is strong evidence that the source size increases with increasing wavelength . the compact mid - infrared sources seen in the other galaxies can not be used to distinguish the ultimate luminosity source . if these ulirgs are powered by compact starbursts , the star formation rates seen in the central few hundred parsecs far exceed the global rates seen in nearby starburst galaxies , and approach the surface brightness of individual clusters in nearby starburst galaxies .

observations of ultraluminous infrared galaxies ( ulirgs ) with an achieved resolution approaching the diffraction limit in the mid - infrared from 8 - 25 m using the keck telescopes are reported . we find extremely compact structures , with spatial scales of ( diameter ) in six of the seven ulirgs observed . these compact sources emit between 30% and 100% of the mid - infrared energy from these galaxies . we have utilized the compact mid - infrared structures as a diagnostic of whether an agn or a compact ( 100 300 pc ) starburst is the primary power source in these ulirgs . in markarian 231 , the upper limit on the diameter of the 12.5 m source , 0.13 , shows that the size of the infrared source must increase with increasing wavelength , consistent with agn models . in iras 05189 - 2524 and iras 08572 + 3915 there is strong evidence that the source size increases with increasing wavelength . this suggests heating by a central source rather than an extended luminosity source , consistent with the optical classification as an agn . the compact mid - infrared sources seen in the other galaxies can not be used to distinguish the ultimate luminosity source . if these ulirgs are powered by compact starbursts , the star formation rates seen in the central few hundred parsecs far exceed the global rates seen in nearby starburst galaxies , and approach the surface brightness of individual clusters in nearby starburst galaxies .

1112.6406

i

in the recent years , deep near - infrared imaging surveys have begun to yield a significant number of candidate galaxies at very high redshifts . the wide - field surveys from the ground have produced a handful of bright candidates at @xmath6 ( e.g. , ouchi et al . 2009 ; hickey et al . 2010 ; castellano et al . 2010 ; capak et al . 2011 ; hsieh et al . 2012 ; hathi et al . 2012 ) , while the pencil - beam survey by the _ hubble space telescope _ ( hst ) wide field camera 3 ( wfc3 ) within the historical advanced camera for surveys ( acs ) hubble ultra deep field ( hereafter acs - hudf ; beckwith et al . 2006 ) and its two parallel fields ( hudf09 ; pi . illingworth ) have probed the fainter populations at @xmath68 ( oesch et al . 2010 ; bouwens et al . 2010 , b10 ; bunker et al . 2010 ; mclure et al . 2010 , m10 ; yan et al . 2010 , y10 ; finkelstein et al . 2010 ) and possibly out to @xmath7 ( yan et al . 2010 ; wyithe et al . 2011 ; bouwens et al . the wfc3 early release science program ( ers , pi . oconnell ; windhorst et al . 2011 ) has played an important role in connecting the `` wide '' and the `` deep '' ends of the exploration , allowing construction of @xmath68 samples at intermediate brightness levels ( wilkins et al . 2011 ; b11 ; lorenzoni et al . 2011 , l11 ) . meanwhile , the hubble infrared pure parallel imaging extragalactic survey ( hippies ; yan et al . 2011 ) and the brightest of reionizing galaxies survey ( trenti et al . 2011a ) have been exploring the bright end of the population through a large number of random , discrete wfc3 pointings obtained during the _ hst _ parallel orbits . surveys in foreground cluster fields utilizing gravitational lensing magnification have also resulted in a handful of promising candidates at @xmath89 ( e.g. , richard et al . 2006 ; bradley et al . 2008 , 2012 ; laporte et al . 2011 ; hall et al . 2012 ) , which complement the surveys in blank - sky fields . the cosmic assembly near - infrared deep extragalactic legacy survey ( candels ; pis : faber & ferguson ; see grogin et al . 2011 and koekemoer et al . 2011 ) employs a two - tiered , `` wide and deep '' strategy , which makes it uniquely positioned in bridging the significant gaps among existing surveys . in particular , its `` deep '' component will cover @xmath9 arcmin@xmath1 in two fields upon completion , and its data will be ideally suited for studying galaxies at very high redshifts . in this paper , we report our preliminary results from the deep observations in the great observatories origins deep survey ( goods ; giavalisco et al . 2004 ) southern field , where we use the nearly complete data set to study the galaxy population at @xmath0 . we use the following cosmological parameters throughout : @xmath10 , @xmath11 and @xmath12 km s@xmath13 mpc@xmath13 . the quoted magnitudes are all in the ab system .

one key goal of the _ hubble space telescope _ cosmic assembly near - infrared deep extragalactic legacy survey is to track galaxy evolution back to . its two - tiered `` wide and deep '' strategy bridges significant gaps in existing near - infrared surveys . here we report on galaxy candidates selected as f105w - band dropouts in one of its deep fields , which covers 50.1 arcmin to 4 ks depth in each of three near - infrared bands in the great observatories origins deep survey southern field .

one key goal of the _ hubble space telescope _ cosmic assembly near - infrared deep extragalactic legacy survey is to track galaxy evolution back to . its two - tiered `` wide and deep '' strategy bridges significant gaps in existing near - infrared surveys . here we report on galaxy candidates selected as f105w - band dropouts in one of its deep fields , which covers 50.1 arcmin to 4 ks depth in each of three near - infrared bands in the great observatories origins deep survey southern field . two of our candidates have mag , and are mag brighter than any previously known f105w - dropouts . we derive constraints on the bright - end of the rest - frame ultraviolet luminosity function of galaxies at , and show that the number density of such very bright objects is higher than expected from the previous schechter luminosity function estimates at this redshift . another two candidates are securely detected in _ spitzer _ infrared array camera images , which are the first such individual detections at . their derived stellar masses are on the order of a few , from which we obtain the first measurement of the high - mass end of the galaxy stellar mass function at . the high number density of very luminous and very massive galaxies at , if real , could imply a large stellar - to - halo mass ratio and an efficient conversion of baryons to stars at such an early time .

1112.6406

i

in this work , we search for candidate galaxies at @xmath0 in the candels deep goods - s field and study their properties . our sample of @xmath14-dropouts hints that the number density of @xmath0 galaxies at the bright - end might be higher than expected from the previous schechter lf estimates , which lends support to the suggestion made by a number of earlier studies that there could be a bright - end excess in the galaxy number density at very high redshifts . furthermore , two of our candidates are securely detected at 3.6 and 4.5 @xmath31 m in _ spitzer _ data . these are the first @xmath14-dropouts individually detected at these wavelengths . their derived stellar masses are on the order of @xmath98 @xmath5 , from which we obtain the first measurement of the high - mass end of the galaxy stellar mass function at @xmath0 . if the high number densities of very luminous and very massive galaxies at @xmath0 are real , they could imply a large stellar - to - halo mass ratio and an efficient conversion of baryons to stars at very early time in the cosmic stellar mass assembly history . we thank the referee for the useful comments , which improved the quality of this work . we also thank b. mobasher and j. dunlop for their comments on an earlier version of this paper . acknowledges the support of nasa grant hst - go-11192.1 . support for program number hst - go-12060 was provided by nasa through a grant from the space telescope science institute , which is operated by the association of universities for research in astronomy , incorporated , under nasa contract nas5 - 26555 . anderson , j. & bedin , l. r. 2010 , , 122 , 1035 beckwith , s. v. w. , stiavelli , m. , koekemoer , a. m. , et al . 2006 , , 132 , 1729 behroozi , p. s. , conroy , c. & wechsler , r. h. 2010 , , 717 , 379 bertin , e. & arnouts , s 1996 , , 117 , 393 bouwens , r. j. , illingworth , g. d. , labbe , i. , et al . 2011a , nature , 469 , 504 bouwens , r. j. , illingworth , g. d. , oesch , p. a. , et al . 2010 , apj , 709 , l133 ( b10 ) bouwens , r. j. , illingworth , g. d. , oesch , p. a. , et al . 2011b , apj , 737 , 90 ( b11 ) bowler r. a. a. ; dunlop , j. s. ; mclure , r. j. ; et al . 2012 , mnras , 426 , 2772 bradley , l. d. , bouwens , r. j. , ford , h. c. , et al . 2008 , apj , 678 , 647 bradley , l. d. , bouwens , r. j. , zitrin , a. , et al . 2012 , apj , 747 , 3 brammer , g. b. , van dokkum , p. g. , & coppi , p. 2008 , , 686 , 1503 bruzual , g. & charlot , s. 2003 , , 344 , 1000 bunker , a. j. , wilkins , s. , ellis , r. s. , et al . 2010 , mnras , 409 , 855 calzetti , d. 2001 , , 113 , 1449 capak , p. , mobasher , b. , scoville , n. z. , et al . 2011 , apj , 730 , 68 castellano , m. , fontana , a. , paris , d. , et al . 2010 , a&a , 524 , a28 chabrier , g. 2003 , , 115 , 763 croton , d. j. , springel , v. , white , s. d. m. , et al . 2006 , mnras , 365 , 11 dekel , a. , birnboim , y. , engel , g. , et al . 2009 , nature , 457 , 451 dickinson , m. , stern , d. , giavalisco , m. , et al . 2004 , apj , 600 , l99 finkelstein , s. l. , papovich , c. , giavalisco , m. , et al . 2010 , apj , 719 , 1250 finkelstein , s. l. , papovich , c. , salmon , b. , et al . 2012 , apj , 756 , 164 gabor , j. m. , dav , r. , oppenheimer , b. d. & finlator , k. 2011 , , 417 , 2676 giavalisco , m. , ferguson , h. c. , koekemoer , a. m. , et al . 2004 , apj , 600 , l93 gonzlez , v. , labb , i. , bouwens , r. j. , et al . 2011 , , 735 , l34 grogin , n. a. , kocevski , d. d. , faber , s. m. , et al . 2011 , apjs , 197 , 35 hall , n. , brada , m. , gonzalez , a. h. , et al . 2012 , , 745 , 155 hathi , n. , mobasher , b. , capak , p. , wang , w .- h . , & ferguson , h. c. 2012 , apj , 757 , 43 hickey , s. , bunker , a. , jarvis , m. j. , chiu , k. & bonfield , d. 2010 , , 404 , 212 hsieh , b .- q . , wang , w .- h . , yan , h. , et al . 2012 , apj , 749 , 88 koekemoer , a. m. , faber , s. m. , ferguson , h. c. , et al . 2011 , , 197 , 36 kron , r. g. 1980 , , 43 , 305 krumholz , m. r. & dekel , a. 2010 , , 406 , 112 labb , i. , gonzlez , v. , bouwens , r. j. , et al . 2010a , , 708 , l26 labb , i. , gonzlez , v. , bouwens , r. j. , et al . 2010b , , 716 , l103 laporte , pell , r. , schaerer , d. , n. , et al . 2011 , a&a , 531 , 74 leggett , s. k. , golimowski , d. a. , fan , x. , et al . 2002 , apj , 564 , 452 lorenzoni , s. , bunker , a. j. , wilkins , s. m. , et al . 2011 , , 414 , 1455 ( l11 ) madau , p. 1995 , , 441 , 18 mclure , r. j. , dunlop , j. s. , cirasuolo , m. , et al . 2010 , , 403 , 960 ( m10 ) meiksin , a. 2006 , , 365 , 807 oesch , p. a. , bouwens , r. j. , carollo , c. m. , et al . 2010 , , 709 , l21 oesch , p. a. , bouwens , r. j. , illingworth , g. d. , et al . 2012 , , 759 , 135 ono , y. , ouchi , m. , mobasher , b. , et al . 2012 , , 744 , 83 ouchi , m. , mobasher , b. , shimasaku , k. , et al . 2009 , , 706 , 1136 papovich , c. , finkelstein , s. l. , ferguson , h. c. , lotz , j. m. & giavalisco , m. 2011 , , 412 , 1123 reddy , n. a. , erb , d. k. , pettini , m. , steidel , c. c. , & shapley , a. e. 2010 , , 712 , 1070 richard , j. , pell , r. , schaerer , d. , le borgne , j .- f . & kneib , j .- 2006 , a&a , 456 , 861 ryan , r. e. , thorman , p. a. , yan , h. , et al . 2011 , , 739 , 83 salpeter , e. e. 1955 , , 121 , 161 somerville , r. s. , hopkins , p. f. , cox , t. j. , robertson , b. e. & hernquist , l. 2008 , , 391 , 481 steidel , c. c. , adelberger , k. l. , giavalisco , m. , dickinson , m. & pettini , m. 1999 , , 519 , 1 steidel , c. c. , adelberger , k. l. , shapley , a. e. , et al . 2003 , apj , 592 , 728 szalay , a. s. , connolly , a. j. & szokoly , g. p. , 1999 , , 117 , 68 trenti , m. , bradley , l. d. , stiavelli , m. , et al . 2011a , , 727 , l39 trenti , m. & stiavelli , m. 2008 , , 676 , 767 trenti , m. , bradley , l. d. , stiavelli , m. , et al . 2012 , apj , 746 , 55 wilkins , s. m. , bunker , a. j. , lorenzoni , s. & caruana , j. 2011 , , 411 , 23 windhorst , r. a. , cohen , s. h. , hathi , n. p. , et al . 2011 , , 193 , 27 wyithe , j. s. b. , yan , h. , windhorst , r. a. & mao , s. 2011 , , 469 , 181 xue , y. q. , luo , b. , brandt , w. n. , et al . 2011 , , 195 , 10 yan , h. , dickinson , m. , eisenhardt , p. r. m. , et al . 2004 , , 616 , 63 yan , h. , dickinson , m. , stern , d. , et al . , 2005 , , 634 , 109 yan , h. , windhorst , r. a. , hathi , n. p. , et al . 2010 , res . astrophys . , 10 , 867 ( y10 ) yan , h. , yan , l. , zamojski , m. a. , et al . 2011 , , 728 , l22 cccccccl auto_048 & 3:32:49.936 @xmath14927:48:18.101 & [email protected] & [email protected] & @[email protected] & c & c & iso_085 ; o12 - 2499448181 + auto_100 & 3:32:41.417 @xmath14927:44:37.831 & [email protected] & [email protected] & [email protected] & b & b & iso_164 + auto_212 & 3:32:20.965 @xmath14927:51:37.073 & [email protected] & [email protected] & [email protected] & @xmath151 & @xmath152 & o12 - 2209751370 + auto_293 & 3:32:20.981 @xmath14927:48:53.467 & [email protected] & @xmath153 & @[email protected] & [email protected] & [email protected] & iso_071 ; o12 - 2209848535 + auto_204 & 3:32:18.185 @xmath14927:52:45.566 & [email protected] & [email protected] & [email protected] & @xmath154 & @xmath152 & o12 - 2181852456 + auto_094 & 3:32:40.675 @xmath14927:45:11.624 & [email protected] & [email protected] & [email protected] & c & c + auto_035 & 3:32:34.998 @xmath14927:49:21.623 & [email protected] & @xmath155 & [email protected] & [email protected] & [email protected] & iso_063 ; o12 - 2350049216 + due to the nature of the dropout selection technique , it is not unusual that samples constructed by independent groups can differ significantly on an object - by - object basis ( see 3 ) . to further demonstrate this point , we constructed a separate @xmath14-dropout sample to mimic an independent study . we used exactly the same data as in 2 , and therefore any difference in this sample should be attributed to the selection technique . we followed the same procedures as in 3 , but used mag_iso instead when calculating colors . the motivation of adopting mag_iso in this exercise is that isophotal apertures are commonly used in measuring lyman - break galaxy colors ( e.g. , steidel et al . 2003 ) because they often lead to higher @xmath156 , even if they do not necessarily include all of the light from each galaxy . hereafter we refer to this sample as the `` iso sample '' to separate from the one described in the main text , which we refer to as the `` auto sample '' . the initial candidates in the iso sample were also visually examined by the same group of six inspectors . the visual inspection of this sample was done about one month later than that for the auto sample , and therefore even when we were examining the same object that is also in the auto sample we did not keep the memory of the result from the last time , and hence we mimicked an `` independent '' study as much as we could . the final iso sample consists of eleven candidates . 6 shows their selection in the @xmath47 color space , while fig . 7 shows the redshift selection function . images of these candidates are displayed in fig . table 2 lists their photometric information . -dropout sample . the labeled magnitude ranges are still based on mag_auto in @xmath15 , as the simulation only has control over the input total magnitudes , which are best represented by mag_auto . to be consistent , the correction of @xmath157 for the iso sample is done at the corresponding mag_auto ranges . , width=226 ] for the sake of completeness , we also compared the iso sample to the o12 s sample . based on the photometry reported in o12 , nine of their candidates are expected to meet our color criteria ( see also however , only three of them are included in our iso sample ( see table 2 ) . among the five that are not in our sample , o12 s candy-2432246169 has @xmath58 in @xmath15 and @xmath16 and is not included in our mag_iso catalog . candy-2272447364 has @xmath158 in @xmath21 and does not satisfy our optical non - detection criterion . candy-2277945141 and 2320345371 have @xmath159 and 0.57 mag based on our photometry and hence do not meet out color criteria . the other two , o12 s candy-2209751370 and 2181852456 , meet all our color criteria , but were rejected during the visual inspection when constructing our iso sample . note that these latter two objects actually are in our auto sample ( auto_212 and 204 , respectively ) and survived the visual inspection for our auto sample ( see below ) . a more constructive comparision is that between this iso sample and the auto sample , which shows that they have four objects in common ( see table 2 ) . there are seven iso candidates not in the auto sample . five of them were rejected in the auto selection because they have s / n @xmath160 within their mag_auto apertures in at least one veto image ( iso_011 , 017 , 157 , 158 , 160 ) . one was rejected because its mag_auto @xmath161 color limit does not satisfy @xmath162 mag ( iso_008 ) . the other one ( iso_082 ) satisfies all the quantitative criteria in the auto selection , however it was rejected in the visual inspection step during the auto selection run . on the other hand , four auto candidates are not in the iso sample . two of them were rejected because they have mag_auto @xmath161 color or limit below the @xmath162 mag threshold ( auto_094 and 368 ) . the other two satisfy all the quantitative criteria in the iso selection , however they were rejected in the visual inspection step during the iso selection run ( auto_204 and 212 ) . this internal comparison of our two samples thus further demonstrates the points addressed earlier : ( 1 ) adoption of different photometry result in samples that can be significantly different on an object - by - object basis , and ( 2 ) visual inspections at different time , especially the inspections of the veto images , can also result in differences in this sense because such inspections are not guaranteed to be fully repeatable for a large sample at the s / n@xmath41 level . nevertheless , the main statistical trends revealed by the iso sample are very similar to those inferred from the auto sample . both samples include the same two bright @xmath14-dropouts ( auto_048/iso_085 and auto_100/iso_184 ) , and the same two irac - detected ones ( auto_293/iso_071 and auto_035/iso_063 ) . for completeness , 9 shows the constraint from the iso sample on the lf , where one can see that the bright - end excess is still present . similarly , the constraints on the mf and the stellar mass density derived from the iso sample agree with those based the auto sample to within @xmath163% , and the small differences are mainly caused by the slightly different @xmath61 corrections over the range of interest . from this exercise , we believe that the main results presents in this work are robust . cccccccl iso_085 & 3:32:49.936 @xmath14927:48:18.100 & [email protected] & [email protected] & @[email protected] & c & c & auto_048 ; o12 - 2499448181 + iso_164 & 3:32:41.417 @xmath14927:44:37.831 & [email protected] & [email protected] & [email protected] & c & c & auto_100 + iso_157 & 3:32:42.882 @xmath14927:45:04.268 & [email protected] & [email protected] & [email protected] & b & b & + iso_071 & 3:32:20.981 @xmath14927:48:53.468 & [email protected] & [email protected] & [email protected] & [email protected] & [email protected] & auto_293 ; o12 - 2209848535 + iso_082 & 3:32:14.133 @xmath14927:48:28.911 & [email protected] & [email protected] & [email protected] & @xmath164 & @xmath165 & + iso_011 & 3:32:14.469 @xmath14927:51:48.542 & [email protected] & [email protected] & [email protected] & b & b & + iso_158 & 3:32:47.953 @xmath14927:44:50.436 & [email protected] & [email protected] & [email protected] & @xmath154 & @xmath166 & + iso_063 & 3:32:34.999 @xmath14927:49:21.622 & [email protected] & @xmath167 & [email protected] & [email protected] & [email protected] & auto_035 ; o12 - 2350049216 + iso_017 & 3:32:18.091 @xmath14927:51:18.492 & [email protected] & [email protected] & @[email protected] & b & b & + iso_160 & 3:32:46.111 @xmath14927:44:47.997 & [email protected] & [email protected] & [email protected] & @xmath154 & @xmath168 & + iso_008 & 3:32:16.915 @xmath14927:52:01.878 & [email protected] & @xmath169 & @[email protected] & @xmath154 & @xmath152 & +

we derive constraints on the bright - end of the rest - frame ultraviolet luminosity function of galaxies at , and show that the number density of such very bright objects is higher than expected from the previous schechter luminosity function estimates at this redshift . another two candidates are securely detected in _ their derived stellar masses are on the order of a few , from which we obtain the first measurement of the high - mass end of the galaxy stellar mass function at . the high number density of very luminous and very massive galaxies at , if real , could imply a large stellar - to - halo mass ratio and an efficient conversion of baryons to stars at such an early time .

one key goal of the _ hubble space telescope _ cosmic assembly near - infrared deep extragalactic legacy survey is to track galaxy evolution back to . its two - tiered `` wide and deep '' strategy bridges significant gaps in existing near - infrared surveys . here we report on galaxy candidates selected as f105w - band dropouts in one of its deep fields , which covers 50.1 arcmin to 4 ks depth in each of three near - infrared bands in the great observatories origins deep survey southern field . two of our candidates have mag , and are mag brighter than any previously known f105w - dropouts . we derive constraints on the bright - end of the rest - frame ultraviolet luminosity function of galaxies at , and show that the number density of such very bright objects is higher than expected from the previous schechter luminosity function estimates at this redshift . another two candidates are securely detected in _ spitzer _ infrared array camera images , which are the first such individual detections at . their derived stellar masses are on the order of a few , from which we obtain the first measurement of the high - mass end of the galaxy stellar mass function at . the high number density of very luminous and very massive galaxies at , if real , could imply a large stellar - to - halo mass ratio and an efficient conversion of baryons to stars at such an early time .

1511.08679

i

exoplanetary system architectures have revealed numerous surprises since the first exoplanets were discovered . one of the earliest surprises was the discovery of exoplanets in highly eccentric orbits , for which there is no analog in the solar system . these eccentric orbits were discovered for giant planets , such as hd 114762b @xcite and 70 vir b @xcite with eccentricities of 0.33 and 0.40 respectively . since those early discoveries , eccentric planets have presented a significant challenge for formation theories to account for the components of planet - planet scattering @xcite and tidal circularization @xcite . such planets tend to be discovered with the radial velocity ( rv ) technique since the observations are able to sample the entire keplerian planetary orbit . subsequent investigations of the eccentricity distribution of planetary orbits that take _ kepler _ transiting exoplanet discoveries into account show that small planets in multi - planet systems are more likely to have low eccentricities @xcite . the discovery and characterization of eccentric orbits is an on - going effort to understand the evolutionary history of these fascinating systems . a particularly eccentric exoplanet was discovered by @xcite orbiting the star hd 20782 . with a minimum mass twice that of jupiter and an orbital period of 597 days , the planet is typical of high - eccentricity planets . the orbit was further revised by @xcite and shown to have an eccentricity as high as 0.97 , making it the highest eccentricity exoplanet yet discovered . however , data during periastron passage is difficult to obtain for such systems since the rv variation predominantly occurs during a very small fraction of the orbital phase . the star continued to be monitored by the transit ephemeris refinement and monitoring survey ( terms ) to improve the orbital parameters of the system @xcite . such orbital refinement may be used to predict and observe events that occur during particular periods of the orbit , such as planetary transits @xcite or phase variations @xcite . here we present new results for the hd 20782 system , including rvs that sample several periastron passages and establish the planet as the most eccentric known exoplanet . follow - up photometry from both ground - based and space - based telescopes rule out a transit of the planet and show evidence of phase variations due to reflected light from the planet close to periastron passage . section [ science ] provides background information and discusses the science motivation for studying the system . section [ stellarprop ] presents analysis of new chiron spectra and the resulting fundamental parameters of the host star as well as stellar abundances . new rv data are combined with those published in section [ orbit ] and a new keplerian orbit for the planet is produced . section [ astrometry ] describes the use of _ hipparcos _ astrometry to constrain the orbital inclination of the planet . section [ transit ] discusses the transit prospects for the system and the effects of both orbital eccentricity and inclination . section [ photometry ] presents the ground - based photometry and an estimate of the stellar rotation period . data from most are used during the transit / periastron window to rule out a transit and also reveal the potential presence of a reflected light signature of the planet as it passes through periastron passage . we discuss future observing opportunities and make concluding remarks in section [ conclusions ] .

planets in highly eccentric orbits form a class of objects not seen within our solar system . here we present new data and analysis for this system as part of the transit ephemeris refinement and monitoring survey ( terms ) . we obtained chiron spectra to perform an independent estimation of the fundamental stellar parameters . new radial velocities from aat and paras observations during periastron passage greatly improve our knowledge of the eccentric nature of the orbit . photometric monitoring of the star during predicted transit and periastron times using most rule out a transit of the planet and reveal evidence of phase variations during periastron . planet separation surrounding the periastron passage .

planets in highly eccentric orbits form a class of objects not seen within our solar system . the most extreme case known amongst these objects is the planet orbiting hd 20782 , with an orbital period of 597 days and an eccentricity of 0.96 . here we present new data and analysis for this system as part of the transit ephemeris refinement and monitoring survey ( terms ) . we obtained chiron spectra to perform an independent estimation of the fundamental stellar parameters . new radial velocities from aat and paras observations during periastron passage greatly improve our knowledge of the eccentric nature of the orbit . the combined analysis of our keplerian orbital and hipparcos astrometry show that the inclination of the planetary orbit is , ruling out stellar masses for the companion . our long - term robotic photometry show that the star is extremely stable over long timescales . photometric monitoring of the star during predicted transit and periastron times using most rule out a transit of the planet and reveal evidence of phase variations during periastron . these possible photometric phase variations may be caused by reflected light from the planet s atmosphere and the dramatic change in star planet separation surrounding the periastron passage .

1511.08390

i

plasmon resonances , collective oscillations of a free - electron gas against a positive ion background , are subject to significant attentions.@xcite plasmon resonances , including both localized - plasmon resonances and plasmon waveguiding modes , can confine electric fields beyond the optical diffraction limit.@xcite this leads to numerous applications such as cancer therapy,@xcite nanophotonics circuits,@xcite nanolasers,@xcite and quantum information processing.@xcite the majority of these developments rely on our insight from classical electrodynamics where the drude model for the intraband plasmonic response of metals stands as a cornerstone.@xcite this celebrated approach explains noble - metal plasmon phenomena extremely well for plasmonic structures with characteristic dimensions well above @xmath0.@xcite however , the maturing nanofabrication allows the realization and exploration of yet smaller feature sizes.@xcite when approaching the few nanometer or even sub nanometer scale , an increasing importance of nonclassical degrees of freedom ( i.e. beyond the drude model ) can be anticipated and with increasing weights.@xcite examples of such nonclassical degrees of freedom include the kinetics associated with the finite compressibility of the quantum electron gas@xcite and the inhomogeneous microscopic equilibrium distribution of the quantum electron gas in the vicinity of a surface.@xcite in maxwell s equations , such aspects modify the local drude permittivity to a generalized nonlocal form.@xcite with respect to different nonlocal models , such as the semi - classical hydrodynamic drude model ( hdm ) and the microscopical random - phase approximation ( rpa ) , the commonly employed drude model is also referred to as the local response approximation ( lra ) . in recent years , efforts have been directed to theoretically@xcite and experimentally@xcite investigating nonclassical effects of plasmon resonances in metals and with interesting extensions to two dimensional ( 2d ) plasmonic materials such as graphene.@xcite in addition to the fundamental interest in quantum plasmonic phenomena , we note that quantum electronic control may open new avenues in applications of nanoscale light confinement@xcite and plasmon - induced hot electrons.@xcite for resonant phenomena , the nonclassical effects usually manifest in broadening and shifting of plasmon resonances.@xcite in turn , nonclassical effects also smear singularity phenomena predicted by the drude model , such as perfect imaging,@xcite nanofocusing@xcite and the field enhancement at the center of a touching dimer@xcite that would otherwise be singular.@xcite nonclassical dynamics may also be associated with phenomena without any classical counterparts , such as the mutipole surface - plasmon resonances at the interface of simple metals,@xcite the charge transfer plasmon resonances for dimers with sub - nanometric gaps,@xcite and the quantized bulk - plasmon resonances above the plasma frequency.@xcite the theoretical understandings of nonclassical effects of plasmon resonances usually employ the semi - classical hdm,@xcite the rpa,@xcite or the time - dependent density - functional theory ( dft).@xcite elevating us beyond these different models , it is interesting to ask if we can introduce a measure to quantify the degree of nonclassical contributions to the plasmon dynamics ? one immediate candidate at hand is to associate such a parameter with the resonance shift of plasmon modes when compared to the lra . obviously , this would work for well developed resonances existing within the lra , while it would not help to appreciate quantum plasmon phenomena not holding classical counterparts . to address a broader variety of nonclassical phenomena , we here propose a _ nonclassical - impact parameter _ ( nci ) to characterize the nonclassical effects from a total energy ( @xmath1 ) perspective : @xmath2 , where @xmath3 for classical ( c ) dynamics , while @xmath4 for entirely nonclassical ( nc ) dynamics . as a key result we show that @xmath5}{q_{\rm pr}}\label{eq : ncirpa}\end{aligned}\ ] ] where @xmath6 is the quality factor of the plasmon resonance while @xmath7 $ ] is the loss function ; both established quantities in the fields of plasmonics and electron - energy loss spectroscopy of plasmons.@xcite the remaining part of the paper is organized as follows : in section ii , with the hdm as the starting point , we partition different forms of the energies of plasmon resonances including the contributions from the nonclassical effects . based on the energy considerations in section ii , we define the nci to characterize the nonclassical effects beyond the hdm assumption in section iii . in section iv , we discuss the relation between the nci and the electron - pressure wave , and demonstrate the fundamental upper limit of the nci for plasmon waveguiding modes in the hdm . in section v , with the nci , we investigate in detail the nonclassical effects by numerical analysis of plasmon waveguiding modes of metallic slab waveguides . in section vi , the formal relation between the hdm and the rpa is discussed in the limit of an infinite work function . in section vii , a summary and conclusions are given . some details of our derivations are left for appendices a , b and c.

plasmons are commonly interpreted with classical electrodynamics , while nonclassical effects may influence the dynamics of plasmon resonances as the plasmon confinement is approaching the few nanometer scale . however , an unambiguous approach to quantify the degree of nonclassical dynamics remains . we propose a _ nonclassical - impact parameter _ ( nci ) to characterize the degree of nonclassical effects from an energy perspective , i.e. which fraction of the total electromagnetic energy is attributed to classical electrodynamic terms and which fraction is correspondingly to be assigned to nonclassical degrees of freedom ? we show that the nci relates directly to two fundamental parameters of plasmon resonances : the loss function and the quality factor . guided by the nci , we discuss the nonclassical effects of plasmon waveguiding modes of metallic slab waveguides , and highlight the general features of the nonclassical effects at different microscopic levels by contrasting the numerical results from the semi - classical hydrodynamic drude model ( hdm ) and the microscopic random - phase approximation ( rpa ) . the formal relation between the hdm and the rpa is also established for metals by exploring the limit of an infinite work function .

plasmons are commonly interpreted with classical electrodynamics , while nonclassical effects may influence the dynamics of plasmon resonances as the plasmon confinement is approaching the few nanometer scale . however , an unambiguous approach to quantify the degree of nonclassical dynamics remains . we propose a _ nonclassical - impact parameter _ ( nci ) to characterize the degree of nonclassical effects from an energy perspective , i.e. which fraction of the total electromagnetic energy is attributed to classical electrodynamic terms and which fraction is correspondingly to be assigned to nonclassical degrees of freedom ? we show that the nci relates directly to two fundamental parameters of plasmon resonances : the loss function and the quality factor . guided by the nci , we discuss the nonclassical effects of plasmon waveguiding modes of metallic slab waveguides , and highlight the general features of the nonclassical effects at different microscopic levels by contrasting the numerical results from the semi - classical hydrodynamic drude model ( hdm ) and the microscopic random - phase approximation ( rpa ) . the formal relation between the hdm and the rpa is also established for metals by exploring the limit of an infinite work function .

astro-ph0209560

i

power spectrum estimation and evaluation of the associated errors in the presence of incomplete sky coverage ; non - homogeneous , correlated instrumental noise ; and foreground emission is a problem of central importance for the extraction of cosmological information from the cosmic microwave background . from a bayesian point of view , power spectrum estimation involves the maximization of the posterior probability density , with error bars given by the set of cosmological parameters or power spectrum whose integrated posterior density achieves some specified level of confidence . a bayesian approach to cmb analysis for large data sets involving a direct evaluation of the likelihood is intractable due to the @xmath4 expense associated with computing the inverse of non - sparse matrices , or their determinants ( @xcite , @xcite ) . the goal of this paper is the development of alternative numerical methods , specifically monte carlo techniques , for the bayesian analysis of the cmb , including the complications of incomplete sky coverage , correlated noise and foregrounds . previous work has demonstrated that for a certain class of scanning strategies , the signal and inverse noise matrices are block diagonal . the block diagonal properties of these matrices give an exact @xmath5 bayesian method , and therefore tractable for data sets as large as will be returned from planck . the complications of this method are that it can not easily accommodate partial sky converge or precessing scan strategies . the method of @xcite computes the maximum of the likelihood through a newton raphson method . the numerical innovations of this method involve monte carlo simulations and the use of conjugate gradient descent , giving an overall expense @xmath5 . the method was proposed and numerically demonstrated in the context of uncorrelated noise , and a region of sky coverage of azimuthal symmetry , where a good preconditioner can be constructed . however , the algorithm is in fact more general , provided there is sufficient memory for storage of the needed matrices , and that conjugate gradient descent converges quickly enough ( i.e. there is a good preconditioner ) . as suggested in @xcite , we can use the ring set approach to supply preconditioners . an outstanding problem to be solved is a way of retaining the mathematical advantages of a ring set scan ( block diagonal inverse noise and signal matrices ) while accommodating partial sky coverage . the approach formulated in this paper handles the problem of partial sky coverage by embedding the data in an azimuthally symmetric region of sky , and using a monte carlo markov chain to numerically marginalize over the unobserved part . for scans close to ring sets , we therefore inherit good preconditioners , allowing an extension of both the ring set and conjugate gradient methods to scan strategies as planned for planck . for observations @xmath6 , where @xmath7 are the cmb signal , foregrounds , and noise respectively , our approach to power spectrum estimation is motivated by the identity ( derived in appendix [ appposterioridentity ] ) @xmath8 p(s , f|\gamma_{0},y)\ ] ] where @xmath9 is any parameterization of conclusions ( such as the power spectrum or cosmological parameters ) , and @xmath10 is any fixed guess . the bayesian posterior ratio on the left is given as an integral over the unknown quantities which are assumed to generate the observed data . maximization of the posterior involves computing the gradient of equation [ posterioridentity ] which will be shown to depend on the expectation value of the power spectrum with respect to the random field @xmath11 , @xmath12 = \int d(s , f ) \ c_{l}(s ) \ p(s , f |\gamma_{0},y)\ ] ] we maximize the posterior ratio in equation [ posterioridentity ] by the expectation maximization algorithm ( @xcite ) which proceeds by iteratively setting @xmath13 $ ] . the algorithm converges to the posterior maximum for a uniform prior , and gives an un - biased , consistent estimator ( see appendix [ appestimator ] ) . in this paper , we focus on computation of the expectation value of the power spectrum @xmath14 $ ] given the data and some guess @xmath15 under the assumption of perfect foreground separation ( although we comment on how the approach can be generalized to include foregrounds later in the paper , and leave its numerical demonstration for future work ) . we compute the expectation value of the power spectrum @xmath14 $ ] numerically with a monte carlo approach , where we sample maps of the cmb from the probability density @xmath16 . conditioning on some estimate of the foregrounds , the method exploits the fact that @xmath17 is a gaussian random field , and therefore completely characterized by the mean field map and covariance matrix of fluctuations about that map . maps are sampled from @xmath17 by first computing the mean field map with conjugate gradient descent , and then sampling fluctuations about the mean field map from a zero mean gaussian field with covariance matrix @xmath18 ( where @xmath19 is the inverse noise matrix , and @xmath20 is the inverse covariance matrix for the cmb ) . these fluctuation maps are sampled by a linear transformation , numerically computed with conjugate gradient descent , of a spatial white noise gaussian process thereby generating maps with all the same statistical properties as samples from @xmath17 . each step of conjugate gradient descent involves a multiplication by the matrix @xmath21 , which can be done very quickly by multiplication by @xmath19 in the basis in which it is diagonal , followed by a transform to the spherical harmonic basis where @xmath22 is diagonal . for spatially uncorrelated noise and circularly symmetric beams , we only need to transform from the pixel to the spherical harmonic domain , with an expense @xmath23 @xcite . in order to accommodate spatially correlated noise , we transform to the time domain , followed by a transform to the spherical harmonics , giving an expense @xmath24 $ ] where @xmath0 is the number of time samples , and @xmath3 depends on the convergence rate of conjugate gradient descent . including the full complications of asymmetric beams , we would need to compute a convolution on the sphere . using the convolution method of ( @xcite ) , the expense of our method is @xmath25 $ ] . the computational feasibility of this method is limited by finding a numerical implementation of conjugate gradient descent which converges quickly so that the prefactor @xmath3 above is small . the strategy here is to embed the data in a region covered by an exact ring set scan , following the intuition that good preconditioners can be constructed for scan strategies close to ring sets @xcite . embedding the data in a region on the sky with no observations ( or where they have been removed ) is accommodated by numerically marginalizing over the missing observations . moreover , the same techniques can be used to marginalize over the foregrounds , and provide monte carlo estimates of the confidence intervals for cosmological parameters . the paper is organized as follows . we first review complications with a direct computation of the likelihood , and provide an overview of our approach . we then discuss a technique we call transformed white noise sampling , which allows us to sample maps representing fluctuations about the mean field map for some guess of the power spectrum . we demonstrate the method with a flat sky @xmath26 test case , including incomplete sky coverage , with uncorrelated , non - homogeneous noise . we close with a discussion of further complications encountered in real cmb experiments , and how they can be accommodated in the framework presented here .

power spectrum estimation and evaluation of associated errors in the presence of incomplete sky coverage ; non - homogeneous , correlated instrumental noise ; and foreground emission is a problem of central importance for the extraction of cosmological information from the cosmic microwave background . maps of the cmb and foregrounds are sampled by a linear transform of a gaussian white noise process , implemented numerically with conjugate gradient descent . for time

power spectrum estimation and evaluation of associated errors in the presence of incomplete sky coverage ; non - homogeneous , correlated instrumental noise ; and foreground emission is a problem of central importance for the extraction of cosmological information from the cosmic microwave background . we develop a monte carlo approach for the maximum likelihood estimatation of the power spectrum . the method is based on an identity for the bayesian posterior as a marginalization over unknowns , and maximization of the posterior involves the computation of expectation values as a sample average from maps of the cosmic microwave background and foregrounds given some current estimate of the power spectrum or cosmological model , and some assumed statistical characterization of the foregrounds . maps of the cmb and foregrounds are sampled by a linear transform of a gaussian white noise process , implemented numerically with conjugate gradient descent . for time series data with samples , and pixels on the sphere , the method has a computational expense $ ] , where is a prefactor determined by the convergence rate of conjugate gradient descent . preconditioners for conjugate gradient descent are given for scans close to great circle paths , and the method allows partial sky coverage for these cases by numerically marginalizing over the unobserved , or removed , region .

1608.07175

i

[ [ section ] ] when experimenting with primes in division algebras , an affinity of primes in @xmath0 and @xmath1 with the structure in the standard model of particle physics emerged : primes in @xmath0 resemble leptons , while equivalence classes of primes in @xmath1 have hadron like features @xcite . in @xmath0 , where besides the ramified gaussian primes of norm @xmath6 like @xmath7 , two other type of primes exist , there is a lepton structure : in @xmath0 we see cartoon versions of neutrini as well as electron - positron pairs . in @xmath1 , where besides the ramified primes above @xmath8 , only one type of primes exists , modulo @xmath9 gauge transformations , the structure of @xmath10-equivalence classes appear to be hadrons " : there are either mesons or baryons , where the individual elements of the equivalence classes resemble quarks . [ [ section-1 ] ] the algebras @xmath11 are naturally distinguished as these two are the only complete associative normed division algebras . not only the unit spheres @xmath4 of in @xmath11 but also the lie group @xmath3 acts on spheres in @xmath1 by diffeomorphisms rotating three complex planes hinged together at the real axes . this non - linear action allows to implement more symmetries or extend any quantum dynamics from @xmath0 to @xmath1 valued fields . these symmetries lead to finite norm preserving group actions on quaternion integers and can be implemented without mentioning lie groups : the weak equivalence is obtained by using multiplication by units in @xmath1 ; the strong symmetries on integers @xmath12 in @xmath1 is generated by the 24 permutations or sign changes . obviously this can be realized using both rotations or reflections in @xmath2 or then by permutations and sign changes in the space components @xmath13 of the quaternion . the upshot is that every integer has a strong equivalence class @xmath12 with non - negative entries where @xmath14 . if we look at weak equivalence classes in such integer classes , the result is that each class has either one , two or three elements , where the case with one element only happens if @xmath15 . [ [ section-2 ] ] the fact that the major gauge groups of the standard model appear as symmetries in @xmath1 suggests to look at * quaternion quantum mechanics * , where waves are @xmath1-valued . such a physics could be realized by looking at quaternion valued wave equations developed by fueter @xcite who also noticed that the dirac equation in quaternion analysis plays the role of the cauchy - riemann differential equations . alternatively , one can extend linear or nonlinear wave evolutions from @xmath0-valued fields in sub planes to quaternion - valued fields : just evolve simultaneously the classical waves on planes spanned by @xmath16 and one of the spacial units like @xmath17 in @xmath1 . if @xmath18 is any self - adjoint hamiltonian operator , then instead of quantum dynamics @xmath19 for a wave @xmath20 , one can consider two other waves @xmath21 and evolve all simultaneously using @xmath22 . this assures that @xmath23 stays invariant . the three evolutions can be merged together to a quaternion with this norm @xmath24 by putting @xmath25 and @xmath26 with sign @xmath27 chosen so that @xmath28 has positive jacobean . this assures that @xmath29 is time invariant . the second equivalence relation , the @xmath10 symmetry comes from the cayley - dickson picture expressing @xmath12 as a pair of two complex numbers @xmath30 for which @xmath31 with the complex matrix @xmath32 built by pauli matrices . these weak symmetries on @xmath33 can be implemented as determinant preserving unitary @xmath34 matrices and so by elements in @xmath10 . obviously , the weak and strong equivalence classes are different . looking at both together in @xmath1 gives the hadron structure on primes . this amusing fact is is pure finite combinatorics . [ [ section-3 ] ] one can ask now why number theory should matter in quantum dynamics , as a random quaternion is almost surely never an integer . one can look however at the dynamics on a geometry " , a space @xmath35 with exterior derivative and measure @xmath36 , where one classically evolves waves in @xmath37 , moving according to some dynamics in the hilbert space @xmath38 with norm @xmath39 . the quaternion quantum evolution preserves this norm but at individual points @xmath40 , the wave amplitude changes . gauge symmetry now can render integers relevant : if a wave amplitude reaches integer arithmetic @xmath1 norm @xmath41 at some point , the wave value @xmath42 can be gauged within the gauge groups to become @xmath1-integer valued at this point . its prime factorization structure features now particles at this point . the switch of factorizations could now be seen as particle processes in which fermions = odd primes exchange vector gauge bosons = units or ramified primes = neutral bosons . unit migration is an exchange of bosons and recombination is particle pair creation or annihilation , mending in some way also the particle - wave duality conundrum . [ [ section-4 ] ] this picture most certainly is just an allegory or caricature even in the realm of particle phenomenology alone when disregarding dynamics : the reason is that even the simplest processes like * beta decay of a neutron * @xmath43 to a proton , electron , electron neutrino , or a * pion decay * @xmath44 , where a meson decays into two leptons can not be explained by unit migration , recombination or meta commutation in @xmath1 alone . also , the way , how charge is defined below , no baryons do exist for which all three quarks have charge @xmath45 . this violates the existence of the @xmath46 baryon . we believe however that the definition of charge given here can be modified to incorporate this . we have just chosen an algorithm ( using lipschitz or hurwitz primes ) which gives us a deterministic charge . there is no other reason why @xmath47 charge triplets are excluded . + [ [ section-5 ] ] the picture drawn here is probably of little value for physics as the later by definition requires to be able to do * quantitative predictions * or * quantitative verifications * of experimentally observable processes . and the picture drawn here does neither . we feel however that the story is of mathematical interest and that it motivates to look more closely at higher arithmetic in @xmath1 as well at the mathematical structure of standard model which appears to suffer from a * lack of inevitability*. while the standard model is one of the most successful physical theories with excellent match between experiment and model , the structure of the involved lagrangians is complicated even if one looks at it from a non - commutative geometry point of view . [ [ section-6 ] ] affinities between mathematical structures and physical phenomena are sometimes useful , sometimes just amusing . here is an example of the more amusing type @xcite : when looking at the rubik group , a finite group , there are permutations available when disassembling and recombining the actual cube which resemble quarks : turn a corner cube by 120 degrees for example . rotating one corner and other corner in the opposite direction gives a quark - anti quark meson and this permutation is realizable . turning three corners by 120 degree can physically be realized and resembles a baryon . also this picture is useless for physics but it is of some value as it helps to learn more about the structure of that particular finite group . [ [ section-7 ] ] the standard model does not answer why the number of generations of hadrons or leptons is limited to three or why the gauge groups are not unified to a larger group like @xmath48 predicted by some grand unified theories . we have seen that @xmath1 naturally features the gauge groups of the standard model , even so the @xmath3 symmetry acts only by diffeomorphisms . the three generations can emerge naturally in a quaternion - valued quantum mechanics as we have to evolve waves in three different planes . since the time scales in the different planes are in general different ( as there is no reason why they should agree ) , a particle involving in a faster plane appears to be lighter . better than * imposing * a wave evolution is to let the system just evolve freely in its isospectral set . wave dynamics then emerges naturally @xcite in the form of isospectral lax deformations of exterior derivatives leading to three generations of geometries . as both leptons and hadrons move in at least one plane and more likely in 2 or 3 planes at the same time , the probability of having a light particles is larger . the heavier particles like the top quark are more rare . the neutrini in the intersection of these planes participate to any of three dynamics producing thought associations with the observed phenomenon of neutrino oscillations . [ [ section-8 ] ] number theory in @xmath1 has started with hurwitz @xcite who built the setup and established some factorization features . the fundamental theorem of arithmetic in @xmath1 was completed @xcite . the fact that quaternions were an outcast in part of the 20th century can historically be traced to the success of vector calculus , especially as formulated by gibbs and wilson @xcite , a book so successful that its content not only structured practically all modern calculus textbooks but also removed quaternions from the curricula . quaternion calculus was still cultivated , like by the swiss number theorist rudolf fueter who found a cauchy integral theorem for quaternions ( see @xcite ) . there is certainly much still to be explored . only recently , the permutation structure of the meta - commutation in the prime factorization has been studied for the first time @xcite .

primes in the two complete associative normed division algebras and have affinities with structures seen in the standard model of particle physics . on the integers in the two algebras , weak equivalence classes within the strong equivalence classes of odd primes in case relate to leptons , the inert ones being neutrino like , and the split ones resembling electron - positron pairs . in the case , for odd primes ,

primes in the two complete associative normed division algebras and have affinities with structures seen in the standard model of particle physics . on the integers in the two algebras , there are two equivalence relations : a strong one , related to a and symmetry allowing to permute and switch signs of the coordinates of the integers , as well as a weak relation with origins from units in the algebra . weak equivalence classes within the strong equivalence classes of odd primes in case relate to leptons , the inert ones being neutrino like , and the split ones resembling electron - positron pairs . in the case , for odd primes , the equivalence classes come in groups of two or three , leading to a caricature of hadrons featuring either mesons built by a quark pair or then baryons obtained by quark triplets . we can now list for every rational prime all these particles and attach fractional charges to its constituents .

0811.1081

i

principal component analysis ( pca ) is one of the most valuable results from applied linear algebra , and probably the most popular method used for compacting higher dimensional data sets into lower dimensional ones for data analysis , visualization , feature extraction , or data compression @xcite . pca provides a statistically optimal way of dimensionality reduction by projecting the data onto a lower - dimensional orthogonal subspace that captures as much of the variation of the data as possible . unfortunately , pca quickly becomes quite expensive to compute for high - dimensional data sets , where both the number of variables and samples is high . therefore , there is a real need in many applications to accelerate the computation speed of pca algorithms . for large data sets , the standard approach is to use an iterative algorithm which computes the components sequentially , and to avoid the global methods which calculate all the components simultaneously . nipals - pca @xcite is the most frequently used iterative algorithm , and often considered as the standard pca algorithm . however , for large data matrices , or matrices that have a high degree of column collinearity , nipals - pca suffers from loss of orthogonality , due to the errors accumulated in each iteration step @xcite . therefore , in practice it is only used to estimate the first few components . here , we address both the speed and orthogonality problems , and we offer new solutions which eliminate these shortcomings of the iterative pca algorithms . we formulate an iterative pca algorithm based on the gram - schmidt re - orthogonalization , which we called gs - pca . this algorithm is stable from the orthogonality point of view , and if necessary , it can be used to calculate the full set of principal components . the speed up issue is tackled with a parallel implementation for graphics processing units ( gpus ) . here , we present the gpu parallel implementation of both nipals - pca and gs - pca algorithms . the numerical results show that the gpu parallel optimized versions , based on cublas ( nvidia ) @xcite , are substantially faster ( up to 12 times ) than the cpu optimized versions based on cblas ( gnu scientific library ) @xcite .

principal component analysis ( pca ) is a key statistical technique for multivariate data analysis . for large data sets the common approach to pca computation is based on the standard nipals - pca algorithm , which unfortunately suffers from loss of orthogonality , and therefore it s applicability is usually limited to the estimation of the first few components . here we present an algorithm based on gram - schmidt orthogonalization ( called gs - pca ) , which eliminates this shortcoming of nipals - pca . also , we discuss the gpu ( graphics processing unit ) parallel implementation of both nipals - pca and gs - pca algorithms . the numerical results show that the gpu parallel optimized versions , based on cublas ( nvidia ) are substantially faster ( up to 12 times ) than the cpu optimized versions based on cblas ( gnu scientific library ) .

principal component analysis ( pca ) is a key statistical technique for multivariate data analysis . for large data sets the common approach to pca computation is based on the standard nipals - pca algorithm , which unfortunately suffers from loss of orthogonality , and therefore it s applicability is usually limited to the estimation of the first few components . here we present an algorithm based on gram - schmidt orthogonalization ( called gs - pca ) , which eliminates this shortcoming of nipals - pca . also , we discuss the gpu ( graphics processing unit ) parallel implementation of both nipals - pca and gs - pca algorithms . the numerical results show that the gpu parallel optimized versions , based on cublas ( nvidia ) are substantially faster ( up to 12 times ) than the cpu optimized versions based on cblas ( gnu scientific library ) . institute for biocomplexity and informatics university of calgary 2500 university drive nw , calgary alberta , t2n 1n4 , canada

hep-th9504098

i

since the previous erice school on ` string quantum gravity ' a host of impressive developments has taken place on strings in curved spacetime . for the state of the art in 1992 we refer to the 1992 proceedings @xcite where the programme on string quantization in curved spacetimes initiated by us in 1987 @xcite is reviewed . a consistent quantum theory of gravity is the strongest motivation for string theory and hence to study strings in curved spacetime@xcite . as stressed in the sec . 1 of the 1992 lectures , a quantum theory of gravity must be a theory able to describe all physics below the planck scale @xmath6tev . that means that a sensible theory of quantum gravity is necessarily part of a unified theory of all interactions . * pure gravity * ( a model containing only gravitons ) can not be a physical and realistic quantum theory . to give an example , a theoretical prediction for graviton - graviton scattering at energies of the order of @xmath7 must include all particles produced in a real experiment . that is , in practice , all existing particles in nature , since gravity couples to all matter . string theory is therefore a serious candidate for a quantum description of gravity since it provides a unified model of all interactions overcoming at the same time the nonrenormalizable character of quantum fields theories of gravity . the present lectures deal mainly with strings in cosmological spacetimes ; substantial results were achieved in this field since 1992 . the classical behaviour of strings in frw and inflationary spacetimes is now understood in a large extent@xcite . this understanding followed the finding of various types of exact and numerical string solutions in frw and inflationary spacetimes@xcite -@xcite . for inflationary spacetimes , the exact integrability of the string propagation equations plus the string constraints in de sitter spacetime @xcite is indeed an important help . this allowed to systematically find * exact * string solutions by soliton methods using the linear system associated to the problem ( the so - called dressing method in soliton theory ) and the multistring solutions @xcite -@xcite . in summary , three different types of behaviour are exhibited by the string solutions in cosmological spacetimes : * unstable , dual * to unstable and * stable*. for the unstable strings , the energy and size grow for large scale factors @xmath0 , proportional to @xmath1 . for the dual to unstable strings , the energy and size blow up for @xmath2 as @xmath3 . for stable strings , the energy and proper size are bounded . ( in minkowski spacetime , all string solutions are of the stable type ) . the equation of state for these string behaviours take the form * \(i ) * unstable * for @xmath8 * \(ii ) * dual to unstable * for @xmath9 . * \(iii ) * stable * for @xmath10 . here @xmath11 and @xmath12 stand for the corresponding string energies and @xmath13 for the number of spatial dimensions where the string solutions lives . for example , @xmath14 for a straight string , @xmath15 for a ring string , etc . this number @xmath16 is obviously less or equal than the number of spacetime dimensions @xmath17 . as we see above , the dual to unstable string behavior leads to the same equation of state than radiation ( massless particles or hot matter ) . the stable string behavior leads to the equation of state of massive particles ( cold matter ) . the unstable string behavior is a purely ` stringy ' phenomenon . the fact that in entails a negative pressure is however physically acceptable . for a gas of strings , the unstable string behaviour dominates in inflationary universes when @xmath18 and the dual to unstable string behavior dominates for @xmath19 . the unstable strings correspond to the critical case of the so called _ coasting universe _ @xcite . that is , classical strings provide a _ concrete _ realization of such cosmological models . the ` unstable ' behaviour is called ` string stretching ' in the cosmic string literature @xcite . it must be stressed that while time evolves , a * given * string solution may exhibit two and even three of the above regimes one after the other ( see sec . intermediate behaviours are also observed in ring solutions @xcite . that is , @xmath20 another new feature appeared in curved spacetimes : * multistring solutions*. that is a single world - sheet simultaneously describes many different and independent strings . this phenomenon has no analogue in flat spacetime . this is a new feature appearing as a consequence of the interaction of the strings with the spacetime geometry . the world - sheet time @xmath21 turns out to be an multi - valued function of the target string time @xmath22 ( which can be the cosmic time @xmath23 , the conformal time @xmath24 or for de sitter universes it can be the hyperboloid time @xmath25 ) . each branch of @xmath21 as a function of @xmath22 corresponds to a different string . in flat spacetime , multiple string solutions are necessarily described by multiple world - sheets . here , a single world - sheet describes one string , several strings or even an infinite number of different and independent strings as a consequence of the coupling with the spacetime geometry . these strings do not interact among themselves ; all the interaction is with the curved spacetime . one can decide to study separately each of them ( they are all different ) or consider all the infinite strings together . of course , from our multistring solution , one _ could _ just choose only one interval in @xmath26 ( or a subset of intervals in @xmath27 ) and describe just one string ( or several ) . this will be just a * truncation * of the solution . the really remarkably fact is that all these infinitely many strings come * naturally together * when solving the string equations in de sitter spacetime as we did in refs . @xcite -@xcite . here , interaction among the strings ( like splitting and merging ) is neglected , the only interaction is with the curved background . the study of string propagation in curved spacetimes provide essential clues about the physics in this context but is clearly not the end of the story . the next step beyond the investigation of * test * strings , consist in finding * self - consistently * the geometry from the strings as matter sources for the einstein equations or better the string effective equations ( beta functions ) . this goal is achieved in ref.@xcite for cosmological spacetimes at the classical level . namely , we used the energy - momentum tensor for a gas of strings as source for the einstein equations and we solved them self - consistently . to write the string equation of state we used the behaviour of the string solutions in cosmological spacetimes . strings continuously evolve from one type of behaviour to another , as is explicitly shown by our solutions @xcite -@xcite . for intermediate values of @xmath28 , the equation of state for gas of free strings is clearly complicated but a formula of the type : @xmath29 where @xmath30 this equation of state is qualitatively correct for all @xmath28 and becomes exact for @xmath19 and @xmath31 . the parameters @xmath32 and @xmath33 are positive constants and the @xmath34 varies smoothly with @xmath1 . the pressure associated to the energy density ( [ rogeni ] ) takes then the form @xmath35 inserting this source into the einstein - friedman equations leads to a self - consistent solution for string dominated universes ( see sec . iv ) @xcite . this solution exhibits the realistic matter dominated behaviour @xmath36 for large times and the radiation dominated behaviour @xmath37 for early times . for the sake of completeness we analyze in sec . iv the effective string equations @xcite . these equations have been extensively treated in the literature @xcite and they are not our central aim . it must be noticed that there is no satisfactory derivation of inflation in the context of the effective string equations . this does not mean that string theory is not compatible with inflation , but that the effective string action approach _ is not enough _ to describe inflation . the effective string equations are a low energy field theory approximation to string theory containing only the _ massless _ string modes . the vacuum energy scales to start inflation are typically of the order of the planck mass where the effective string action approximation breaks down . one must also consider the _ massive _ string modes ( which are absent from the effective string action ) in order to properly get the cosmological condensate yielding inflation . de sitter inflation does not emerge as a solution of the the effective string equations . in conclusion , the effective string action ( whatever be the dilaton , its potential and the central charge term ) is not the appropriate framework in which to address the question of string driven inflation . early cosmology ( at the planck time ) is probably the best place to test string theory . in one hand the quantum treatment of gravity is unavoidable at such scales and in the other hand , observable cosmological consequences are derivable from the inflationary stage . the natural gravitational background is an inflationary universe as de sitter spacetime . such geometries are not string vacua . this means that conformal and weyl symmetries are broken at the quantum level . in order to quantize consistently strings in such case , one must enlarge the physical phase space including , in particular , the factor @xmath38 in the world - sheet metric [ see eq.([liou ] ) ] . this is a very interesting and open problem . physically , the origin of such difficulties in quantum string cosmology comes from the fact that one is not dealing with an * empty * universe since a cosmological spacetime necessarily contains matter . in the other hand , conformal field theory techniques are only adapted to backgrounds for which the beta functions are identically zero , i. e. sourceless geometries . the outline of these lectures is as follows . section ii presents an introduction to strings in curved spacetimes including basic notions on classical and quantum strings in minkowski spacetime and introducing the main physical string magnitudes : energy - momentum and invariant string size . section iii deals with the string propagation and the string energy - momentum tensor in cosmological spacetimes . ( in sections iii.a , iii.b and iii.c we treat the straight strings , ring strings and generic strings respectively and derive the corresponding string equations of state ) . in section iv we treat self - consistent string cosmology including the string equations of state . ( section iv.a deals with general relativity , iv.b with the string thermodynamics ) . section v discuss the effective ( beta functions ) string equations in the cosmological perspective and the search of inflationary solutions . finally , in sec . vi , we briefly review the systematic construction of string solutions in de sitter universe _ via _ soliton methods and the new feature of multistring solutions .

progress on string theory in curved spacetimes since 1992 are reviewed . after a short introduction on strings in minkowski and curved spacetimes , we focus on strings in cosmological spacetimes . the classical behaviour of strings in frw and inflationary spacetimes is now understood in a large extent from various types of explicit string solutions . three different types of behaviour appear in cosmological spacetimes : * unstable , dual * to unstable and * stable*. for the unstable strings , the energy and size grow for large scale factors , proportional to . for the dual to unstable strings , the energy and size blow up for as . for stable strings , the energy and proper size are bounded . ( in minkowski spacetime , all string solutions are of the stable type ) . recent progress on self - consistent solutions to the einstein equations for string dominated universes is reviewed . the energy - momentum tensor for a gas of strings is then considered as source of the spacetime geometry and from the above string behaviours the string equation of state is determined . the self - consistent string solution exhibits the realistic matter dominated behaviour for large times and the radiation dominated behaviour for early times . finally , we report on the exact integrability of the string equations plus the constraints in de sitter spacetime that allows to systematically find * exact * string solutions by soliton methods and the multistring solutions . that is , a single world - sheet simultaneously describes many different and independent strings . this phenomenon has no analogue in flat spacetime and appears as a consequence of the coupling of the strings with the spacetime geometry . lectures delivered at the erice school `` current topics in astrofundamental physics '' 4 - 16 september 1994 , to appear in the proceedings edited by n. snchez .

progress on string theory in curved spacetimes since 1992 are reviewed . after a short introduction on strings in minkowski and curved spacetimes , we focus on strings in cosmological spacetimes . the classical behaviour of strings in frw and inflationary spacetimes is now understood in a large extent from various types of explicit string solutions . three different types of behaviour appear in cosmological spacetimes : * unstable , dual * to unstable and * stable*. for the unstable strings , the energy and size grow for large scale factors , proportional to . for the dual to unstable strings , the energy and size blow up for as . for stable strings , the energy and proper size are bounded . ( in minkowski spacetime , all string solutions are of the stable type ) . recent progress on self - consistent solutions to the einstein equations for string dominated universes is reviewed . the energy - momentum tensor for a gas of strings is then considered as source of the spacetime geometry and from the above string behaviours the string equation of state is determined . the self - consistent string solution exhibits the realistic matter dominated behaviour for large times and the radiation dominated behaviour for early times . finally , we report on the exact integrability of the string equations plus the constraints in de sitter spacetime that allows to systematically find * exact * string solutions by soliton methods and the multistring solutions . * multistring solutions * are a new feature in curved spacetimes . that is , a single world - sheet simultaneously describes many different and independent strings . this phenomenon has no analogue in flat spacetime and appears as a consequence of the coupling of the strings with the spacetime geometry . lectures delivered at the erice school `` current topics in astrofundamental physics '' 4 - 16 september 1994 , to appear in the proceedings edited by n. snchez .

gr-qc0406121

i

the purpose of this paper is to present a novel approach to the unification of space - time physics and quantum theory . we take the view that classical space - time itself is not to be regarded as a primary object which is then subjected to some form of quantisation procedure . in our framework the central object is a mathematical structure that we call a quantum space - time . intuitively , this structure can be regarded as the space of all space - time valued quantum operators . that is to say , each point in the infinite - dimensional quantum space - time corresponds to a quantum operator with the property that its expectation , in any quantum state , is a space - time point . the space of all such operators has a rich structure that appears to contain all the elements one needs both for a characterisation of the causal structure of relativistic space - time as well as a representation of the phenomena of quantum theory . many attempts to unify gravitational physics with other fundamental forces have pursued the idea of extending four - dimensional space - time to higher dimensions . beginning with the introduction of the kaluza - klein theory of gauge potentials , such extensions have typically been carried out by increasing the spatial dimension of the space - time , while retaining the special role played by time . in methodologies of this sort , however , it can not be said that quantum mechanical characteristics of the fundamental forces are adequately incorporated into the structure of the higher dimensional space - time . nor can it be said that the space - time itself is being treated in any useful sense as a quantum entity . in what follows , however , we demonstrate that if we take the point of view that the universe is itself intrinsically quantum mechanical in an appropriate sense , then the most natural extension of space - time into higher dimensions has a completely different character from that suggested by the kaluza - klein theory and its generalisations . the basic idea is as follows . the points of minkowski space are in natural correspondence with two - by - two matrices of the form @xmath0 satisfying a hermitian condition . lorentz transformations are then given by multiplying @xmath0 on the right and on the left by an element of @xmath1 and its complex conjugate , and the minkowskian metric for the interval between two points @xmath0 and @xmath2 is obtained by taking the determinant of their difference . hermitian matrices are , on the other hand , familiar objects in quantum mechanics in their role as physical observables . in quantum mechanics , the dimensionality of the hilbert space is directly related to the dimensionality of the corresponding space of hermitian operators . thus , if quantum theory is to be unified with space - time physics , it seems natural to extend the space of matrices representing space - time points to higher dimensions , and thus to assume that the dimensionality of space - time is much larger than four , perhaps infinite . a higher - dimensional extension of space - time in this manner is also consistent with the philosophy often put forward that spinors ( or twistors ) are in some respects just as fundamental , or possibly even more fundamental , than the space - time points themselves . the framework we introduce here is motivated by the idea that the symmetries of space - time and the symmetries of quantum theory are , at the deeper level , indistinguishable . this generalised ` equivalence principle ' reflects the notion that the fundamental symmetries or approximate symmetries we observe in nature should have a common origin , and that the breakdown of these symmetries should also have a common cause . in view of the generalised equivalence principle we shall therefore postulate in this investigation that _ space - time events are themselves infinite - dimensional hermitian matrices_. as in ordinary quantum mechanics , however , it is both legitimate and desirable to consider finite dimensional realisations of the framework in some circumstances . these finite dimensional realisations are given by spaces of @xmath3-by-@xmath3 hermitian matrices . in this way we obtain for each @xmath4 an @xmath5-dimensional space - time @xmath6 . the standard four - dimensional minkowski space @xmath7 then emerges as the simplest case . as we explain later in the paper , we regard such finite dimensional cases not merely as toy models , but rather as special situations where a finite - dimensional part of the infinite - dimensional space - time is ( or effectively can be regarded as ) disentangled from the rest of the space - time . in this way the fundamental role played by the segr embedding in the geometry of quantum theory is carried over to the relativistic domain . indeed , it is an important feature of our approach that many of the familiar ideas relevant to the geometry of the quantum state space are directly applicable to space - time itself , and as such take on a new physical significance , some aspects of which we explore in what follows . the structure of the paper is as follows . in 2 we introduce the algebraic formalism appropriate for the manipulation of @xmath3-component hyperspinors . the concept of hyperspinors as a natural higher dimensional generalisation of the familiar two - component spinors of relativity theory and as a basis for higher - dimensional space - time theories was introduced by finkelstein ( 1986 ) and finkelstein _ et al_. ( 1987 ) , and we build on that work here . the @xmath5-dimensional quantum space - time @xmath8 then arises as the tensor product of the space of @xmath3-dimensional hyperspinors with its complex conjugate . in 3 we investigate the causal structure of @xmath6 . this structure is shown to arise by virtue of a resolution of the vector separating any two points in @xmath6 into a canonical form involving a sum of terms , each of which can be expressed as a product of a hyperspinor with its complex conjugate , together with a plus or minus sign . in particular , we can introduce the concept of future and past pointing time - like and null vectors in @xmath8 . this structure exists despite the fact that @xmath8 does not possess a pseudo - riemannian metric . instead , @xmath6 possesses a chronometric form of rank @xmath3 , which induces a pseudo - finslerian geometry on @xmath8 . in 4 we look at the variational problem for determining the geodesic between two time - like separated points , and show that this reduces to an appropriate linear expression , despite the fact that the chronometric form is itself a polynomial of degree @xmath3 in the separation vector for the given points . in 5 - 6 we study the higher dimensional analogue of the poincar group that acts on @xmath8 . we prove that the symmetries of this space are generated by a system of @xmath9 irreducible killing tensors , each of rank @xmath10 . since @xmath6 does not have a pseudo - riemannian structure for @xmath11 , the link between symmetries and killing vectors is lost in general , and is replaced by this more subtle manifestation of symmetry . we show that the conserved quantities associated with the hyper - poincar group can be obtained in terms of algebraic expressions formed from the killing tensors . we also derive appropriate hyper - relativistic generalisations of the familiar expressions for the momentum , angular momentum , mass , and spin of a relativistic system . in 7 we make a detailed study of the algebraic geometry of the complex light - cone at a point of @xmath8 , and examine the structures arising for various values of @xmath3 . we show that the space of complex light - like directions is a complex hypersurface @xmath12 of degree @xmath3 in the complex projective space @xmath13 . the hypersurface @xmath14 can be completely characterised by the fact that it admits a special hyperspinorial subvariety of the form @xmath15 . in 8 we present a higher dimensional analogue of the klein representation , and show how @xmath8 , when complexified and compactified , can be represented as the grassmannian of complex @xmath16-planes in @xmath17 . we show that the causal relations between points of @xmath8 can be understood in terms of the intersection properties of the corresponding @xmath16-planes . in 9 we show how the conformal symmetry of the geometry of the generalised klein representation can be reduced to the hyper - poincar group by the introduction of elements determining the structure of infinity for this space . the range of possibilities for structure at infinity is considerably larger than it is for four - dimensional space - time . as a consequence , as we show in 10 , the choice of structure at infinity can also give rise to interesting classes of cosmological models . we point out that there is a mechanism within our framework whereby the same structures at infinity responsible for the reduction of the symmetry of space - time can also be responsible for the breaking of microscopic symmetries . in 11 we further explore the notion of symmetry breaking , and introduce the idea of the segr embedding as the basis of the mechanism according to which space - time degrees of freedom can be disentangled from microscopic or internal degrees of freedom . according to this scheme the dimension of the hyperspinor space is assumed to be even , and each hyperspinor index @xmath18 with the range @xmath19 is regarded as a clump consisting of a conventional two - component spinor index @xmath20 and an `` internal '' index @xmath21 . it follows as a consequence of this symmetry breaking scheme that the points of @xmath22 can be interpreted as _ space - time valued operators_. this is the sense in which @xmath23 can be regarded as a quantum space - time . finally , in support of this interpretation , in 12 we consider maps from @xmath22 to minkowski space @xmath24 . we show that if such a map @xmath25 is in a suitably defined sense ( i ) linear , ( ii ) poincar invariant , and ( iii ) causal , then @xmath25 is a density matrix , and the map can be interpreted as the expectation . thus within our scheme an important element of the probabilistic interpretation of quantum theory arises as an emergent property deriving from the causal nature of space - time .

it is shown that the causal geometry of such a quantum space - time possesses a rich hierarchical structure . in particular , we prove that the symmetry group of a quantum space - time is generated in general by a system of irreducible killing tensors . it is shown that the general such map satisfying appropriate causality - preserving conditions ensuring linearity and poincar invariance is necessarily a density matrix .

quantum mechanics , quantum entanglement , causal spaces , + density matrices , cosmological models , hyperspinors + working paper : 29 june 2004 a generalised equivalence principle is put forward according to which _ space - time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking_. based on this principle , a higher - dimensional extension of minkowski space is proposed and its properties examined . in this scheme the structure of space - time is intrinsically quantum mechanical . it is shown that the causal geometry of such a quantum space - time possesses a rich hierarchical structure . the natural extension of the poincar group to quantum space - time is investigated . in particular , we prove that the symmetry group of a quantum space - time is generated in general by a system of irreducible killing tensors . when the symmetries of a quantum space - time are spontaneously broken , then the points of the quantum space - time can be interpreted as _ space - time valued operators_. the generic point of a quantum space - time in the broken symmetry phase thus becomes a minkowski space - time valued operator . classical space - time emerges as a map from quantum space - time to minkowski space . it is shown that the general such map satisfying appropriate causality - preserving conditions ensuring linearity and poincar invariance is necessarily a density matrix .

cond-mat0307619

i

linear response theory ( lrt ) @xcite is the leading formalism to deal with driven systems . such systems are described by a hamiltonian @xmath2 where @xmath3 is a set of time dependent classical parameters ( `` fields '' ) . the kubo formula is the corner stone of lrt . it allows the calculation of the response coefficients , and in particular the _ conductance matrix _ ( @xmath4 ) of the system . if we know @xmath4 , we can calculate the charge ( @xmath0 ) which is transported through the system during one cycle of a periodic driving . this is called _ pumping_. pumping of charge in mesoscopic @xcite and molecular size devices is regarded as a major issue in the realization of future quantum circuits or quantum gates , possibly for the purpose of quantum computing . in order to explain the motivation for the present work , and its relation to the published literature , we have to give a better definition of the problem . for presentation purpose we focus on a model system with a ring geometry ( fig.1 ) . the shape of the ring is controlled by some parameters @xmath5 and @xmath6 . these parameters can be gate voltages that determine the location of some boundaries , or the height of some barriers . the third parameter is the flux through the ring : @xmath7 we shall use units such that the elementary charge is . note that the hamiltonian @xmath8 has gauge invariance for @xmath9 . another system with a ring topology is presents in fig . 1b , and its abstraction is represented in fig . 2c . the dot " can be represented by an @xmath1 matrix that depends on @xmath5 and @xmath6 . in fig . 1d also the flux @xmath10 is regarded as a parameter of the dot . if we cut the wire in fig.1d we get the open two lead geometry of fig.1e . finally we can put many such units in series ( no flux ) , hence getting the periodic system of fig.1f . in the latter case the hamiltonian is invariant for unit translations , and therefore the quasi momentum @xmath11 is a constant of motion . it follows that the mathematical treatment of a driven periodic structure reduces to an analysis of a driven ring system with flux . _ pumping " _ means that net charge ( or maybe better to say net integrated probability current " ) is transported through the ring per cycle of a periodic driving . using the common jargon of electrical engineering this can be described as ac - dc conversion . we distinguish between + * pumping in open systems ( such as in fig . * pumping in closed systems ( such as in fig . 1d ) * pumping in periodic systems ( such as in fig . 1f ) for a reason that was explained at the end of the previous subsection we regard the last category @xcite as mathematically equivalent to the second category . we also regard the first category @xcite as a special ( subtle ) limit of the second category : in a follow up paper @xcite we demonstrate that in the limit of open geometry the kubo formula reduces to the @xmath1-matrix formula of bttiker prtre and thomas @xcite . there are works in the literature regarding rectification " and ratchets " @xcite . these can be regarded as studies of pumping in periodic systems with the connotation of having _ damped _ non - hamiltonian dynamics . these type of systems are beyond the scope of the present paper . there is also a recent interest in hamiltonian ratchets@xcite , which is again a synonym for pumping in periodic systems , but with the connotation of having a _ non - linear _ pumping mechanism . we are going to clarify what are the conditions for having a _ linear _ pumping mechanism . only in case of linear pumping mechanism the kubo formula can be used , which should be distinguished from the non - linear mechanism of ref.@xcite . the purpose of this paper is to explain and demonstrate that the kubo formula contains all the physically relevant ingredients for the calculation of the charge ( @xmath0 ) which is pumped during one cycle of a periodic driving . in the limit of a very slow time variation ( small @xmath12 ) , the emerging picture coincides with the adiabatic picture of refs.@xcite . in this limit the response of the system is commonly described as a non - dissipative geometric magnetism " @xcite effect , or as adiabatic transport . a major objective of this paper is to bridge between the adiabatic picture and the more general lrt / kubo picture , and to explain how _ dissipation _ emerges in the quantum mechanical treatment . for one - parameter driving a unifying picture that bridges between the quantum mechanical adiabatic picture and lrt has been presented in @xcite . a previous attempt @xcite had ended in some confusion regarding the identification of the linear response regime , while @xcite had avoided the analysis of the mechanism that leads to dissipation in the quantum mechanical case . the presented ( kubo based ) formulation of the pumping problem has few advantages : it is not restricted to the adiabatic regime ; it allows a clear distinction between _ dissipative _ and _ adiabatic _ contributions to the pumping ; the classical limit is manifest in the formulation ; it gives a level by level understanding of the pumping process ; it allows the consideration of any type of occupation ( not necessarily fermi occupation ) ; it allows future incorporation of external environmental influences such as that of noise ; it regards the voltage over the pump as electro motive force , rather than adopting the conceptually more complicated view @xcite of having a chemical potential difference . of particular interest is the possibility to realize a pumping cycle that transfers _ exactly _ one unit of charge per cycle . in open systems @xcite this quantization " holds only approximately , and it has been argued @xcite that the deviation from exact quantization is due to the dissipative effect . furthermore it has been claimed @xcite that exact quantization would hold in the strict adiabatic limit , if the system were _ closed_. in this paper we would like to show that the correct picture is quite different . we shall demonstrate that the deviation from exact quantization is in fact of adiabatic nature . this deviation is related to the so - called thouless conductance " of the device . we give several examples for the application of the kubo formula to the calculation of the pumped charge @xmath0 : + * classical dissipative pumping * classical adiabatic pumping ( by translation ) * quantum pumping in the double barrier model the last example is the main one . in the context of open geometry it is known as pumping around a resonance " @xcite . we explain that this is in fact an diabatic transfer scheme , and we analyze a particular version of this model which is represented by a 3 site lattice hamiltonian . this is definitely the simplest pump circuit possible , and we believe that it can be realized as a molecular size device . it also can be regarded as an approximation for the closed geometry version of the two delta potential pump @xcite . in section 2 we define the main object of the study , which is the conductance matrix @xmath4 of eq.([e_8 ] ) . the conductance matrix can be written as the sum of a symmetric ( @xmath13 ) and an anti - symmetric ( @xmath14 ) matrices , which are later identified as the dissipative and the adiabatic contributions respectively . in the first part of the paper ( sections 2 - 8 ) we analyze the adiabatic equation ( section 3 ) , and illuminate the distinction between its zero order solution ( section 4 ) , its stationary first order solution ( section 5 ) , and its non - stationary solution ( section 6 ) . the outcome of the analysis in section 5 is eq.([e_30 ] ) for the conductance matrix @xmath4 . this expression is purely adiabatic , and does not give any dissipation . in order to get dissipation we have to look for a non - stationary solution . the standard textbook derivation of the kubo formula ( eq.([e_33 ] ) ) for the conductance matrix @xmath4 _ implicitly _ assumes a non - stationary solution . we show how to get from it eq.([e_34 ] ) for @xmath13 and eq.([e_35 ] ) for @xmath14 . the latter is shown to be identical with the adiabatic result ( eq.([e_30 ] ) ) . in section 7 we further simplify the expression for @xmath13 leading to the fluctuation - dissipation relation ( eq.([e43 ] ) ) . the disadvantages of the standard textbook derivation of kubo formula make it is essential to introduce a different route toward eq.([e43 ] ) for @xmath13 . this route , which is discusssed in section 8 , _ explicitly _ distinguishes the dissipative effect from the adiabatic effect , and allows to determine the conditions for the validity of either the adiabatic picture or lrt . in particular it is explained that lrt is based , as strange as it sounds , on perturbation theory to infinite order . in section 9 we clarify the general scheme of the pumping calculation ( eq.([e6 ] ) ) . section 10 and section 11 give two simple classical examples . in section 12 we turn to discuss quantum pumping , where the cycle is around a chain of degeneracies . the general discussion is followed by presentation of the double barrier model ( section 13 ) . in order to get a quantitative estimate for the pumped charge we consider a 3 site lattice hamiltonian ( section 14 ) . the summary ( section 15 ) gives some larger perspective on the subject , pointing out the relation to the @xmath1-matrix formalism , and to the born - oppenheimer picture . in the appendices we give some more details regarding the derivations , so as to have a self - contained presentation .

we explain that the kubo formula contains all the physically relevant ingredients for the calculation of the pumped charge ( ) within the framework of linear response theory . we distinguish between adiabatic and dissipative contributions to . on the one hand we observe that adiabatic pumping does not have to be quantized . on the other hand we define circumstances in which quantized adiabatic pumping holds as an approximation . the deviation from exact quantization is related to the thouless conductance . as an application we discuss the following examples : classical dissipative pumping by conductance control , classical adiabatic ( non dissipative ) pumping by translation , and quantum pumping in the double barrier model . in the latter context we analyze a 3 site lattice hamiltonian , which represents the simplest pumping device . we remark on the connection with the popular matrix formalism which has been used to calculate pumping in open systems .

quantum pumping in closed systems is considered . we explain that the kubo formula contains all the physically relevant ingredients for the calculation of the pumped charge ( ) within the framework of linear response theory . the relation to the common formulations of adiabatic transport and geometric magnetism " is clarified . we distinguish between adiabatic and dissipative contributions to . on the one hand we observe that adiabatic pumping does not have to be quantized . on the other hand we define circumstances in which quantized adiabatic pumping holds as an approximation . the deviation from exact quantization is related to the thouless conductance . as an application we discuss the following examples : classical dissipative pumping by conductance control , classical adiabatic ( non dissipative ) pumping by translation , and quantum pumping in the double barrier model . in the latter context we analyze a 3 site lattice hamiltonian , which represents the simplest pumping device . we remark on the connection with the popular matrix formalism which has been used to calculate pumping in open systems .

1311.3675

i

spectrahedra are fundamental objects in convex algebraic geometry @xcite . a spectrahedron is the intersection of the cone of positive - semidefinite matrices with an affine subspace of the space of real symmetric @xmath2-matrices . in this paper , the subspace has dimension three and is identified with @xmath3 . the algebraic boundary of a three - dimensional spectrahedron in @xmath3 is a surface @xmath4 in complex projective space @xmath5 . its defining polynomial @xmath6 is the determinant of a symmetric matrix @xmath7 of linear forms . explicitly , @xmath8 the surfaces @xmath4 are known as _ symmetroids _ in classical algebraic geometry @xcite . generally , we allow the entries in the symmetric @xmath2-matrices @xmath9 to be arbitrary complex numbers . we say that @xmath4 is a _ real symmetroid _ if all @xmath10 coefficients of @xmath11 are real numbers and that @xmath4 is a _ very real symmetroid _ if @xmath9 can be chosen to have real entries . the _ spectrahedron _ associated to a very real symmetroid @xmath4 is the set @xmath12 the constraint is denoted @xmath13 and is called a _ linear matrix inequality _ ( lmi ) . maximizing a linear function over the spectrahedron @xmath14 is a _ semidefinite program_. in optimization theory , one often considers the spectrahedron @xmath14 is an affine hyperplane , e.g. @xmath15 . while much of the underlying geometry does not change , it is more convenient for us to use the language of projective geometry , rather than work in affine space . using grding s theory of _ hyperbolic polynomials _ @xcite , one sees that @xmath14 is determined by @xmath16 , i.e. the matrices @xmath9 are not needed to identify the set @xmath14 . we say that a symmetroid @xmath4 is _ spectrahedral _ if it is very real and @xmath14 is full - dimensional in @xmath17 . a symmetroid is called _ nodal _ if all its singular points are nodes , i.e. isolated quadratic singularities . generically there are @xmath18 nodes on @xmath4 . a point @xmath19 where the matrix @xmath7 has rank @xmath20 will be called a _ rank-@xmath20-point_. such a point is singular on the surface @xmath4 and generically it is a node . a nodal symmetroid has exactly @xmath21 rank-@xmath22 points @xcite and is called _ transversal _ if it does not have any further nodes . a spectrahedron @xmath14 is _ nodal _ ( resp . _ transversal _ ) if its symmetroid @xmath4 has this property . for example , the _ kummer symmetroid _ in figure [ fig : kummer ] is nodal but not transversal : it has @xmath23 nodes , not just @xmath24 . the set @xmath25 of symmetroids forms an irreducible variety in the projective space @xmath26 of all surfaces of degree @xmath27 in @xmath5 , and a generic point in @xmath28 corresponds to a transversal symmetroid . the set @xmath29 of spectrahedral symmetroids is zariski dense in the variety @xmath25 of complex symmetroids . the objects above form a nested sequence of semialgebraic subsets : @xmath30 for @xmath31 , every spectrahedron is a halfspace . for @xmath32 , a spectrahedron is a quadratic cone and the left inclusion in ( [ eq : inclusions ] ) is an equality . the quadric @xmath33 lies in @xmath34 , because no triple of real symmetric @xmath35-matrices satisfies @xmath36 and @xmath37 . -0.42 cm -0.42 cm a transversal cubic spectrahedron has either four nodes or two nodes . , height=172 ] -0.4 cm the case @xmath38 of cubic spectrahedra is visualized by the two pictures in figure [ fig : redyellow ] . here the algebraic boundary is cayley s _ cubic symmetroid_. such a cubic surface has four complex nodes , and it is unique up to projective transformations over @xmath39 . it is obtained by blowing up @xmath40 at the six intersection points of four general lines . cubic symmetroids in @xmath41 correspond to configurations of four lines that can be defined collectively over @xmath42 . there are three types : * all four lines are defined over @xmath42 . this gives the left picture with four real nodes . * two lines are defined over @xmath42 and the others form a complex conjugate pair of lines . this gives the right picture , with two real nodes , both in the boundary of the spectrahedron . * there are two complex conjugate pairs of lines . the two first types are shown in figure [ fig : redyellow ] . very real cubic symmetroids of type ( c ) have no real nodes , and they belong to the set @xmath43 ( cf . remark [ cubicspec ] and example [ nonspec ] ) . in this paper we investigate the case @xmath44 of quartic spectrahedra . the corresponding variety @xmath45 has codimension @xmath24 in the @xmath46 of all quartics . in the context of convex algebraic geometry it has appeared in ( * ? ? ? * theorem 3 ) , where it parametrizes extremal non - negative quartics that are not sums of squares . such symmetroids , like the choi - lam - reznick quartic in ( * ? ? ? * ( 8) ) , are in @xmath47 . see example [ nonspec ] for a quartic symmetroid in @xmath43 . in response to a question by the third author , degtyarev and itenberg @xcite studied the location of the ten nodes on a spectrahedral symmetroid . they proved the following result : [ thm : di ] there exists a transversal quartic spectrahedron with @xmath48 nodes on its boundary and @xmath49 real nodes in its symmetroid if and only if @xmath50 , both are even , and @xmath51 . the proof given by degtyarev and itenberg in @xcite is very indirect . it translates the problem into the period domain for k3 surfaces via the global torelli theorem , and it proceeds by characterizing the various strata in @xmath45 in terms of intersection lattices . that approach can not be used to actually construct matrices @xmath7 for quartic spectrahedra . we here present a new proof which is elementary , computational , and self - contained . for the if - direction of theorem [ thm : di ] , section 2 exhibits twenty matrices @xmath7 which realize the allowed pairs of parameters @xmath52 . that list generalizes figure [ fig : redyellow ] , which depicts the classification of cubic spectrahedra into two types , @xmath53 . our proof of the only - if direction uses classical projective geometry , and it will be given in section 4 . the idea is to build an explicit parametrization of the semi - algebraic set @xmath54 in terms of the ramification data of the projection of a symmetroid from one of its nodes . the projection of a quartic surface from a node @xmath55 is a double cover of @xmath40 ramified along a sextic plane curve @xmath56 with a totally tangent conic @xmath57 , the image of the tangent cone at @xmath55 . this picture goes back to cayley @xcite who used it to characterize nodes on quartic symmetroids . we extend cayley s result to the real numbers , with focus on spectrahedra . [ thm : cayley ] let @xmath55 be a node on a quartic surface @xmath58 in @xmath5 . then @xmath58 is a symmetroid if and only if the ramification curve is the union of two cubic curves @xmath59 . suppose that @xmath58 contains no line through @xmath55 . then @xmath58 is transversal if and only if @xmath60 and @xmath61 are smooth , intersect transversally in 9 points , and the conic @xmath57 is smooth . in this case , the surface @xmath58 and the point @xmath55 are real if and only if the curves @xmath62 and @xmath57 are real . furthermore , 1 . @xmath58 is very real and @xmath55 is real if and only if @xmath62 is real and @xmath57 has a real point . @xmath58 is spectrahedral and @xmath55 lies on the spectrahedron if and only if the cubics @xmath60 and @xmath61 are complex conjugates and the conic @xmath57 has a real point . @xmath58 is very real and @xmath55 is a real node that does not lie on the spectrahedron if and only if the cubics @xmath60 and @xmath61 are real and the conic @xmath57 has a real point . theorem [ thm : cayley ] characterizes the location of generic points in the various strata of ( [ eq : inclusions ] ) . special points are obtained as limits of these . a special symmetroid may contain a line that passes through a node @xmath55 , and the cubics @xmath63 may be singular . for instance , the kummer symmetroid shown in figure [ fig : kummer ] contains @xmath23 lines and each cubic @xmath64 factors into three lines . the paper is organized as follows . section 2 contains our gallery of transversal quartic spectrahedra . section 3 develops the projective geometry of ( real ) quartic symmetroids and their projections from nodes . it furnishes a self - contained proof of theorem [ thm : cayley ] . section 4 completes the proof of theorem [ thm : di ] and develops a further extension of theorem [ thm : cayley ] in terms of interlacing cubics . section 5 serves `` spectrahedral treats '' : various families of quartics seen in the convex algebraic geometry literature . we explain how they fit into our general theory .

quartic spectrahedra in-space form a semialgebraic set of dimension . there are twenty maximal strata , identified recently by degtyarev and itenberg , via the global torelli theorem for real k3 surfaces . we here give a new proof that is self - contained and algorithmic . this paper represents a first step towards the classification of all spectrahedra of a given degree and dimension .

quartic spectrahedra in-space form a semialgebraic set of dimension . this set is stratified by the location of the ten nodes of the corresponding real quartic surface . there are twenty maximal strata , identified recently by degtyarev and itenberg , via the global torelli theorem for real k3 surfaces . we here give a new proof that is self - contained and algorithmic . this involves extending cayley s characterization of quartic symmetroids , by the property that the branch locus of the projection from a node consists of two cubic curves . this paper represents a first step towards the classification of all spectrahedra of a given degree and dimension .

1512.00202

i

one paradigm in studies of quantum chaos is the kicked harper model ( khm ) . it was originally introduced in ref . @xcite to model a kicked charge in a magnetic field . later a whole class of generalized versions of khm were introduced , which may also be realized via a periodically kicked charge in a magnetic field @xcite . remarkably , more than two decades ago , the khm was already used to study topological phase transitions in floquet states and to understand possible connections between large floquet band chern numbers , delocalization of floquet eigenstates , and the underlying classical chaos @xcite . @xcite were perhaps the first two studies illuminating on topological phases of matter in periodically driven systems , a topic of wide interest at present due to the finding of floquet topological insulators @xcite . studies of topological phase transitions in the khm opened up stimulating questions of interest to different communities , connecting concepts from different areas such as condensed matter physics and nonlinear dynamics . the relevance of the khm to studies of topological phases becomes even more evident in recent years . in particular , it was shown that the khm and a variant of another paradigm of quantum chaos , namely , the double - kicked rotor model ( dkr ) , have a certain kind of topological equivalence though their spectrum has many distinctively different features @xcite . furthermore , it was shown that the khm has drastically different edge states as compared with that associated with the dkr , even though all their bulk floquet bands have exactly the same chern numbers @xcite . this result is useful for ongoing investigations of the issue of bulk - edge correspondence in floquet topological states as well as the issue of weak topological insulators . in previous studies @xcite , we already showed that adding one periodic system parameter to the conventional khm hamiltonian can serve the purpose of introducing an artificial dimension , thus enabling us to study the properties of two - dimensional ( @xmath3d ) systems from the perspective of one - dimensional ( @xmath4d ) systems . it was found that the quasienergy spectrum of this effective @xmath3d khm is able to host as many @xmath3d dirac cones as possible at both quasienergy @xmath1 and quasienergy @xmath2 by simply increasing the kicking strength . this suggests that the khm might be a good platform to study gapless topological phases , such as weyl semimetal @xcite and nodal line semimetal @xcite in floquet systems . motivated by these results regarding the khm , in this paper we propose to study an extended khm by introducing two periodic system parameters into the hamiltonian . with two periodic system parameters available , together with the conserved quasimomentum variable due to the translational invariance in the sole physical ( lattice ) dimension , it is possible to obtain floquet bands that can be effectively associated with three - dimensional ( @xmath0d ) systems . this thus creates an interesting opportunity to explore the khm from a perspective related to @xmath0d gapless topological phases of matter , which has recently become an interesting topic @xcite . in order to make both periodic system parameters nontrivial , we propose to introduce modulations to both the lattice hopping term and the kicking potential in the khm . these modulations are characterized by two phase shift parameters playing the role of two periodic system parameters . the model hamiltonian can thus also be deemed as a kicked version of a recently proposed off - diagonal harper model @xcite . having two periodic system parameters leads to one direct advantage in understanding the implications of various topological phases for the dynamics . specifically , it is now possible to execute adiabatic loops in the @xmath3d parameter space spanned by the two phase shift parameters , by directly and slowly tuning the two system parameters . therefore , even for a single quasimomentum component of the system , it is possible to realize closed adiabatic loops to manifest the topological phases . the purpose of this paper is to present a variety of interesting and motivating results for the simplest two - band case of the above - mentioned extended khm . first of all , we observe the emergence of isolated @xmath0d dirac cones ( weyl points ) as well as line nodes ( two bands touching along a line ) in the floquet bands , at quasienergies @xmath1 and @xmath2 . this strongly suggests that even @xmath4d driven systems can be useful to study @xmath0d floquet topological phases . in particular , the emergence of weyl points and line nodes at quasienergy @xmath2 is a finding that is absent in static systems . secondly , by taking advantage of the simplicity of the two - band case , we also analytically show how it is possible to obtain as many weyl points and line nodes as possible in our extended khm . thirdly , when we take open boundary conditions ( obc ) along the only physical dimension , we observe a line connecting two weyl points with opposite chiralities , which is analogues to the so - called fermi arc @xcite in static weyl semimetal systems , at both quasienergies @xmath1 and @xmath2 . fourthly , we also perform dynamics studies and demonstrate how the chirality of the ( floquet ) weyl points and the @xmath2 berry phase around the ( floquet ) line nodes can be manifested in the adiabatic dynamics of the system . by considering an adiabatic loop with an appropriate initial state in the @xmath3d parameter space enclosing a weyl point , its chirality can be captured . furthermore , by adiabatically driving a floquet eigenstate at a fixed quasimomentum over one adiabatic cycle , the @xmath2 berry phase can be observed . these results should be of experimental interest , especially for waveguide and optical lattice realizations of @xmath4d driven systems . this paper is organized as follows . in sec . [ ii ] , we start by describing the hamiltonian studied in this paper , which is referred to as the off - diagonal modulated kicked harper model ( odkhm ) , and a possible experimental realization . by focusing on the situation where the floquet operator associated with this hamiltonian consists of only two bands , we analytically show the emergence of band touching points in a form of isolated weyl points or line nodes as the hopping strength and kicking strength are varied . in sec . [ iii ] , we present numerically the emergence of localized edge states associated with the weyl points and line nodes by taking obc along the physical or artificial dimension of the system . in sec . [ iv ] a , we design an adiabatic pumping scheme surrounding a weyl point and show how its chirality can be captured by choosing an appropriate initial state . we further show that by using the same adiabatic pumping scheme and initial state , the chirality of weyl points at quasienergy @xmath1 and quasienergy @xmath2 are captured in different manners , which may suggest the distinction between the two types of weyl point . in sec . [ iv ] b , we also show a possible way to capture the @xmath2 berry phase of the line node by adiabatically pumping a floquet eigenstate at a fixed value of its quasimomentum . finally , we summarize our results and present possible future directions in sec .

recent discoveries on topological characterization of gapless systems have attracted interest in both theoretical studies and experimental realizations . examples of such gapless topological phases are weyl semimetals , which exhibit 3d dirac cones ( weyl points ) , and nodal line semimetals , which are characterized by line nodes ( two bands touching along a line ) . inspired by our previous discoveries that the kicked harper model exhibits many fascinating features of floquet topological phases , in this manuscript we consider a generalization of the model , where two additional periodic system parameters are introduced into the hamiltonian to serve as artificial dimensions , so as to simulate ad system . some of them are weyl points , while the others form line nodes in the parameter space . by taking open boundary conditions along the physical dimension , edge states analogues to fermi arcs in static weyl semimetal systems are observed . finally , by designing an adiabatic pumping scheme , the chirality of the weyl points and the berry phase around line nodes can be manifested .

recent discoveries on topological characterization of gapless systems have attracted interest in both theoretical studies and experimental realizations . examples of such gapless topological phases are weyl semimetals , which exhibit 3d dirac cones ( weyl points ) , and nodal line semimetals , which are characterized by line nodes ( two bands touching along a line ) . inspired by our previous discoveries that the kicked harper model exhibits many fascinating features of floquet topological phases , in this manuscript we consider a generalization of the model , where two additional periodic system parameters are introduced into the hamiltonian to serve as artificial dimensions , so as to simulate ad system . we observe that by increasing the hopping strength and the kicking strength of the system , many new band touching points at floquet quasienergies and will start to appear . some of them are weyl points , while the others form line nodes in the parameter space . by taking open boundary conditions along the physical dimension , edge states analogues to fermi arcs in static weyl semimetal systems are observed . finally , by designing an adiabatic pumping scheme , the chirality of the weyl points and the berry phase around line nodes can be manifested .

0708.3660

i

the pipe nebula , at a distance of 130 pc , is one of the closest molecular cloud complexes in the galaxy . with a mass of 10@xmath6@xmath0 , it spans @xmath5 48 degs@xmath10 on the sky but contains little evidence for active star formation . in addition to tracing the larger - scale molecular gas associated with the pipe nebula , a , , and ( 10 ) ( highly undersampled ) survey of the region @xcite detected a small number of dense cores . the densest of these , associated with the dark cloud b59 , appears to be the only site within the pipe nebula where active star formation is occurring . indeed , recent _ spitzer _ observations reveal an embedded cluster of young stellar objects within b59 @xcite . recent extinction studies of the pipe nebula ( @xcite ; alves , lombardi , & lada 2007 ) reveal many compact dust cores that likely represent incipient sites of star formation . these cores were identified using 2mass extinction maps derived from the jhk photometry of over 4.5 million stars ( fig . [ pipe ] ; @xcite ) . the individual compact cores were extracted from the larger - scale , more diffuse lower - column density material associated with the molecular cloud via a wavelet transform technique ( see @xcite ) . in total , 159 cores were identified and span a range in peak a@xmath11 and core mass and are distributed throughout the pipe nebula @xcite . this large sample represents a critical data base for measuring the initial conditions for star formation and testing theories of core formation and evolution . indeed , the dense core mass function ( cmf ) generated from these cores reveals a similarity to the shape of the stellar initial mass function ( imf ; e.g. @xcite ) with the profound implication that the stellar imf is in fact predetermined by the form of the cmf . the origin of the stellar imf may be , therefore , directly linked to the origin of dense cores . while the pipe nebula represents an excellent example of a molecular cloud in a very early stage of star formation , little work has been done to ascertain the dynamical and evolutionary status of its cores . our aim is to study these cores in detail via the combination of their extinction and molecular line properties ; the extinction map reveals measurements of the core masses and sizes while the molecular line observations reveal the kinematics and gas temperatures within the cores . to this end , we are conducting extensive ground- and space - based surveys of the cores located within the pipe nebula . the pipe cores are well suited for studies of core formation and evolution because they are distributed over a large area , are well separated and well defined , and represent a complete sample of dense cores within a single cloud with accurate masses in the mass range of @xmath5 0.2 to 20.4@xmath0 . to begin , we have obtained ( 10 ) observations toward a sample of 94 cores distributed throughout the nebula . the details of these observations and results are presented in @xcite . in brief summary , all cores show strong emission , have measured linewidths , @xmath12v , of @xmath5 0.14 0.61 , and show no size - linewidth correlation . because ( 10 ) emission traces all molecular gas along the line of sight , the measured linewidths will trace both the lower density intercore material in addition to the dense gas associated with the core . to isolate the emission from the dense core , we have also obtained nh@xmath1 observations toward a sample of the pipe cores and report the results of these observations here . because nh@xmath1 requires such high densities to be excited ( @xmath13 10@xmath6@xmath7 ) , only the densest gas will exhibit significant nh@xmath1 emission . thus , nh@xmath1 observations will reveal the fraction of cores in the pipe nebula that contain dense gas . determination of the dense core fraction and how it varies across the core mass function and with kinematical state will provide crucial data for understanding the evolutionary status of these objects . the combination of the extinction and molecular line studies ( and nh@xmath1 ) , and the implications for core formation and evolution , is discussed in @xcite , the third paper in this series on the pipe nebula . by accurately measuring the linewidths from the nh@xmath1 ( 1,1 ) emission in each core , and by combining this with measurements of the core masses , one can determine the fraction of cores that are unbound and the core stabilty , which can provide important clues to their formation and evolution . indeed , @xcite find that the majority of pipe cores are pressure confined , gravitationally unbound objects whose properties are dominated by thermal processes in a pressurized medium . ammonia has been used extensively to study both high- and low - mass star - forming regions ( e.g.@xcite ) . because it is the least depleted species in , and , thus , the most reliable tracer of , cold dense gas within starless cores , we use nh@xmath1 to trace the densest gas in the pipe nebula . the 18 individual hyperfine components of the nh@xmath1 ( 1,1 ) transitions can be used to measure the intrinsic one dimensional velocity dispersion ( @xmath14 ) , optical depth ( @xmath15 ) , and excitation temperature ( t@xmath16 ) . observations of the nh@xmath1 ( 2,2 ) transition were also obtained in order to directly measure the gas temperatures of the brightest cores in the sample . ratios of the nh@xmath1 ( 1,1 ) and ( 2,2 ) lines reveal the kinetic temperature ( t@xmath9 ) and , therefore , density of the cores . to probe the very densest gas and to determine the chemical evolution of the cores , we also obtained ccs ( 2@xmath21@xmath3 ) and hc@xmath4n ( 9,8 ) observations . these molecules are found in very dense starless cores ( e.g. @xcite ) . the abundance of carbon - chain molecules ( e.g. ccs and hc@xmath4n ) compared to nh@xmath1 is thought to trace the chemical evolution of cores ; carbon - chain molecules being more abundant in the very earliest stages in core evolution , compared to nh@xmath1 which is more abundant in the later stages ( e.g. @xcite ) . thus , the combination of these data can reveal the youth and star - forming potential of the cores . in this paper , we present the results of a survey for nh@xmath1 ( 1,1 ) , nh@xmath1 ( 2,2 ) , ccs ( 2@xmath21@xmath3 ) , and hc@xmath4n ( 9,8 ) emission toward a sample of 46 of the extinction cores identified in the pipe nebula . all but one of these cores has been observed as part of the survey @xcite . we find that most cores are indeed associated with dense gas . their measured linewidths are narrow , with several cores having linewidths comparable to their thermal linewidths . the derived properties ( t@xmath9 , intrinsic @xmath12v , non - thermal @xmath12v , radius ) of the cores within the pipe nebula are similar to cores within other low - mass star - forming regions : the only difference is that the pipe cores typically have weaker nh@xmath1 emission and most show no current star formation .

recent extinction studies of the pipe nebula ( d=130 pc ) reveal many cores spanning a range in mass from 0.2 to 20.4 . we present a survey of nh ( 1,1 ) , nh ( 2,2 ) , ccs ( 2 ) , and hcn ( 9,8)emission toward 46 of these cores . an atlas of the 2mass extinction maps is also presented . in total the derived properties of the pipe cores are similar to cores within other low - mass star - forming regions : the only differences are that the pipe cores have weaker nh emision and most show no current star formation as evidenced by the lack of embedded infrared sources

recent extinction studies of the pipe nebula ( d=130 pc ) reveal many cores spanning a range in mass from 0.2 to 20.4 . these dense cores were identified via their high extinction and comprise a starless population in a very early stage of development . here we present a survey of nh ( 1,1 ) , nh ( 2,2 ) , ccs ( 2 ) , and hcn ( 9,8)emission toward 46 of these cores . an atlas of the 2mass extinction maps is also presented . in total , we detect 63% of the cores in nh ( 1,1 ) , 22% in nh ( 2,2 ) , 28% in ccs , and 9% in hcn emission . we find the cores are associated with dense gas ( 10 ) with 9.5 t 17 k. compared to , we find the nh linewidths are systematically narrower , implying that the nh is tracing the dense component of the gas and that these cores are relatively quiescent . we find no correlation between core linewidth and size . the derived properties of the pipe cores are similar to cores within other low - mass star - forming regions : the only differences are that the pipe cores have weaker nh emision and most show no current star formation as evidenced by the lack of embedded infrared sources . such weak nh emission could arise due to low column densities and abundances or reduced excitation due to relatively low core volume densities . either alternative implies that the cores are relatively young . thus , the pipe cores represent an excellent sample of dense cores in which to study the initial conditions for star formation and the earliest stages of core formation and evolution .

0708.3660

c

using the 100 m gbt we have conducted an nh@xmath1 ( 1,1 ) , nh@xmath1 ( 2,2 ) , ccs ( 2@xmath21@xmath3 ) , and hc@xmath4n ( 9,8 ) survey toward a sample of 46 cores within the pipe nebula . these cores were identified via their high extinction and appear to be dense starless cores which likely represent the initial conditions of star formation . in total , we detect nh@xmath1 ( 1,1 ) emission in 29 cores ( @xmath5 63% ) , nh@xmath1 ( 2,2 ) emission in 10 cores ( @xmath5 22% ) , ccs emission in 13 cores ( @xmath5 28% ) , and hc@xmath4n emission in 4 cores ( @xmath5 9% ) . not surprisingly , the detection rate is higher toward those cores with higher peak a@xmath11 and higher mass ; in the case of nh@xmath1 ( 1,1 ) we detected emission toward all cores with a peak a@xmath11@xmath13 15 magnitudes and with masses @xmath13 11@xmath0 . we find that the cores are associated with dense ( @xmath1310@xmath6@xmath7 ) gas . the nh@xmath1 emission revealed n(h@xmath28 ) typically three times greater than the mean densities measured from the extinction maps . this is expected given that the cores likely have inwardly increasing density gradients ; the nh@xmath1 is tracing the densest centers of the cores . using a forward - fitting modelling routine , we estimated the physical properties of the gas ( t@xmath9 , @xmath15 , and t@xmath16 ) for 12 cores . we find that t@xmath9 ranges from 9.5 to 17 k , with a median value of @xmath5 12 @xmath29 2 k. cores with higher mass tend to have lower t@xmath9 values ( 10 @xmath29 1 k ) compared to lower - mass cores ( 13 @xmath29 3 k ) . the measured one dimensional velocity dispersion , @xmath14 , for the cores show that the lines are narrow , with several cores having dispersions close to thermal ( for a 10 k gas ) . a comparison between the linewidths measured for the cores from and nh@xmath1 , reveal that while the general trends are the same , i.e. neither dataset show a size - linewidth relation , the nh@xmath1 linewidths are systematically lower than those measured from the emission . this arises because the traces all emission along the line of sight , whereas nh@xmath1 traces only the densest gas associated with the core . the derived properties of the pipe cores are similar to dense cores within other star - forming regions , i.e.perseus , taurus , ophiuchus . the most obvious difference is that the cores within the pipe nebula typically have weaker nh@xmath1 emission and most show no evidence for current star formation . the weak nh@xmath1 emission may arise due to the low abundance of nh@xmath1 because the cores are chemically young or because the excitation conditions ( densities ) within the gas are insufficient to excite the observed transitions . detailed radiative transfer models are needed to resolve this issue . although we have a limited number of cores , we estimate their evolutionary ages to be @xmath5 6 @xmath35 10@xmath27 years . thus , the cores within the pipe nebula represent an excellent sample of dense cores in which to study the initial conditions of star - formation and the earliest stages of core formation and evolution . we are extremely grateful to erik rosolowsky for the use of the nh@xmath1 forward - fitting routine ahead of publication and for the many informative discussions . we also thank the support staff at the gbt , in particular frank ghigo , for help will the observing setup and data reduction . we acknowledge funding support through nasa origins grant nag-13041 .

these dense cores were identified via their high extinction and comprise a starless population in a very early stage of development . here , we detect 63% of the cores in nh ( 1,1 ) , 22% in nh ( 2,2 ) , 28% in ccs , and 9% in hcn emission . . such weak nh emission could arise due to low column densities and abundances or reduced excitation due to relatively low core volume densities . thus , the pipe cores represent an excellent sample of dense cores in which to study the initial conditions for star formation and the earliest stages of core formation and evolution .

recent extinction studies of the pipe nebula ( d=130 pc ) reveal many cores spanning a range in mass from 0.2 to 20.4 . these dense cores were identified via their high extinction and comprise a starless population in a very early stage of development . here we present a survey of nh ( 1,1 ) , nh ( 2,2 ) , ccs ( 2 ) , and hcn ( 9,8)emission toward 46 of these cores . an atlas of the 2mass extinction maps is also presented . in total , we detect 63% of the cores in nh ( 1,1 ) , 22% in nh ( 2,2 ) , 28% in ccs , and 9% in hcn emission . we find the cores are associated with dense gas ( 10 ) with 9.5 t 17 k. compared to , we find the nh linewidths are systematically narrower , implying that the nh is tracing the dense component of the gas and that these cores are relatively quiescent . we find no correlation between core linewidth and size . the derived properties of the pipe cores are similar to cores within other low - mass star - forming regions : the only differences are that the pipe cores have weaker nh emision and most show no current star formation as evidenced by the lack of embedded infrared sources . such weak nh emission could arise due to low column densities and abundances or reduced excitation due to relatively low core volume densities . either alternative implies that the cores are relatively young . thus , the pipe cores represent an excellent sample of dense cores in which to study the initial conditions for star formation and the earliest stages of core formation and evolution .

1611.02901

i

a dessin denfant , introduced by grothendieck in its _ esquisse de un programme _ @xcite , is a @xmath0-cell embedding of a finite and connected bipartite graph @xmath1 on a closed orientable surface @xmath2 ; see @xcite for some generalities . the dessin denfant is called orientable if its faces can be labelled by signs @xmath3 and @xmath4 , so that adjacent faces have different label . as a consequence of belyi s theorem @xcite , there is a natural action of the absolute galois group @xmath5 on dessins denfants , which is known to be faithful @xcite . grothendieck observed that using that action may permits to obtain information on the internal structure of @xmath5 by codified by such an action in terms of simple combinatorial objects . in the recent years there has been an interest on dessins denfants in the field of supersymmetric gauge theories @xcite and conformal field theories @xcite to mention some of the applications in theoretical physics . in this way , it seems interesting searching for algorithms to provide examples of dessins denfants , together some of their invariants , up to isomorphisms . by the definition , a dessin denfant has associated a bipartite graph , but the dessin is not uniquely determined up to isomorphisms by it . in this paper we provide an algorithm which permits to construct all non - isomorphic dessins denfants , together their automorphims group , monodromy groups and orientability type , having the same underlaying bipartite graph . in section [ sec : appendix ] we describe , for a particular bipartite graph , the implementation of the above algorithm into gap @xcite which we have used for all our examples in section [ sec : ejemplos ] for certain classical bipartite graphs . as an example of our algorithm , for the double - prism shown in figure [ doubleprism ] ( see example [ sec : doble - prisma ] ) , we are able to find two non - isomorphic dessins denfants @xmath6 and @xmath7 with the same bipartite graph , both of genus one , the same passport @xmath8 and isomorphic monodromy groups . the dessin denfant @xmath6 is chiral and @xmath7 is reflexive ; so they can not be in the same galois orbit . the dessin @xmath9 is defined by the following permutations @xmath10 @xmath11 @xmath12 @xmath13 : 1 . a finite connected bipartite graph ( vertices are either black or white ) @xmath1 whose @xmath14 black vertices are @xmath15 , its @xmath16 white vertices are @xmath17 , and it has @xmath18 edges . 2 . the group @xmath19 of bipartite graph automorphisms of @xmath1 ( graph automorphisms preserving vertices of a fixed colour ) . : 1 . a maximal collection of non - isomorphic dessins denfants together their monodromy groups , automorphisms group and orientability type , whose subjacent bipartite graph is @xmath1 . : 1 . fix an enumeration of the @xmath20 edges of @xmath1 with numbers in the set @xmath21 without repeating . the above enumeration provides a natural injective homomophism from @xmath22 . 3 . for each black vertex @xmath23 ( respectively , white vertex @xmath24 ) we consider the collection @xmath25 ( respectively , @xmath26 ) all possible cycles @xmath27 ( respectively , @xmath28 ) of length equal to the degree of such vertex in @xmath1 using the numbers at all the edges at such a vertex . set @xmath29 , where @xmath30 is the collection of all the permutations @xmath31 , where @xmath32 , and @xmath33 is the collection of all the permutations @xmath34 , where @xmath35 . the connectivity of @xmath1 asserts that for each pair @xmath36 , the group @xmath37 is a transitive subgroup of @xmath38 , so it defines a dessin denfant @xmath39 whose bipartite subjacent graph is @xmath1 . 5 . consider the natural action of @xmath19 on the set @xmath40 given as : @xmath41 in the above , multiplication of permutations are from the left to the right as is done in gap @xcite . 6 . as a consequence of theorem [ teomain ] ( see section [ sec : mainpart ] ) we obtain the following facts . 1 . if @xmath42 is a dessin denfant whose underlying bipartite graph is isomorphic to @xmath1 , then it is isomorphic to @xmath39 for a suitable @xmath36 . 2 . two pairs in @xmath40 define isomorphic dessins denfant if and only if they belong to the same @xmath19-orbit . the group of automorphism of the dessin denfant @xmath43 , where @xmath36 is naturally isomorphic to the @xmath19-stabilizer of @xmath44 .

recently , dessins denfants has been proven to be a powerful tool in certain types of supersymmetry gauge theories , bringing a relationship to combinatorics and number theory . dessins denfants are-cell embeddings of a finite and connected bipartite graph in a closed orientable surface . in general , a finite and connected bipartite graph may appear as the underlying bipartite graph of many non - isomorphic dessins denfants . in this article we provide a constructive procedure to compute all those non - isomorphic dessins denfants having the same underlying bipartite graph , together their automorphims group , monodromy group and orientability type .

recently , dessins denfants has been proven to be a powerful tool in certain types of supersymmetry gauge theories , bringing a relationship to combinatorics and number theory . dessins denfants are-cell embeddings of a finite and connected bipartite graph in a closed orientable surface . in general , a finite and connected bipartite graph may appear as the underlying bipartite graph of many non - isomorphic dessins denfants . in this article we provide a constructive procedure to compute all those non - isomorphic dessins denfants having the same underlying bipartite graph , together their automorphims group , monodromy group and orientability type .

1504.05667

i

there is a large number of problems that are well known to be hardly tractable with standard computational approaches and resources , mainly due to the many - body nature of strongly correlated many particle systems . to overcome this limitation , the idea of a quantum simulator was originally proposed by feynman @xcite : any arbitrary complex quantum systems could in fact be simulated by another quantum system mimicking its dynamical evolution , but under the experimenter control . this idea was later refined and mathematically formalized in quantum information perspectives by lloyd @xcite . + over the past twenty years , different approaches have been proposed to realize quantum simulators of the most relevant models in condensed matter physics , quantum field theories , and quantum chemistry @xcite . most efficient protocols have been proposed and experimentally realized with trapped ions @xcite . generally speaking , quantum simulators can be broadly classified into two main categories : in _ digital simulators _ the state of the target system is encoded in qubits and its trotter - decomposed time evolution is implemented by a sequence of elementary quantum gates @xcite , whereas in _ analog simulators _ a certain quantum system directly emulates another one . digital architectures are usually able to simulate broad classes of hamiltonians , whereas analog ones are restricted to specific target hamiltonians . for a recent review on these different approaches , we refer to @xcite and references therein . + lately , superconducting circuits and resonators have emerged as an extremely promising platform for quantum information and quantum simulation architectures @xcite . the first and unique proposal for a general - purpose digital simulator has been put forward only very recently @xcite . in this proposal qubits encoded in transmons are dispersively coupled through a photon mode of a single resonator , and such coupling is externally tuned by controlling the transmon energies . however , the reported fidelities and the intrinsic serial nature of this setup ( i.e. , the need of addressing each pair of qubits sequentially ) , may hinder the scalability to a sizeable number of qubits . in addition , superconducting units are not ideal for encoding qubits owing to their relatively short coherence times . indeed , spin - ensembles @xcite or even photons @xcite have been proposed as memories to temporarily store the state of superconducting computational qubits . + here we consider an array of superconducting resonators as the main technological platform , on which hybrid spin - photon qubits are defined by introducing strongly coupled spin ensembles ( ses ) in each resonator @xcite . one- and two - qubit quantum gates can be implemented by individually and independently tuning the resonators modes through external magnetic fields . this setup can realize a universal digital quantum simulator , whose scalability to an arbitrary large array is naturally fulfilled by the inherent definition of the single qubits , represented by each coupled se - resonator device . the possibility to perform a large number of two - qubit gates in parallel makes the manipulation of such large arrays much faster than in a serial implementation , thus making the simulation of complex target hamiltonians possible in practice . a key novelty of the present proposal is that ensembles of effective @xmath0 spins are used in the hybrid encoding , which allows to exploit the mobility of photons across different resonators to perform two - qubit gates between physically distant qubits . this is done much more efficiently than by the straightforward approach of moving the states of the two qubits close to each other by sequences of swap gates , and makes the class of hamiltonians which can be realistically addressed much larger . long - distance operations arise whenever mapping the target system of the simulation onto the register implies two - body terms between distant qubits . besides the obvious case of hamiltonians with long - range interactions , this occurs with any two - dimensional model mapped onto a linear register , or with models containing @xmath1-body terms , including the many - spin terms which implement the antisymmetric nature of fermion wavefunctions . + the time evolution of a generic hamiltonian is decomposed into a sequence of local unitary operators , which can be implemented by means of elementary single- and two - qubits gates . then we combine the elementary gates of our setup in order to mimic the dynamics of spin and hubbard - like hamiltonians for fermions . we explicitly report our results for the digital quantum simulation of the transverse - field ising model on 3 qubits , the tunneling dynamics of a spin one in a rhombic crystal field and the hubbard hamiltonian . the robustness of the scheme is demonstrated by including the effects of decoherence in a master equation formalism . finally , we discuss the main sources of errors in the present simulations and the possibility to overcome them . in particular , we show how potentially harmful effects of inhomogeneous broadening of the spin ensemble are circumvented by operating the scheme in a cavity - protected regime . spins , placed at the antinodes of the magnetic field ( rotational lines ) of the cavity mode . the _ auxiliary _ resonator contains a nonlinear element ( transmon ) coupled to the electric field of the fundamental mode . ( b ) detailed sequence of time steps required to produce controlled-@xmath2 two - qubit gate between qubits @xmath3 and @xmath4 ( see appendix b for details ) . _ logical _ cavities are represented by square boxes , whereas _ auxiliary _ resonators are depicted as circular boxes . blue lines represent photon frequencies in the idle configuration ( @xmath5 in the _ logical _ and @xmath6 in the _ auxiliary _ cavities ) . the transmon ( @xmath7 and @xmath8 ) and spin ( @xmath9 , continuous , and @xmath10 , dashed ) transition energies are indicated by red lines . ( i ) qubits are initially into state @xmath11 , with the excitations ( red arrows ) stored into the photonic degrees of freedom ( blue lines ) ; ( ii ) _ logical _ cavity 3 is brought into resonance with the _ auxiliary _ resonator @xmath12 , thus ( iii ) bringing the photon to the auxiliary cavity . in the meantime _ auxiliary _ resonator 3 is detuned from the others to avoid unwanted photon hoppings . in ( iv ) the photon is absorbed by the transmon ( @xmath13 transition ) . the same hopping process ( v ) is repeated for the photon originally in cavity 2 , which is brought to the _ auxiliary _ resonator ( vi ) and then absorbed and emitted by the transmon ( @xmath14 transition ) in a semi - resonant rabi process ( vii ) . the procedure is then repeated to bring photons back to _ logical _ cavities 2 and 3 , leading the state back to @xmath11 with an additional phase @xmath2 acquired during the semi - resonant process.,width=302 ]

a solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits , i.e. by implementing a _ digital quantum simulator_. superconducting circuits and resonators are emerging as an extremely - promising platform for quantum computation architectures , but a digital quantum simulator proposal that is straightforwardly scalable , universal , and realizable with state - of - the - art technology is presently lacking . here as representative examples we consider the transverse - field ising model , a spin-1 hamiltonian , and the two - dimensional hubbard model ; for these , we numerically simulate the scheme by including the main sources of decoherence . in addition , we show how to circumvent the potentially harmful effects of inhomogeneous broadening of the spin systems . 3 cm

resolving quantum many - body problems represents one of the greatest challenges in physics and physical chemistry , due to the prohibitively large computational resources that would be required by using classical computers . a solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits , i.e. by implementing a _ digital quantum simulator_. superconducting circuits and resonators are emerging as an extremely - promising platform for quantum computation architectures , but a digital quantum simulator proposal that is straightforwardly scalable , universal , and realizable with state - of - the - art technology is presently lacking . here we propose a viable scheme to implement a universal quantum simulator with hybrid spin - photon qubits in an array of superconducting resonators , which is intrinsically scalable and allows for local control . as representative examples we consider the transverse - field ising model , a spin-1 hamiltonian , and the two - dimensional hubbard model ; for these , we numerically simulate the scheme by including the main sources of decoherence . in addition , we show how to circumvent the potentially harmful effects of inhomogeneous broadening of the spin systems . 3 cm

1611.06360

i

in this paper , we present a numerical method for solving scattering problems from locally perturbed periodic surfaces . scattering problems for periodic or quasiperiodic incident fields from periodic structures have been well studied over at least 25 years . the common way of solving is reduction to one periodicity cell , which avoids the need for computing numerical solutions in unbounded domains . however , if such reduction fails due to non - periodicity of the incident field or the surface , one needs to seek for new approaches . the approach we present in this paper is based on the floquet - bloch transform . it builds up a relationship between a non - periodic problem and a family of quasiperiodic problems reduced to one single period . with this transform , the scattering problems from periodic surfaces and non - periodic incident fields have been discussed in @xcite and @xcite . based on these theoretic results , a numerical scheme has been developed to solve these kinds of scattering problems in @xcite . following this type of technique , we introduce in this paper an algorithm for solving scattering problems from local perturbations of periodic surfaces that is pretty close to the one from the recent paper @xcite . our convergence analysis is for various reasons different , as @xcite for instance strongly relies on integral equations in the spatial variable . the source of inspiration for all these techniques seems to be the paper @xcite on wave propagation in full - space periodic media . to briefly present our numerical approach in some detail , we firstly rely on the floquet - bloch transform , defined on functions living in periodic domains , and hence reformulate the locally perturbed problem by a suitable diffeomorphism between the locally perturbed and the purely periodic domain . applying the bloch transform to the new problem yields a family of quasiperiodic scattering problems posed in one single periodicity cell . we state the classic error analysis for finite element discretizations using low - order approximation in @xmath0 . the interesting feature of this discretization is that all integrals in the quasiperiodicity parameters can be computed by hand , such that standard solvers become attractive to tackle the full problem . by finite element discretizations for the spatial parts of the problem and , roughly , the trapezoidal rule discretizing the inverse bloch transform , one gets a large but sparse block - linear system to solve . to this end , we use the gmres iteration with a specially designed incomplete @xmath1-decomposition as pre - conditioner for the numerical solution of the linear system . for dirichlet scattering problems on perturbed periodic surfaces one can , at least in two dimensions , of course exploit the corresponding numerical convergence theory for boundary integral equation approximations from rough surface scattering theory , see , e.g. , @xcite . there are , however , few methods specifically designed for such locally perturbed periodic scatterers . in @xcite and @xcite , the authors give a method that approximates the dirichlet - to - neumann map on the transparent edges of a periodic waveguide modeled by the helmholtz equation . another method that uses the so - called recursive doubling procedure constructs the sommerfeld - to sommerfeld maps at artificial boundaries of such a waveguide , see @xcite and @xcite . both of these methods are motivated by the infinite half - guide and inspired by the limiting absorption principle . this paper is organized as follows . in section [ se : scatter ] , we describe the direct scattering problem corresponding to a locally perturbed periodic surface . in sections [ se : persca ] and [ se : qpscattperturb ] , we use the bloch transform to obtain an equivalent family of quasiperiodic problems . in section [ se : invbloch ] we give a discrete inverse bloch transform and estimate the finite element method applied to the individual quasiperiodic scattering problems . the numerical implementation for the bloch transform based method is illustrated in section [ se : nummet ] . in the last section [ se : numeg ] , several numerical examples indicate the efficiency of that method . appendix [ se : bloch ] briefly introduces the bloch transform and some of its mapping properties . _ notation : _ we denote quasiperiodic sobolev spaces with regularity @xmath2 and quasiperiodicity @xmath0 by @xmath3 , such that @xmath4 denotes a _ periodic _ sobolev space and _ not _ a space of functions that vanish on some boundary . despite functions in sobolev spaces are merely defined almost everywhere , we usually omit to write this down . moreover , @xmath5 is a generic constant with value that might change from one appearance to the other .

is to reduce such problems to one periodicity cell . in contrast to periodic settings , scattering from locally perturbed periodic surfaces is way more challenging . in this paper , we introduce and analyze a new numerical method to simulate scattering from locally perturbed periodic structures based on the bloch transform . as this transform is applied only in periodic domains , we firstly rewrite the scattering problem artificially in a periodic domain . with the help of the bloch transform , we secondly transform this problem into a coupled family of quasiperiodic problems posed in the periodicity cell . we also provide a simple and efficient way of implementation that does not require numerical integration in the quasiperiodicity , together with numerical examples for scattering from locally perturbed periodic surfaces computed by this scheme .

scattering problems for periodic structures have been studied a lot in the past few years . a main idea for numerical solution methods is to reduce such problems to one periodicity cell . in contrast to periodic settings , scattering from locally perturbed periodic surfaces is way more challenging . in this paper , we introduce and analyze a new numerical method to simulate scattering from locally perturbed periodic structures based on the bloch transform . as this transform is applied only in periodic domains , we firstly rewrite the scattering problem artificially in a periodic domain . with the help of the bloch transform , we secondly transform this problem into a coupled family of quasiperiodic problems posed in the periodicity cell . a numerical scheme then approximates the family of quasiperiodic solutions ( we rely on the finite element method ) and backtransformation provides the solution to the original scattering problem . in this paper , we give convergence analysis and error bounds for a galerkin discretization in the spatial and the quasiperiodicity s unit cells . we also provide a simple and efficient way of implementation that does not require numerical integration in the quasiperiodicity , together with numerical examples for scattering from locally perturbed periodic surfaces computed by this scheme .

1412.7547

i

algorithms for solving polynomial systems have become increasingly important over the past years , because of the many situations where such algebraic systems appear , including both theoretical problems ( algorithmic geometry , polynomial inversion ) , and real - life applications ( cryptography , robotics ) . examples of such algorithms include eigenvalues methods for systems with a finite number of solutions , or resultant calculations for polynomial elimination ( see @xcite for a survey ) . the theory of grbner bases is another tool which has proved useful for this purpose , and many algorithms for computing grbner bases have been described since their introduction . they include direct algorithms , computing the grbner basis of any system : to name only a few , the historical buchberger algorithm @xcite , and later the faugre 4 @xcite and 5 @xcite algorithms ; as well as change of order algorithms , computing a grbner basis of an ideal from another grbner basis : the main examples are the algorithm @xcite for systems with a finite number of solutions , and the grbner walk @xcite for the general case . systems arising from applications usually have some structure , which makes the resolution easier than for generic systems . in this paper , we consider one such structure , namely _ weighted homogeneous _ polynomials : a polynomial @xmath11 is weighted homogeneous with respect to a system of weights @xmath0 ( or @xmath1-homogeneous ) if and only if @xmath12 is homogeneous in the usual sense . moreover , in order to obtain precise results , we will assume that the systems satisfy some _ generic _ properties , which are satisfied by almost any system drawn at random . this is a usual assumption for grbner basis complexity estimates . more generally , we will also consider affine systems with a _ weighted homogeneous structure _ , that is systems whose component of maximal weighted degree will satisfy these generic properties . the complexity estimates given in this paper can be applied to a wide range of grbner basis algorithms . however , we mainly focus on two algorithms : matrix-5 , which is a matrix variant of 5 described in @xcite , allowing for complexity analyses , and . [ [ sec : previous - work ] ] prior work + + + + + + + + + + the special case @xmath13 is the usual homogeneous case . in this case , all the results from this paper specialize to known results . furthermore , some hypotheses are always satisfied , making the properties and definitions simpler . in particular , the description of the hilbert series of a homogeneous complete intersection is adapted from @xcite , and the asymptotics of the degree of regularity of a semi - regular sequence were studied in @xcite . weighted homogeneous systems have been studied before , from the angle of singularity theory and commutative algebra . in particular , some results about the hilbert series and the hilbert function of weighted homogeneous ideals , including the weighted bzout bound , can be found in most commutative algebra textbooks . the computational strategy for systems with a weighted structure is not new either , for example it is already implemented ( partially : only for weighted homogeneous systems with a degree order ) in the computer algebra system magma @xcite . additionally , the authors of @xcite proposed another way of taking into account the weighted structure , by way of the hilbert series of the ideal . the authors of @xcite generalized this algorithm to systems homogeneous with respect to a multigraduation . their definition of a system of weights is more general than the one we use in the present paper . to the best of our knowledge , nobody presented a formal description of a computational strategy for systems with a weighted homogeneous structure ( not necessarily weighted homogeneous ) , together with complexity estimates . some of the results presented in this paper about regular sequences previously appeared in a shorter conference paper @xcite , of which this paper is an extended version : these results are the weak form of the weighted macaulay bound and the formal description of the algorithmic strategy for weighted homogeneous systems , with the complexity estimates and . this conference paper lacked a hypothesis ( reverse chain - divisible systems of weights ) , and as such lacked the precise description of hilbert series required to obtain results for semi - regular sequences . the sharp variant of the weighted macaulay bound , under the assumption of simultaneous noether position , was also added in the present paper . finally , the benchmarks section of the current paper contains additional systems , arising in polynomial inversion problems . the conference paper was using _ quasi - homogeneous _ to describe the studied structure , instead of _ weighted homogeneous_. while both names exist in the literature , _ weighted homogeneous _ seems to be more common , and to better convey the notion that this structure is a generalization of homogenity , instead of an approximation . the same notion is sometimes also named simply _ homogeneous _ ( in which case the weights are determined by the degree of the generators ; see for example @xcite ) , or homogeneous for a _ nonstandard graduation _ @xcite . [ [ sec : main - results ] ] main results + + + + + + + + + + + + by definition , weighted homogeneous polynomials can be made homogeneous by raising all variables to their weight . the resulting system can then be solved using algorithms for homogeneous systems . however , experimentally , it appears that solving such systems is much faster than generic homogeneous systems . in this paper , we show that the complexity estimates for homogeneous systems , in case the system was originally @xmath1-homogeneous , can be divided by @xmath14 , where @xmath15 is the complexity exponent of linear algebra operations ( @xmath16 for naive algorithms , such as the gauss algorithm ) . these complexity estimates depend on two parameters of the system : its _ degree of regularity _ @xmath17 and its _ degree _ @xmath18 . these parameters can be obtained from the _ hilbert series _ of the ideal , which can be precisely described under generic assumptions . to be more specific , we will consider systems defined by a _ regular sequence _ [ def : regular ] ) and systems which are in _ simultaneous noether position _ [ def : snp ] ) . [ thm : intro - comp ] let @xmath0 be a system of weights , and @xmath19 a zero - dimensional @xmath1-homogeneous system of polynomials in @xmath20 $ ] , with respective @xmath1-degree @xmath21 . the complexity ( in terms of arithmetic operations in @xmath22 ) of algorithm 5 to compute a @xmath1-grevlex grbner basis of @xmath23 is bounded by @xmath24 if @xmath25 is a regular sequence ( and in particular @xmath26 ) , then @xmath17 can be bounded by the _ weighted macaulay bound _ : @xmath27 if additionally @xmath25 is in simultaneous noether position w.r.t the order @xmath28 , then the weighted macaulay bound can be refined : @xmath29 the complexity of algorithm to perform a change of ordering is bounded by @xmath30 if @xmath25 forms a regular sequence , then @xmath18 is given by the _ weighted bzout bound _ @xmath31 in particular , the bound indicates that in order to compute a grbner basis faster for a generic enough system , one should order the variables by decreasing weights whenever possible . the hypotheses of the theorem are not too restrictive . in the homogeneous case , regularity and simultaneous noether position are generic properties . however , in the weighted homogeneous case , there are systems of weights and systems of weighted degrees for which they are not generic . in this paper , we identify large families of systems of weights and systems of weighted degrees for which they are ( prop . [ thm : gen-2 ] ) . all sequences in simultaneous noether position are regular . in the homogeneous case , conversely , all regular sequences are in simultaneous noether position up to a generic linear change of coordinates . in the weighted homogeneous case , it is no longer true . worse still , there are systems of weights for which there exists no non - trivial change of coordinates . in order to work around this limitation , we consider _ reverse chain - divisible _ systems of weights , that is systems of weights such that @xmath32 . this property ensures that there are non - trivial change of coordinates of the form @xmath33 for all @xmath34 , with @xmath35 a @xmath1-homogeneous polynomial with @xmath1-degree @xmath36 . under this assumption , many properties from the homogeneous case remain valid in a weighted setting , and in particular , any regular sequence is , up to a @xmath1-homogeneous change of coordinates , in simultaneous noether position ( th . [ thm : gen - linchg ] ) . for many systems from practical applications , the weights can be chosen to be reverse chain - divisible . we give a few examples in the last section of this paper . if @xmath37 , there is no regular sequence . instead , we will consider systems defined by a _ semi - regular _ sequence , that is systems for which no reduction to zero appear in a run of algorithm 5 . this property has several equivalent definitions in the homogeneous case . while these definitions can be easily extended to the weighted case , their equivalence is not necessarily true . however , we prove that these definitions are equivalent in the special case where the weights form a reverse chain - divisible sequence . in the homogeneous case , the property of being semi - regular is only conjectured to be generic , but this conjecture is proved in a handful of cases ( ( * ? ? ? 1.5 ) . in this paper , we adapt the proof of one of these cases , namely the case @xmath38 in a base field of characteristic @xmath39 . for semi - regular systems with @xmath38 , we obtain a bound on the degree of regularity of the system . more generally , in the homogeneous case , one can compute asymptotic estimates on the degree of regularity of a semi - regular sequence @xcite . these estimates can be adapted to the weighted homogeneous case . as an example , we give an asymptotic bound on the degree of regularity for semi - regular systems with @xmath40 for a given integer @xmath41 : [ thm : intro - dreg ] let @xmath42 and @xmath41 be two positive integers , and let @xmath40 . let @xmath43 and @xmath44 be two positive integers such that @xmath45 . consider the system of @xmath42 weights @xmath46 . let @xmath25 be a semi - regular sequence in @xmath20 $ ] , made of @xmath1-homogeneous polynomials with @xmath1-degree @xmath44 . then the highest degree reached in the computation of a @xmath1-grevlex grbner basis of @xmath47 is asymptotically bounded by @xmath48 where @xmath49 is the largest root of the @xmath41th hermite s polynomial . experimentally , if we lift the assumption that the system of weights is reverse chain - divisible , the degree of regularity does not appear to rise too far beyond the bound . future work on the topic could include characterizing the hilbert series of @xmath1-homogeneous semi - regular sequences in full generality , in order to obtain bounds on the @xmath1-degree of regularity . in practice , taking advantage of the weighted structure when applicable yields significant speed - ups . some instance of a weighted structure has already been successfully exploited for an application in cryptography @xcite . we also present timings obtained with several polynomial inversion problems , with speed - ups ranging from 12 to almost 100 . in particular , we use these techniques in order to compute the relations between fundamental invariants of several groups ( see @xcite ) . for some groups such as the cyclic-5 group or the dihedral group @xmath50 , computing these relations is intractable without considering the weighted structure of the system , while it takes only a few seconds or minutes when exploiting the weighted structure . all these systems are examples of applications where the weights giving the appropriate @xmath1-homogeneous structure are naturally reverse chain - divisible . these experimentations have been carried using 5 and with the grbner basis library fgb @xcite and 4 with the computer algebra system magma @xcite . there are other applications where grbner bases are computed for polynomial systems with a weighted - homogeneous structure , for example in coding theory , both for generating codes ( @xcite , @xcite ) and for decoding through guruswami - sudan s algorithm ( see @xcite for an overview ) . [ [ sec : organisation - paper ] ] organisation of the paper + + + + + + + + + + + + + + + + + + + + + + + + + in section [ sec : notat - prev - results ] , we define weighted graded algebras and some generic properties of weighted homogeneous systems . in section [ sec : regular - systems ] , we focus on regular systems and complete intersections . we describe the hilbert series of a weighted homogeneous complete intersection and give the sharp variant of the weighted macaulay bound . in section [ sec : semi - regular - systems ] , we consider semi - regular systems . we give some equivalent definitions of this property , and we show how asymptotic estimates of the degree of regularity can be adapted from the homogeneous case to the weighted case . additionally , we prove that frberg s conjecture in the case @xmath38 is true in the weighted case , as in the homogeneous case , provided that the base field is large enough . in section [ sec : cons - comp ] , we describe strategies for computing grbner bases for weighted homogeneous systems , and we give complexity estimates for these strategies . finally , in section [ sec : applications ] , we show how weighted structures can appear in applications , and we give some benchmarks for each example .

solving polynomial systems arising from applications is frequently made easier by the structure of the systems . weighted homogeneity ( or quasi - homogeneity ) is one example of such a structure : given a system of weights ,-homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree . grbner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case . we show that in this case , the complexity estimate for algorithm 5 can be divided by a factor . for zero - dimensional systems , the complexity of algorithm ( where is the number of solutions of the system ) can be divided by the same factor . under genericity assumptions , for zero - dimensional weighted homogeneous systems of-degree , these complexity estimates are polynomial in the weighted bzout bound . furthermore , the maximum degree reached in a run of algorithm 5 is bounded by the weighted macaulay bound , and this bound is sharp if we can order the weights so that . for overdetermined semi - regular systems , estimates from the homogeneous case can be adapted to the weighted case . we provide some experimental results based on systems arising from a cryptography problem and from polynomial inversion problems . they show that taking advantage of the weighted homogeneous structure can yield substantial speed - ups , and allows us to solve systems which were otherwise out of reach . , ,

solving polynomial systems arising from applications is frequently made easier by the structure of the systems . weighted homogeneity ( or quasi - homogeneity ) is one example of such a structure : given a system of weights ,-homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree . grbner bases for weighted homogeneous systems can be computed by adapting existing algorithms for homogeneous systems to the weighted homogeneous case . we show that in this case , the complexity estimate for algorithm 5 can be divided by a factor . for zero - dimensional systems , the complexity of algorithm ( where is the number of solutions of the system ) can be divided by the same factor . under genericity assumptions , for zero - dimensional weighted homogeneous systems of-degree , these complexity estimates are polynomial in the weighted bzout bound . furthermore , the maximum degree reached in a run of algorithm 5 is bounded by the weighted macaulay bound , and this bound is sharp if we can order the weights so that . for overdetermined semi - regular systems , estimates from the homogeneous case can be adapted to the weighted case . we provide some experimental results based on systems arising from a cryptography problem and from polynomial inversion problems . they show that taking advantage of the weighted homogeneous structure can yield substantial speed - ups , and allows us to solve systems which were otherwise out of reach . , ,

1404.1863

i

spectral measures associated to the compact lie group @xmath1 and its maximal torus , nimrep graphs associated to the @xmath2 modular invariants , and the mckay graphs for finite subgroups of @xmath2 were studied in @xcite using information about the generating series of the moments of the spectral measure and the jones series which is related to the poincar series of the subfactor planar algebra associated to the graph ( see e.g. @xcite ) . in @xcite the authors studied spectral measures associated to the compact lie groups @xmath1 and @xmath3 and their maximal tori , nimrep graphs associated to the @xmath2 and @xmath4 modular invariants , and the mckay graphs for finite subgroups of @xmath2 and @xmath4 , using braided subfactor theory . spectral measures associated to the compact rank two lie groups @xmath5 and @xmath6 are studied in @xcite , and for other compact rank two lie groups in @xcite . in this paper and its sequel @xcite we focus on the lie group @xmath7 , the automorphism group of the octonions @xmath8 . it is a simply connected , compact , real rank two lie group of dimension 14 and is the smallest of the exceptional lie groups . it is isomorphic to the subgroup of @xmath9 that fixes any particular vector in its 8-dimensional real spinor representation . we determine spectral measures and joint spectral measures for ( the adjacency matrices of ) various graphs related to the lie group @xmath0 : the mckay ( or representation ) graphs for the irreducible representations of @xmath0 and its maximal torus @xmath10 , nimrep graphs or fusion modules associated to the @xmath0 modular invariants , and in the sequel @xcite , the mckay graphs for finite subgroups of @xmath0 . suppose @xmath11 is a unital @xmath12-algebra with state @xmath13 . if @xmath14 is a self - adjoint operator then there exists a compactly supported probability measure @xmath15 , the spectral measure of @xmath16 , on the spectrum @xmath17 of @xmath16 , uniquely determined by its moments @xmath18 , for all non - negative integers @xmath19 . note that @xmath15 depends on the choice of state @xmath13 on @xmath11 . in the cases we consider , the @xmath12-algebra @xmath11 will be a space of operators which act on the following hilbert space @xmath20 . for the mckay graphs for irreducible representations of @xmath0 we have @xmath21 , whilst for the irreducible representations of its maximal torus @xmath10 we have @xmath22 . for a nimrep graph @xmath23 ( either associated to a @xmath0 modular invariant or the mckay graph for finite subgroups of @xmath0 ) with vertex set @xmath24 , we take @xmath25 . as @xmath0 has rank two , its characters are functions on the maximal torus @xmath10 of @xmath0 . for @xmath2 and @xmath4 it was convenient to determine the spectral measures for the operator @xmath16 given by the adjacency matrices of the various graphs related to these groups ( the mckay graphs for the irreducible representations of the group and its maximal torus , nimrep graphs associated to modular invariants , and the mckay graphs for finite subgroups ) by first determining corresponding measures @xmath26 over the maximal tori of @xmath2 or @xmath4 respectively . this approach is described as a spectral measure blowup in @xcite . in the case of @xmath0 , the maximal torus @xmath10 has dimension one greater than the spectrum @xmath17 , so that there is a loss of dimension when passing from the measure @xmath26 to @xmath15 . this means that there is an infinite family of measures @xmath26 over @xmath10 which correspond to the spectral measure @xmath15 ( details of the relation between @xmath26 and @xmath15 are given in section [ sect : measures - different_domains ] ) . in order to remove this ambiguity , we also consider measures over the joint spectrum @xmath27 of commuting self - adjoint operators @xmath16 and @xmath28 . the abelian @xmath12-algebra @xmath29 generated by @xmath16 , @xmath28 and the identity 1 is isomorphic to @xmath30 , where @xmath31 is the spectrum of @xmath29 . then the joint spectrum is defined as @xmath32 . in fact , one can identify the spectrum @xmath31 with its image @xmath33 in @xmath34 , since the map @xmath35 is continuous and injective , and hence a homeomorphism since @xmath31 is compact @xcite . in the case where the operators @xmath16 , @xmath28 act on a finite - dimensional hilbert space , this is the set of all pairs of real numbers @xmath36 for which there exists a non - zero vector @xmath37 such that @xmath38 , @xmath39 . then there exists a compactly supported probability measure @xmath40 on @xmath33 , which is uniquely determined by its cross moments @xmath41 for all non - negative integers @xmath19 , @xmath42 . the spectral measure for @xmath16 is then given by the pushforward @xmath43 of the joint spectral measure @xmath40 under the orthogonal projection @xmath44 onto the spectrum @xmath45 . to study the spectral measures for the nimrep graphs associated to the @xmath0 modular invariants , we use the theory of braided subfactors and @xmath46-induction , which we now briefly review . for a fuller discussion on braided subfactors and @xmath46-induction see @xcite . the verlinde algebra of @xmath0 at level @xmath47 is represented by a non - degenerately braided system of endomorphisms @xmath48 on a type @xmath49 factor @xmath50 . its fusion rules @xmath51 reproduce exactly those of the positive energy representations of the loop group of @xmath0 at level @xmath47 , @xmath52 . furthermore its statistics generators @xmath53 , @xmath54 obtained from the braided tensor category @xmath48 match exactly those of the kac - peterson modular @xmath53 , @xmath54 matrices which perform the conformal character transformations ( see footnote 2 in @xcite ) . from the verlinde formula we see that this family @xmath55 of commuting normal matrices can be simultaneously diagonalised , i.e. @xmath56 , where the summation is over each @xmath57 and @xmath58 is the trivial representation . the intriguing aspect being that the eigenvalues @xmath59 and eigenvectors @xmath60 are described by the modular @xmath53 matrix . a braided subfactor is an inclusion @xmath61 where the dual canonical endomorphism decomposes as a finite combination of elements of the verlinde algebra , i.e. a finite combination of endomorphisms in @xmath48 . such subfactors yield modular invariants through the procedure of @xmath46-induction which allows two extensions of @xmath62 on @xmath50 , depending on the use of the braiding or its opposite , to endomorphisms @xmath63 of @xmath64 , so that the matrix @xmath65 is a modular invariant @xcite . the systems @xmath66 are called the chiral systems , whilst the intersection @xmath67 is called the neutral system . then @xmath68 , where @xmath69 denotes a system of endomorphisms consisting of a choice of representative endomorphisms of each irreducible subsector of sectors of the from @xmath70 $ ] , @xmath71 , where @xmath72 is the inclusion map . although @xmath48 is assumed to be braided , the systems @xmath66 or @xmath73 are not braided in general . the action of each @xmath50-@xmath50 sector @xmath71 on the @xmath64-@xmath50 sectors @xmath74 produces a nimrep ( non - negative integer matrix representation of the original verlinde algebra ) @xmath75 , i.e. @xmath76 . the spectrum of ( each ) @xmath75 reproduces exactly the diagonal part of the modular invariant @xcite . since the nimreps are a family of commuting matrices , they can be simultaneously diagonalised and thus the eigenvectors @xmath77 are the same for the nimrep graphs @xmath75 for all @xmath71 . we have @xmath78 , where the summation is over each @xmath57 with multiplicity given by the modular invariant , i.e. the spectrum of @xmath75 is given by @xmath79 with multiplicity @xmath80 . the set of @xmath81 with multiplicity @xmath82 is called the set of exponents of @xmath83 . along with the identity invariants for @xmath0 for all levels @xmath47 , there are two exceptional invariants due to conformal embeddings at levels 3 , 4 @xcite and another exceptional invariant at level 4 @xcite . these are all the known @xmath0 modular invariants . since the centre of @xmath0 is trivial , there are no orbifold modular invariants . this list was shown to be complete for all prime heights @xmath84 such that @xmath85 @xcite , and for all other @xmath86 @xcite . the paper is organised as follows . in section [ sect : rep_theoryg2t2 ] we describe the representation theory of @xmath0 and its maximal torus @xmath10 , and in particular focus on the fundamental representations of @xmath0 . in section [ sect : measures - different_domains ] we discuss spectral measures for @xmath0 over different domains , showing how measures over a region in the complex plane yields a unique @xmath87-invariant measure over @xmath10 , where @xmath87 is the weyl group of @xmath0 . in section [ sect : measure : a12infty(g2 ) ] we determine the ( joint ) spectral measures associated to the ( adjacency matrices of the ) mckay graphs given by the action of the irreducible characters of @xmath0 on its maximal torus @xmath10 , and in section [ sect : measureainftyg2 ] the ( joint ) spectral measures associated to the ( adjacency matrices of the ) mckay graphs of @xmath0 itself . in both cases we focus on the fundamental representations of @xmath0 , and determine these ( joint ) spectral measures over @xmath10 and the ( joint ) spectrum of these adjacency matrices . finally in section [ sect : measures_nimrepg2 ] we determine joint spectral measures over @xmath10 for nimrep graphs arising from @xmath0 braided subfactors .

spectral measures provide invariants for braided subfactors via fusion modules . in this paper we study joint spectral measures associated to the rank two lie group , including the mckay graphs for the irreducible representations of and its maximal torus , and fusion modules associated to all known modular invariants .

spectral measures provide invariants for braided subfactors via fusion modules . in this paper we study joint spectral measures associated to the rank two lie group , including the mckay graphs for the irreducible representations of and its maximal torus , and fusion modules associated to all known modular invariants .

1108.3564

r

in this section , we present the evolution of the collapsing cloud and the outflow for typical models in [ sec : typical ] ( model n08 , less massive cloud case ) and [ sec : typical2 ] ( model n06 , massive cloud case ) . then , we describe the mass accretion rate ( [ sec : accretion ] ) and masses of the protostar and circumstellar disk ( [ sec : mass ] ) , and the mass ejected by the protostellar outflow ( [ sec : out ] ) . the properties of the protostellar outflow are described in [ sec : out2 ] . figure [ fig:1 ] plots the cloud evolution for model n08 from the initial state until the end of the main accretion phase ; only the @xmath106 region is shown . note that although the structure only around the initial cloud scale ( @xmath107 ) is plotted in figure [ fig:1 ] , the computational domain has a size of @xmath108 . as seen in figure [ fig:1]_a _ , we adopted a spherical cloud with the be density profile and the radius of @xmath109 as the initial state . as described in [ sec : setting ] , since we ignored the gravity outside the be sphere ( @xmath110 ) , only the gas in the @xmath111 region ( inside the white dotted line in fig . [ fig:1 ] ) can collapse to fall onto the center of the cloud . for this model , the number density exceeds @xmath90 and a protostar forms at @xmath112 , where @xmath87 ( @xmath113yr ) is the freefall timescale of the initial cloud at the center . figure [ fig:1]_b _ shows the density distribution just after protostar formation . the red contours of @xmath114 in figure [ fig:1]_a _ and _ b _ indicate that the cloud gradually contracts toward the center with time . the blue contour in the figure corresponds to the boundary of the protostellar outflow , inside which the gas moves outward against the center of the cloud . thus , this contour shows the shape of the protostellar outflow . the outflow is driven by the circumstellar disk that originates from the first core , which appears before protostar formation @xcite . after protostar formation , the first core becomes the circumstellar disk @xcite . the outflow is then driven by the circumstellar disk after a smooth transition from the first core to the circumstellar disk @xcite . the protostellar outflow remains in the host cloud ( @xmath111 ) for @xmath115yr ( fig . [ fig:1]_c _ ) ; it reaches the boundary of the host cloud at @xmath116yr ( fig . [ fig:1]_d _ ) and penetrates the host cloud boundary and propagates into the interstellar space ( @xmath110 ) for @xmath117yr ( fig . [ fig:1]_e_-_h _ ) . the outflow driving halts inside the host cloud at @xmath118yr ( @xmath119 ) . the infalling envelope is depleted and the mass accretion is almost over by this epoch ( [ sec : mass ] ) . thus , the circumstellar disk can not drive the outflow at this epoch because the outflow is powered by gas accretion onto the circumstellar disk . since the freefall timescale of the cloud boundary is @xmath120yr , a large fraction of the gas inside the host cloud has already fallen onto either the circumstellar disk or the protostar by this epoch . although the outflow at the host cloud scale completely disappears in @xmath121yr ( = @xmath122@xmath87 = @xmath123 ) , the density cavity formed by the protostellar outflow remains around the host cloud as seen in figure [ fig:1]_i_. figure [ fig:1 ] also shows that the infalling envelope in the host cloud depletes with time . part of the gas inside the initial host cloud is ejected by the protostellar outflow , and the remainder falls onto either the circumstellar disk or the protostar . in figures [ fig:1]_h _ and _ i _ , we can see only a disk - like structure with the size of @xmath124200au , because the infalling gas is depleted by this epoch . at these epochs , the density of the infalling envelope ( @xmath125 ) is less than @xmath126 the initial cloud density ( @xmath127 ) . at the end of the calculation ( @xmath128 ) , the mass ratio of the infalling envelope to the total mass of the initial cloud is only @xmath129 . thus , the main accretion phase has already ended by this epoch . the evolution of the outflow configuration is shown in figure [ fig:2 ] . each panel corresponds to the same epoch as in figure [ fig:1]_d _ , _ e _ , _ f _ , and _ h_. figure [ fig:2 ] shows that the protostellar outflow propagates into the interstellar space while maintaining good collimation . however , figure [ fig:2]_a _ and _ b _ indicate that , early in the evolution , the outflow also extends in a transverse direction and increases in width . after its width becomes comparable to the host cloud scale , the outflow extends only in the vertical direction while maintaining its width . the magnetic field lines that guide the outflow are anchored by the host cloud ( or the gravitationally bound sphere ) . thus , the final width of the outflow is comparable to that of the host cloud . therefore , the outflow collimation improves with time after the outflow width becomes comparable to the host cloud scale , whereas the collimation is not good when its width is smaller than the host cloud scale or the outflow remains within the host cloud . figures [ fig:3 ] and [ fig:4 ] show the density and velocity distributions for model n06 at @xmath130yr ( @xmath131=@xmath132 ) . for this model , the protostar forms at @xmath133yr after the cloud begins to collapse . thus , the figures show the structure @xmath134yr after the protostar formation . by this epoch , the outflow penetrated the host cloud that has a radius of 4800au and reaches @xmath135au from the center of the cloud , as seen in figure [ fig:3 ] left panel . the figure also shows the bow shocks caused by the protostellar outflow at @xmath136au . the upper right panel in figure [ fig:3 ] plots the structure around the host cloud and shows that the gas flows out from the host cloud in the vertical direction by the protostellar outflow . in addition , inside the white dotted line that denotes the size of the initial cloud , the gas density is considerably lower than the ambient medium . this is because a part of the gas falls onto the central region to form the protostar and circumstellar disk , while the remainder is ejected from the host cloud by the outflow . the lower right panel is 16 times magnified view of the central region of the upper right panel . this panel shows that the outflow is strongly driven by the disk - like structure around the protostar . on this scale , the gas accretes onto the protostar through the circumstellar disk , and a part of the accreting mater is ejected by the outflow . figure [ fig:4 ] shows the structure around the circumstellar disk on @xmath137 ( left panel ) and @xmath138 ( right panel ) planes . these panels show that the rotating disk exits around the protostar and drives the outflow . thus , it is expected that the outflow is mainly driven by the magnetocentrifugal mechanism @xcite . figures [ fig:3 ] and [ fig:4 ] indicate that large scale outflow with a size of @xmath139au ( fig . [ fig:3 ] left panel ) originates from the disk wind driven by the circumstellar or rapidly rotating disk with a size of @xmath140au . the disk wind propagates into the infalling envelope , and thus it sweeps and collects a larger fraction of the infalling matter . finally , a large fraction of the swept material is expelled from the host cloud . thus , the outflow significantly affects the final protostellar mass or star formation efficiency . figure [ fig:5 ] shows the mass accretion rate onto the protostar and the protostellar mass against the time after protostar formation @xmath141 . here , we describe the time after the protostar formation as @xmath141 , which is defined as @xmath142 where @xmath143 is the elapsed time after the cloud begins to collapse ( or the calculation starts ) , and @xmath144 is the protostar formation epoch and is listed in table [ table:1 ] . in each model , the gas density exceeds @xmath145 , and the protostar forms @xmath146 after the cloud begins to collapse ( table [ table:1 ] ) . note that model n39 shows no continuous collapse and no protostar appears ; this is because the initial cloud density for model n39 is too high to induce continuous collapse . in our models , since the gas becomes adiabatic at @xmath147 ( [ sec : setting ] ) , the initial cloud density ( @xmath148 ) for model n39 is very close to this critical value @xmath149 . as a result , model n39 shows repeated contraction and expansion around the initial configuration , not continuous collapse . below , we describe only the models showing protostar formation ( n35 , n06 , n36 , n07 , n37 , n08 , n38 , n09 ) and do not mention model n39 again . as described in [ sec : sink ] , we removed the gas having a number density of @xmath145 in the region @xmath150au from the computational domain . we regarded the removed gas as the accreted mass onto the protostar and estimated the mass accretion rate in each time step . figure [ fig:5 ] shows that , in each model , the mass accretion rate is as high as @xmath151 just after protostar formation ( @xmath152yr ) . in theoretical analyses , the mass accretion rate is defined as @xmath153 , where @xmath36 is a numerical factor ( e.g. , @xmath154 in @xcite , @xmath155 in @xcite ) . since gas clouds have temperatures of @xmath56k ( @xmath156 ) , the accretion rate in the main accretion phase is @xmath157 . thus , the accretion rate derived in our calculations corresponds well to the theoretical expectation . then , in each model , the mass accretion rate gradually decreases with time , to @xmath158 at @xmath159 and @xmath160 at @xmath161 . thus , gas accretion almost halts and the protostar rarely increases in mass at @xmath162 . as shown in figure [ fig:5 ] , all models show a qualitatively and quantitatively similar mass accretion rate trend when the mass accretion rate onto the protostar is normalized by the freefall timescale of the initial cloud . however , since the real ( or dimensional ) time of the freefall timescale depends on the initial cloud density ( or the initial cloud mass ) , the duration of the main accretion phase is different in models with different cloud masses . a cloud with a larger mass ( or lower density ) has a longer duration of the main accretion phase . for example , model n35 with @xmath163 has the mass accretion of @xmath164 for @xmath165yr , while model n09 with @xmath166 has that only for @xmath167yr . figure [ fig:5 ] also shows that the protostar formed in a massive cloud is more massive than that formed in a less massive cloud . this is because the massive cloud has a longer gas accretion phase , so the protostar has enough time to acquire sufficient mass and evolves into a relatively massive star . in figure [ fig:5 ] , the mass accretion rate oscillates in models having an initially massive cloud . this is caused by a non - axisymmetric structure appearing in the circumstellar disk . since the circumstellar disk is more massive than the protostar just after protostar formation @xcite , a non - axisymmetric or spiral structure develops owing to gravitational instability . such structure effectively transfers angular momentum outward and intermittently promotes mass accretion onto the protostar . as a result , these models show time variability in the mass accretion rate @xcite . in figure [ fig:5 ] , models n35 , n06 , n36 , n07 and n37 show time variability in the mass accretion rate . the mass of the protostar , circumstellar disk , protostellar outflow , and infalling envelope are plotted against time after protostar formation @xmath141 in figure [ fig:6 ] . in addition , these masses at @xmath88 after protostar formation are listed in table [ table:2 ] . the circumstellar disk mass is estimated according to the formula in @xcite . to estimate the outflowing gas @xmath168 , we integrated the gas with velocity @xmath169 for the entire computational domain and subtracted the gas swept by the protostellar outflow outside the host cloud @xmath35 from the integrated mass . for later convenience , we divide the outflowing mass into two parts , @xmath170 where @xmath171 is the mass ejected from the host cloud , and @xmath172 is the outflowing mass having @xmath173 inside the host cloud ( @xmath111 ) . to calculate the mass of the infalling envelope , we calculated the total mass @xmath174 inside the host cloud ( @xmath34 ) . then , we subtracted the disk mass @xmath175 and the outflowing mass @xmath172 in the @xmath34 region from the total mass , @xmath176 in our models , the sum of the protostellar mass , circumstellar mass , and infalling envelope mass is not conserved inside the host cloud ( i.e. , @xmath34 ) because part of the gas is ejected from the host cloud by the protostellar outflow . however , we confirmed that the sum of the total mass and the protostellar mass is well conserved before the outflow reaches the boundary of the host cloud , as described in [ sec : setting ] . figure [ fig:6 ] shows that , in each model , the mass of the infalling envelope decreases to @xmath177 at @xmath161 ( table [ table:2 ] ) , where @xmath178 is the initial cloud mass . thus , the mass of the infalling envelope is depleted and the main accretion phase is almost over by this epoch . note that , in figure [ fig:6 ] , we subtracted the time ( @xmath144 ) until the protostar forms from the time ( @xmath143 ) after the cloud begins to collapse . thus , at the epoch @xmath88 , indicated by the arrow in figure [ fig:6 ] , a longer time than @xmath88 has passed since the cloud begins to collapse ( table [ table:1 ] ) . therefore , it is reasonable that almost all the gas has already fallen onto the center of the cloud at this epoch @xmath179 , because the gas falls onto the cloud center in several times freefall timescale @xcite and the freefall timescale at the cloud boundary ( @xmath88 ) has already passed by this epoch . figure [ fig:6 ] also indicates that the circumstellar disk mass dominates the protostellar mass just after protostar formation in each model . the circumstellar has been reported to originate from the first core @xcite , which is about 10 - 100 times more massive than the protostar at the protostar formation epoch @xcite . @xcite showed that the circumstellar disk is inevitably more massive than the protostar in the early main accretion phase because the first core evolves directly into the circumstellar disk after protostar formation . in the later main accretion phase , however , in some models , the protostellar mass dominates the circumstellar disk mass . in the initially massive clouds ( models n35 , n06 , and n36 ) , the protostellar mass continues to increase , whereas the circumstellar disk mass gradually decreases until the end of the main accretion phase . in addition , in models n35 and n06 , the protostar becomes more massive than the circumstellar disk for @xmath180 . the massive circumstellar disk becomes gravitationally unstable and tends to exhibit a non - axisymmetric structure that can transfer angular momentum outward ; the gas in the circumstellar disk effectively falls onto the protostar . therefore , the accretion rate onto the protostar from the circumstellar disk dominates the accretion rate onto the circumstellar disk from the infalling envelope , and the mass of the disk begins to decrease . figure [ fig:7 ] shows the density distribution on the equatorial plane around the center of the cloud at @xmath181 for models n35 , n06 , n08 and n09 . the figure shows that a rotating disk with a size of @xmath182au forms around the center of the cloud by this epoch . as seen in figure [ fig:7]_a _ , two clumps appear in model n35 , in which fragmentation occurs in the circumstellar disk about @xmath165yr after protostar formation . in models n35 and n06 , the circumstellar disk is rather massive in the early main accretion phase . as shown in figure [ fig:6 ] , the circumstellar disk has a mass of @xmath183 in model n35 and @xmath184 in model n06 in the early main accretion phase for @xmath185 . such a massive disk becomes gravitationally unstable and tends to develop a non - axisymmetric structure and show subsequent fragmentation , as seen in figure [ fig:7]_a_. although model n06 shows no fragmentation until the end of the calculation , non - axisymmetric ( or spiral ) structure develops in the circumstellar disk , as seen in figure [ fig:7]_b_. the circumstellar disk mass begins to decrease after the non - axisymmetric structure develops because such structure transfers angular momentum outward , and the gas in the circumstellar disk effectively falls onto the central protostar . finally , the protostellar mass dominates the circumstellar disk mass in the later main accretion phase for models n35 and n06 ( fig . [ fig:6 ] ) . for model n36 , the circumstellar disk mass gradually decreases in the main accretion phase ( fig . [ fig:6 ] ) , whereas it is greater than the protostellar mass at @xmath186 . the efficiency of angular momentum transfer for model n36 is considered to be lower than those for models n35 and n06 because only a weak spiral structure appears in this model . on the other hand , for models n07 , n37 , n08 and n38 , the circumstellar disk mass does not decrease greatly in the main accretion phase and is slightly greater than or comparable to the protostellar mass at the end of the main accretion phase . although the circumstellar disk is more massive than the protostar during the main accretion phase , no non - axisymmetric structure develops in these models . this is because the size of the circumstellar disk is not sufficiently larger than the jeans length , and the disk is stable against gravity ( @xcite ) . as shown in figure [ fig:7 ] , model n08 has an almost axisymmetric structure . thus , angular momentum transfer due to non - axisymmetric structure is not so effective , and a massive disk remains until the end of the main accretion phase . as seen in figure [ fig:6 ] , for model n09 , the protostar becomes more massive than the circumstellar disk just after the protostar formation , and the protostellar mass dominates the circumstellar disk mass by the end of the calculation . since model n09 has no sufficient cloud mass at the initial state , the circumstellar disk can not increase its mass significantly by gas accretion . for this model , the protostar and the circumstellar disk just after the protostar formation has a mass of @xmath187 and @xmath188 , respectively . thus , the sum of protostellar and circumstellar disk masses ( @xmath189 ) is comparable to the initial cloud mass ( @xmath190 ) . therefore , mass accretion onto the circumstellar disk from the infalling envelope rapidly declines immediately after the protostar formation . on the other hand , the protostar gradually increases its mass by the mass accretion from the circumstellar disk . figure [ fig:6 ] indicates that , in each model , the protostellar mass rapidly increases for @xmath191 , and slightly increases for @xmath192 . for @xmath162 , the protostellar mass rarely increases because the infalling envelope is almost depleted by this epoch . to compare the protostellar mass evolution among models , the time averaged mass accretion rate for @xmath193 is estimated as @xmath194 , where @xmath195 is the protostellar mass at @xmath186 . for all models , the averaged mass accretion rates are in the range of @xmath196 . the difference of the mass accretion rate among models is only a factor of about 2 . thus , a protostar has a similar accretion history when the protostellar evolution is normalized by the freefall timescale of the initial cloud . in reality , however , initially massive cloud has a longer freefall timescale and longer duration of the main accretion phase . thus , the protostar formed in massive cloud has a greater mass at the end of the main accretion phase . in the main accretion phase , the mass of the protostellar outflow dominates , or is comparable to , both the protostellar and circumstellar disk masses for models n35 , n06 , n36 , n07 , and n37 , as shown in figure [ fig:6 ] . this indicates that the protostellar outflow greatly affects star formation efficiency because it ejects a large fraction of the mass of the host cloud . in other words , the protostellar outflow controls the protostellar mass or star formation efficiency in the star formation process as pointed by @xcite . figure [ fig:8 ] shows the density and velocity distribution on the @xmath137 cutting plane for models n35 , n06 , n08 , and n09 at @xmath197 @xmath198 . note that the models and epochs in figure [ fig:8 ] are the same as those in figure [ fig:7 ] , but the spatial scales differ . in each panel , the outflowing region is denoted by a white contour , inside of which radial velocity of the gas is supersonic ( @xmath169 ) . figure [ fig:8 ] shows that the gas is strongly ejected from the host cloud by the protostellar outflow in any model . in addition , the outflow width ( i.e. , the horizontal length in the direction of travel ) is comparable to the radius of the host cloud ( @xmath199 ) , and thus , the outflow has a wide opening angle . at this epoch , on the cloud scale of @xmath33 , the outflow has opening angles of @xmath200 ( n35 ) , @xmath201 ( n06 ) , @xmath202 ( n08 ) , and @xmath203 ( n09 ) . note that the opening angle continues to increase until it becomes comparable to the cloud radius . as a result , the protostellar outflow with a wide opening angle sweeps up a large fraction of the infalling material and ejects it into the interstellar space . in addition to this swept material , a part of the mass in the circumstellar disk is ejected directly by the outflow . figure [ fig:9 ] shows the ratio of the outflowing to infalling masses for models n35 , n36 , n37 , and n38 . to investigate outflow efficiency and mass ejection rate , we calculated the outflowing / infalling mass rate on the @xmath204 and @xmath205 grid surfaces . in each model , the @xmath204 grid covers the entire circumstellar disk , and @xmath206 grid has a size of @xmath207 times the disk radius . since the protostellar outflow is originally driven by the circumstellar disk , the mass ejected from the @xmath204 grid almost corresponds to the outflowing mass directly driven by the circumstellar disk . on the other hand , the mass ejected from the @xmath206 is the sum of the outflowing mass directly driven by the circumstellar disk and the swept mass by the outflow that propagates into the dense ( or massive ) infalling envelope . according to @xcite , we estimated the outflow @xmath208 and inflow @xmath209 masses as @xmath210\ , ds,\ ] ] and @xmath211\ , ds,\ ] ] respectively , where @xmath212 is the unit vector outwardly normal to the surface of the @xmath204 or @xmath205 grid . figure [ fig:9 ] shows that the ratio of the outflowing to inflowing mass around the circumstellar disk ( @xmath204 , thin line ) has a peak of @xmath213 at @xmath214 . thus , the mass ejection rate is comparable to the mass infalling rate at this epoch . note that since the circumstellar disk and the outflow driving region are embedded in the grid of @xmath204 , the mass swept up by the outflow may be slightly included in the estimation of the outflowing rate . then , in all the models , the ratio in the @xmath204 grid gradually decreases with time . the ratio decreases to @xmath215 at @xmath216 and reaches @xmath217 at @xmath218 . figure [ fig:9 ] also shows that the ratio of @xmath219 in the @xmath220 grid exceeds that in the @xmath221 grid for a short period after the protostar appears . thus , the outflowing mass ( rate ) increases with distance from the driving source . this indicates that a wide - opening - angle outflow sweeps up the infalling gas and ejects it toward the center of the cloud . especially , for @xmath180 , the rate in the @xmath206 grid is about 10 times larger than that in the @xmath206 grid . this indicates that the protostellar outflow collects the matter in the infalling envelope 10 times more massive than that directly blown away from the circumstellar disk . note that since the boundary of the host cloud is located more far away from @xmath206 grid , the outflow sweeps more matter in the infalling envelope to be ejected from the host cloud . the thick line in figure [ fig:9 ] indicates that the outflow on a larger scale gradually decreases for @xmath222 and disappears in @xmath223 . thus , the lifetime of the outflow is about 10 times the freefall timescale of the center of the host cloud , or 3 - 5 times of the freefall timescale of the outer edge of the host cloud . the protostar forms @xmath146 after the cloud begins to collapse ( table [ table:1 ] ) . thus , roughly speaking , the protostellar outflow continues to be driven by the circumstellar disk until the freefall timescale of the cloud boundary passes after the protostar formation . this is natural that the almost all the gas inside the cloud fall onto the circumstellar disk in @xmath88 ( figs . [ fig:5 ] and [ fig:6 ] ) , and the protostellar outflow is powered by the mass accretion onto the circumstellar disk . figure [ fig:10 ] shows the outflow length ( upper panel ) and width ( lower panel ) against the time normalized by the freefall timescale at the center of the cloud for all models . note that the length and width in figure [ fig:10 ] right panels are normalized by the initial each cloud radius @xmath109 . we defined the outflow as the gas having the ( positive ) radial velocity larger than the sound speed ( @xmath169 ) . the outflow expands with time and reaches @xmath224au at @xmath225 ( fig . [ fig:10 ] upper left panel ) . the final size of the outflow depends on the size ( or mass ) of the initial cloud . the outflow extends up to about 10 times the initial cloud radius except for model n09 ( fig . [ fig:10 ] upper right panel ) . the outflow in a massive cloud has a longer lifetime to reach a greater distance from the protostar because a massive cloud has a longer freefall timescale and the outflow continues to be driven on @xmath226 times the freefall timescale . the lower panels of figure [ fig:10 ] indicates that the outflow also expands in the horizontal direction and becomes comparable in size to the host cloud radius @xmath199 . the outflow propagates into the infalling envelope along the magnetic field lines . although the magnetic field lines that drive the outflow are strongly bundled around the circumstellar disk , they spread with the distance from the center of the cloud up to @xmath227 because they are connected to the cloud scale lines . therefore , the outflow width also spreads in the horizontal direction and has an opening angle of @xmath228 on the host cloud scale . figure [ fig:11 ] shows the evolution of the collimation factor of the outflow , which is defined as @xmath229 where @xmath230 and @xmath231 are the length and width of the outflow , respectively . the figure indicates that the collimation factors remain @xmath232 for @xmath233 . then , they begin to increase for @xmath234 . at the end of the calculation , the collimation factors reach @xmath235 . as seen in figure [ fig:2 ] , although the outflow has a wide - opening - angle in the early main accretion phase , it is a very well collimated in the later main accretion phase . in addition , the width of the protostellar outflow reflects the size of the host cloud . thus , we can acquire information on the prestellar cloud core from the size and width of the protostellar outflow .

, the protostellar outflow is driven by the circumstellar disk . the outflow extends also in the transverse direction until its width becomes comparable to the initial cloud scale , and thus , the outflow has a wide opening angle of . as a result , the protostellar outflow sweeps up a large fraction of the infalling material and ejects it into the interstellar space . a massive circumstellar disk comparable in mass to the protostar remains .

star formation efficiency controlled by the protostellar outflow in a single cloud core is investigated by three - dimensional resistive mhd simulations . starting from the prestellar cloud core , the star formation process is calculated until the end of the main accretion phase . in the calculations , the mass of the prestellar cloud is parameterized . during the star formation , the protostellar outflow is driven by the circumstellar disk . the outflow extends also in the transverse direction until its width becomes comparable to the initial cloud scale , and thus , the outflow has a wide opening angle of . as a result , the protostellar outflow sweeps up a large fraction of the infalling material and ejects it into the interstellar space . the outflow can eject at most over half of the host cloud mass , significantly decreasing star formation efficiency . the outflow power is stronger in clouds with a greater initial mass . thus , the protostellar outflow effectively suppresses star formation efficiency in a massive cloud . the outflow weakens significantly and disappears in several free - fall timescales of the initial cloud after the cloud begins to collapse . the natal prestellar core influences the lifetime and size of the outflow . at the end of the main accretion phase , a massive circumstellar disk comparable in mass to the protostar remains . calculations show that typically ,% of the initial cloud mass is converted into the protostar and% remains in the circumstellar disk , while% is ejected into the interstellar space by the protostellar outflow . therefore , a single cloud core typically has a star formation efficiency of% .

1108.3564

i

in this study , we investigated the impact of protostellar outflow on the star formation process . we constructed nine models with different initial cloud masses in the range of @xmath63 , and calculated the cloud evolution until the cloud mass is depleted . in the calculation , without artificially inputting outflow ( momentum ) to the computational domain as seen in any other studies , outflow is naturally or automatically driven by the circumstellar disk . as a result of the calculation , we found that a large fraction of the initial cloud mass is ejected from the host cloud into the interstellar space by the protostellar outflow . thus , the protostellar outflow significantly affects the star formation process and determination of the star formation efficiency . the following results are obtained . the protostellar outflow continues to be driven by the circumstellar disk for about 10 times the freefall timescale of the initial cloud after the cloud begins to collapse . the final size of the outflow is different among models , because different models have different initial central densities and different freefall timescales . in each model , the protostellar outflow reaches @xmath224au far from the protostar in @xmath290 . when the outflow remains inside the host cloud , the outflow extends also to the vertical direction toward the direction of travel , because the outflow is anchored by large - scale ( host cloud scale ) magnetic field lines . after the outflow penetrates the host cloud and propagates into the interstellar space , it extends only in the direction of the travel keeping its width . thus , in this period , the outflow collimation improves to reach @xmath274 . before disappearing , the outflow has a length of 10 times the natal cloud radius and a maximum width comparable to the natal cloud radius . thus , we can expect natal cloud size ( or mass ) from the length and width of observed outflow . in this study , since we did not resolve protostar itself , no high - velocity jet appears . however , outflow momentum and momentum flux derived in our simulation well agree with observations . this indicates that the outflow driven by the circumstellar disk is responsible for total outflow momentum , and high velocity jet rarely affects the star formation efficiency . in addition , it is expected that the entrained mass by the high velocity jet can be ignored to estimate the mass ejection from the host cloud , because observed outflow momentum can be explained only by the disk driven outflow . although the high velocity jet may promote the mass ejection further , a larger fraction of the mass can be ejected only by the outflow . the protostellar outflow can eject @xmath291% of the host cloud mass into the interstellar space . the mass ejection rate increases as the initial cloud mass increases ; a large fraction of the initial cloud mass is ejected in a massive cloud . this is because a massive cloud retains a large amount of the infalling matter even after the protostar formation , and outflow can sweep and collect a large fraction of the infalling matter when it propagates into the infalling envelope . thus , the protostellar outflow can suppress the star formation efficiency to @xmath292 . in addition , a massive circumstellar disk comparable to the protostellar mass remains even after the infalling envelope is depleted . although we need to calculate further evolution of the protostellar system to determine the star formation efficiency , the star formation efficiency of @xmath293% may be realized when ( a part of ) the circumstellar disk is blown away in further evolution stage . plane are plotted with the initial cloud scale . the white dashed circle represents initial cloud radius ( i.e. , the host cloud ) . the blue line is the boundary of the outflow inside which the gas moves outwardly toward the center of the cloud ( or the protostar ) with a supersonic velocity . the elapsed time @xmath143 in unit of the freefall timescale ( @xmath87 ) and year is plotted on the upper side of each panel . the white squares in each panel denote the outer boundary of the subgrid . , width=566 ] inside which the gas is outflowing from the center of the cloud with the supersonic velocity @xmath294 . the blue sphere corresponds to the initial host cloud . the elapsed time @xmath143 in unit of the freefall timescale ( @xmath87 ) and year is plotted on the upper side of each panel . , width=566 ] plane at @xmath295 for model n06 with different spatial scales . the white dashed circle represents initial cloud radius ( i.e. , be radius ) . the red contours denote the outflow inside which the gas moves outwardly toward the center of the cloud with a supersonic velocity ( thick line ) and half of the supersonic velocity ( thin line ) . , width=566 ] ( left ) and @xmath138 ( right ) planes at the same epoch as in fig . [ fig:3 ] . the red contour denotes the outflow inside which the gas moves outwardly toward the center of the cloud with a supersonic velocity . , width=566 ] ( = @xmath296 , where @xmath144 is time at the protostar formation ) after the protostar formation for each model . the vertical lines in each panel corresponds to the freefall timescale of the host cloud at the center ( @xmath87 , solid line ) and cloud boundary ( @xmath88 , broken line ) . the initial host cloud mass is plotted by the cross ( @xmath297 ) on the right axis . , width=566 ] (= @xmath296 ) after the protostar formation for each model . the vertical lines in each panel corresponds to the freefall timescale of the host cloud at the center ( @xmath87 , solid line ) and cloud boundary ( @xmath88 , broken line ) . , width=566 ] plane for models n35 , n06 , n08 and n09 . the elapsed time @xmath143 in unit of @xmath87 and year is plotted on the upper side of each panel . the white dashed circle represents initial cloud radius ( i.e. , be radius ) . the white solid line is the boundary of the outflow inside which the gas moves outwardly toward the center of the cloud ( or the protostar ) with a supersonic velocity . the white squares in each panel denote the outer boundary of the subgrid . , width=566 ] and @xmath205 grid against the time for model n35 , n36 , n37 and n38 . the vertical lines are the freefall timescale of the host cloud at the center ( @xmath87 , solid line ) , cloud boundary ( @xmath88 , broken line ) , and 10 times the freefall timescale of the host cloud at the center ( @xmath298 , dotted line ) . , width=566 ]

the outflow can eject at most over half of the host cloud mass , significantly decreasing star formation efficiency . the outflow weakens significantly and disappears in several free - fall timescales of the initial cloud after the cloud begins to collapse . calculations show that typically ,% of the initial cloud mass is converted into the protostar and% remains in the circumstellar disk , while% is ejected into the interstellar space by the protostellar outflow .

star formation efficiency controlled by the protostellar outflow in a single cloud core is investigated by three - dimensional resistive mhd simulations . starting from the prestellar cloud core , the star formation process is calculated until the end of the main accretion phase . in the calculations , the mass of the prestellar cloud is parameterized . during the star formation , the protostellar outflow is driven by the circumstellar disk . the outflow extends also in the transverse direction until its width becomes comparable to the initial cloud scale , and thus , the outflow has a wide opening angle of . as a result , the protostellar outflow sweeps up a large fraction of the infalling material and ejects it into the interstellar space . the outflow can eject at most over half of the host cloud mass , significantly decreasing star formation efficiency . the outflow power is stronger in clouds with a greater initial mass . thus , the protostellar outflow effectively suppresses star formation efficiency in a massive cloud . the outflow weakens significantly and disappears in several free - fall timescales of the initial cloud after the cloud begins to collapse . the natal prestellar core influences the lifetime and size of the outflow . at the end of the main accretion phase , a massive circumstellar disk comparable in mass to the protostar remains . calculations show that typically ,% of the initial cloud mass is converted into the protostar and% remains in the circumstellar disk , while% is ejected into the interstellar space by the protostellar outflow . therefore , a single cloud core typically has a star formation efficiency of% .

cond-mat0109250

i

questions concerning the nature of thermal fluctuations in fluids in thermal nonequilibrium states have been the subject of many studies during the past two decades . specifically , in this paper we consider thermal fluctuations in a horizontal layer of a one - component fluid that is heated either from above or from below in such a way that the fluid is still in a stable convection - free state . a number of different and independent approaches for dealing with various aspects of this problem have appeared in the literature . most of the earlier studies focused on the nonequilibrium fluctuations close to the convective rayleigh - bnard instability because of their possible influence on the pattern - selection process when convection appears @xcite . the effects of both linear and nonlinear terms in the hydrodynamic fluctuations close to the convection threshold have been evaluated . this line of research turned out to be very important , mainly because it lead to the development of convection model equations for dealing with spatiotemporal - pattern formation above the threshold , as reviewed by cross and hohenberg @xcite . a second and independent line of research developed when investigators became interested in the nature of the fluctuations in nonequilibrium steady states far away from any hydrodynamic instability . the first important theoretical work along this line was done by kirkpatrick et al . , who calculated the correct expression for the structure factor of a fluid subjected to a stationary temperature gradient @xcite . althought their result was originally obtained on the basis of the same mode coupling theory that in equilibrium leads to long - time tail contributions to the correlation functions for the transport coefficients , it turned out that the same result could also be obtained from the simpler scheme of landau s fluctuating hydrodynamics @xcite . this line of research received an important momentum from the experimental side when the research group of sengers and coworkers verified from light - scattering experiments the main conclusion of the theoretical result , namely that the nonequilibrium contribution to the structure factor of a liquid is proportional to the square of the temperature gradient @xmath5 and inversely proportional to the fourth power of the wave number @xmath0 of the fluctuations @xcite . theory and experiments have subsequently been extended to also deal with nonequilibrium fluctuations in liquid mixtures and polymer solutions , as reviewed elsewhere @xcite . a third line of independent research has focused on the real - space behavior of the nonequilibrium correlations resulting from the heat - diffusion equation @xcite . a study of the correlations resulting from the heat - diffusion equation is equivalent to a study of the nonequilibrium correlations in a liquid in the direction co - incident with the temperature gradient . this line of research has shown how the nonequilibrium correlation function of the fluctuating variables encompasses the entire system not involving any intrinsic lenght scales . the real - space analysis has demonstrated the long - range nature of the nonequilibrium fluctuations in the direction of the temperature gradient , which has been further confirmed by numerical integration of the equations @xcite , by computer simulations @xcite and by a lattice - gas automaton approach @xcite . it is our present goal to further extend the second aforementioned research so as to describe nonequilibrium fluctuations far away from any convective instability , nonequilibrium fluctuations close to the convective instability and nonequilibrium fluctuations produced by the heat - diffusion equation from one unified point of view . the original work of kirkpatrick et al . and of others @xcite yielded an expression for the structure factor of a fluid in thermally nonequilibrium states without considering any gravity or boundary effects . segr at al . extended the theory to include gravity effects , first in a one - component liquid @xcite and then in a liquid mixture @xcite . they predicted that gravity will cause the singular @xmath1 dependence of the structure factor to saturate at small values of @xmath0 . this prediction was confirmed experimentally by vailati and giglio from light - scattering experiments at ultra - small scattering angles @xcite . more recently , ortiz de zrate et al . evaluated the nonequilibrium structure factor including finite - size effects but neglecting gravity @xcite . they concluded that deviations from the @xmath1 dependence due to finite - size effects will be just as important as deviations due to gravity . hence , for a quantitative interpretation of ultra - low - angle light scattering or shadowgraph experiments it is important to account for both gravity and finite - size effects . in this paper we extend the previous work so as to include gravity and finite - size effects simultaneously . starting from the linearized fluctuating boussinesq equations , we shall derive a complete expression for the structure factor of the nonequilibrium fluid making no other approximations than the ones incorporated in the boussinesq equations . we shall then show that the resulting expression is capable of describing nonequilibrium fluctuations both far away and close to the convective instability . close to the convective instability we shall recover the linear swift - hohenberg correlation function as an approximation to our more complete result . from the study of the behavior of the nonequilibrium correlation function in real space , we shall recover with appropriate approximations , expressions and plots previously obtained by other investigators for the case of the heat - diffusion equation . thus it will be shown how these various conclusions can be reached from one single theoretical result . attempts to arrive at a unified description of nonequilibrium fluctuations both far away and close to the convective instability has been made by kirkpatrick and cohen @xcite and by schmitz and cohen @xcite , but the consequences of their theoretical results for the interpretation of actual experiments are not clear . in contrast , we shall be able to make a connection with available experimental data for the thermal fluctuations near the convective rayleigh - bnard instability @xcite . there has been an extensive debate whether fluctuating hydrodynamics can properly account for the thermal fluctuations close to the onset of convection @xcite , but the most recent answer to this question appears to be positive @xcite . the present paper will provide additional evidence for the validity of fluctuating hydrodynamics to describe nonequilibrium fluctuations close to the onset of the classical rayleigh - bnard instability in simple fluids . we shall proceed as follows . we start from the linear fluctuating boussinesq equations which will be written in a form most suitable for our analysis in section [ sec:0 ] . in section [ sec:1 ] we review the derivation of the well - known expression for the structure factor of a fluid subjected to a stationary temperature gradient without taking into account the presence of boundaries , but including the effects of gravity . the relationship of the resulting expression for the effect of gravity with that obtained previously by segr et al . @xcite will be elucidated . in section [ sec:2 ] we then consider the modifications to the nonequilibrium structure factor due to the finite height of the fluid layer . in section [ sec : ls ] we present a detailed analysis of how the combined effects of gravity and finite - size will appear in low - angle light scattering and in shadowgraph experiments . sections [ sec:2 ] and [ sec : ls ] contain the most important new features of the present work . in section [ sec : ins ] we introduce an approximation valid close to the convective instability and show how one can recover the linear swift - hohenberg model for the fluctuations near the convective threshold . in section [ sec : rs ] we discuss the spatial behavior of the nonequilibrium structure factor and we shall make contact with the results obtained by previous investigators for the long - range nature of the nonequilibrium fluctuations in the direction of the temperature gradient . our results are summarized in section [ sec : con ] .

the relevance of this theoretical result for the interpretation of light scattering and shadowgraph experiments is elucidated . the relationship with studies on various aspects of the problem by other investigators is discussed . the paper thus provides a unified treatment for dealing with fluctuations in fluid layers subjected to a stationary temperature gradient regardless of the sign of the rayleigh number , provided that is smaller than the critical value associated with the appearance of rayleigh - bnard convection . boussinesq equations , light scattering , nonequilibrium fluctuations , rayleigh - bnard convection , shadowgraph experiments , swift - hohenberg equation 05.40 , 05.70.l , 44.25 , 47.20 , 78.35

starting from the linearized fluctuating boussinesq equations we derive an expression for the structure factor of fluids in stationary convection - free thermal nonequilibrium states , taking into account both gravity and finite - size effects . it is demonstrated how the combined effects of gravity and finite size causes the structure factor to go through a maximum value as a function of the wave number . the appearance of this maximum is associated with a crossover from a dependence for larger to a dependence for very small . the relevance of this theoretical result for the interpretation of light scattering and shadowgraph experiments is elucidated . the relationship with studies on various aspects of the problem by other investigators is discussed . the paper thus provides a unified treatment for dealing with fluctuations in fluid layers subjected to a stationary temperature gradient regardless of the sign of the rayleigh number , provided that is smaller than the critical value associated with the appearance of rayleigh - bnard convection . boussinesq equations , light scattering , nonequilibrium fluctuations , rayleigh - bnard convection , shadowgraph experiments , swift - hohenberg equation 05.40 , 05.70.l , 44.25 , 47.20 , 78.35

gr-qc0111028

i

following up the investigation of holonomy in the schwarzschild spacetime by rothman et al @xcite , maartens et al @xcite have extended the work in @xcite on closed circular trajectories to the kerr spacetime where the spacetime rotation further complicates matters by introducing new features . maartens et al @xcite study the parallel transport of a generic vector @xmath0 ( @xmath1 in their notation ) in the equatorial plane of the kerr spacetime along the orbit of the spacelike killing vector associated with the axial symmetry . assuming the standard boyer - lindquist form of the kerr metric with @xmath2 , the time coordinate @xmath3 parametrizes each orbit of the stationary symmetry killing vector field @xmath4 and the azimuthal coordinate @xmath5 parametrizes each orbit of the axial killing vector @xmath6 . the transport equations reduce to a single fundamental second - order ordinary differential equation for the @xmath5-derivative of the @xmath3-component of @xmath0 [ eq : mmm ] + f^2 z = 0 , z= , f^2= 1 - -- . [ eq : fundam ] recalling that @xmath7 is a constant along these orbits , this is trivially solved for @xmath8 , resulting in solutions characterized by a real or purely imaginary dimensionless frequency @xmath9 . the other components @xmath10 , @xmath11 and @xmath12 , and @xmath13 itself are then easily calculated . maartens et al @xcite discuss the holonomy question by studying the behavior of these solutions , which clearly depends on the sign of the frequency - squared function @xmath14 , with the roots of the quartic equation @xmath15 in @xmath7 distinguishing oscillatory and exponential solutions of the system . they show that @xmath16 has exactly one positive root @xmath17 ( called @xmath18 in the schwarzschild discussion of rothman et al @xcite ) , but find no obvious significance for this value . when @xmath19 , which occurs for @xmath20 , rational values of the real frequency @xmath9 lead to the transported vector @xmath0 returning to its original value after a certain number of loops . here we show that @xmath21 and its sign have a geometrical significance directly associated with clock effects @xcite and then extend the study to the closed geodesic circuits associated with these clock effects and also studied by rothman et al @xcite for the schwarzschild spacetime . the results hold for any stationary axisymmetric spacetime for which clock effects can be studied . this requires the existence of pairs of oppositely - rotating timelike circular geodesics which intersect periodically , forming a double helix in spacetime contained within a single @xmath3-@xmath5 symmetry group orbit . for a general family of stationary axisymmetric circularly - rotating observers , with an intermediate angular velocity between the two distinct angular velocities of such a pair of timelike circular geodesics within a given circular orbit cylinder , if the two oppositely - rotating geodesics ( as seen by these observers ) depart from a given observer world line simultaneously , then they will in general not return to that world line simultaneously . instead there will be a proper time difference in their arrival times as measured by the observer clock . this is the observer - dependent single - clock clock effect , where the observer both defines the complete closed circuit and measures the difference in arrival times for it , interpreted as the difference in the observer - measured orbital periods . the observer - dependent two - clock clock effect is instead the difference in proper times elapsed on the clocks carried by the geodesics themselves for the same observer - defined circuit . finally the observer - independent two - clock clock effect is the difference in proper times elapsed on the clocks carried by these geodesics between three successive meeting points ; this effect is equivalent to the observer - dependent two - clock clock effect for the ` geodesic meeting point observers ' ( gmpos ) when the latter are timelike . the trajectories with constant angular velocity which pass through every other meeting point of the pair of geodesics are the geodesic meeting point ( gmp ) trajectories . when these trajectories are timelike , they define the world lines of the gmpos @xcite . it turns out that the zero @xmath17 of the frequency - squared function @xmath21 corresponds to the radius @xmath22 of the observer horizon for these gmpos . each such observer sees the pair of corotating and counter - rotating geodesics which leave it simultaneously also return simultaneously , and thus sees vanishing single - clock clock effect . this observer family has a number of special geometrical and kinematical properties and is also useful ( by definition ) in the discussion of the observer - independent two - clock clock effect . outside the radius @xmath17 , these observers are able to ` resist ' the clock effect by counter - rotating sufficiently fast to synchronize the geodesic arrival times , but within this radius the rotation of the spacetime itself is too great to overcome . the gmp trajectories are well - defined whether the circular geodesics are timelike , null or spacelike ; it is convenient to define their direction using their unit tangent when the tangent is non - null . only when timelike can these gmp trajectories be interpreted as the congruence of world lines of a test observer family . the clock effect compares the spacetime arclength for different pairs of timelike paths between two spacetime points , each pair together forming a closed loop in spacetime . one can also compare parallel transport around such closed loops , investigating special elements of the holonomy group of the spacetime . this requires first solving the equations of parallel transport for a vector along a general circular orbit with constant angular velocity , which is done here . for comparison , the simpler case of closed @xmath5-coordinate curves is studied , followed by the loops formed by the two oppositely - rotating timelike geodesics . in the first case the geometry depends crucially on the gmpos , while in the latter case both the gmpos and the carter observers come into play . the geometry of circular orbits and of the circular geodesics which give rise to both of these observer families requires preliminary study . the extremely accelerated observers @xcite also appear in this discussion as the only observers which see the parallel transport geometry symmetrically for pairs of orbits with equal magnitude but oppositely - signed relative velocities like the circular geodesics themselves . the holonomy invariance found at a dense subset of special radii and particular loop numbers for @xmath5-coordinate loops and geodesic loops in the static case @xcite and for @xmath5-coordinate loops in the stationary case @xcite and referred to as a ` band ' structure is reduced to a set of radii at most of measure zero for closed geodesic loops in the nonstatic case . in the kerr spacetime the dimensionless frequencies associated with parallel transport rotations can be expressed as ratios of the proper and average coordinate periods of the circular geodesics . establishing these results is an elegant exercise in geometry . the process of discovering them , however , initially required a computer algebra system to jumpstart the investigation and to derive certain consequences which could then be confirmed by hand . the entire discussion is a further example of how various geometrically defined circularly orbiting observer families continue to play a key role in understanding the geometry of stationary axisymmetric spacetimes .

the band of holonomy invariance found for a dense subset of special geodesic orbits outside a certain radius in the static case does not exist in the nonstatic case . in the kerr spacetime the dimensionless frequencies associated with parallel transport rotations can be expressed as ratios of the proper and average coordinate periods of the circular geodesics .

stationary axisymmetric spacetimes containing a pair of oppositely - rotating periodically - intersecting circular geodesics allow the study of various so - called ` clock effects ' by comparing either observer or geodesic proper time periods of orbital circuits defined by the observer or the geodesic crossing points . this can be extended from a comparison of clocks to a comparison of parallel transported vectors , leading to the study of special elements of the spacetime holonomy group . the band of holonomy invariance found for a dense subset of special geodesic orbits outside a certain radius in the static case does not exist in the nonstatic case . in the kerr spacetime the dimensionless frequencies associated with parallel transport rotations can be expressed as ratios of the proper and average coordinate periods of the circular geodesics . june 28 , 2001 revised october 13 , 2001

1406.0442

i

superconductivity in transition metal oxides ( copper oxides or cuprates ) , pnictides ( iron arsenides ) , or chalcogenides ( fese , kfe@xmath0se@xmath0 ) have attracted increasing attention recently , not only because of the extraordinary high transition temperatures achieved in some systems , but also because of the proximity of those systems to long - range magnetic orders in form of antiferromagnetism ( cuprates)@xcite or spin density waves ( pnictides).@xcite as a consequence , `` unconventional '' pairing symmetries ( d - wave in cuprates , s@xmath1 in pnictides ) mediated by spin fluctuations have been proposed to explain the superconducting properties of these systems.@xcite the magnetic fluctuations play a significant role@xcite and evidence for a magnetic quantum critical point , hidden in the superconducting dome , was found in several pnictides.@xcite structurally , cuprates and pnictides have in common the layered structure with active superconducting layers ( cuo@xmath0 in cuprates and feas in pnictides ) separated by charge reservoir blocks . superconductivity commonly arises through charge doping from a nonsuperconducting parent compound which , in most cuprates and pnictides , exhibits magnetic order in the ground state . charge doping can be achieved by either varying the oxygen content ( in cuprates the oxygen content can be controlled by synthesis and annealing , in pnictides oxygen can be replaced by fluorine or hydrogen ) or by replacing cations with ions of different valency ( for example , sr for la in la@xmath0cuo@xmath2 or k for ba in bafe@xmath0as@xmath0 ) . however , there are exemptions from the rule . lifeas was found to be a stoichiometric self - doped superconductor which does not need additional doping.@xcite isovalent doping of phosphorous for arsenic@xcite as well as hydrostatic pressure@xcite have also been shown to induce superconductivity in the parent compounds of some pnictides . in view of the exciting superconducting properties of layered cuprates and pnictides as well as the wealth of interesting physical phenomena that originate from the strong correlations between magnetism and superconductivity , various attempts have been made to search for other layered transition metal oxides / pnictides where superconductivity could be established near magnetic or other instabilities . one of the compound families with interesting magnetic and electronic properties are the ti - based layered pnictide oxide systems of the general formula @xmath3ti@xmath4o , with @xmath3=na@xmath0 , ba , ( srf)@xmath0 , etc . and @xmath5=as , sb , bi . the first synthesis of na@xmath0ti@xmath0as@xmath0o and na@xmath0ti@xmath0sb@xmath0o by adam and schuster@xcite in 1990 revealed an interesting anti - k@xmath0nif@xmath2 structure , the existence of magnetic interactions in the ti@xmath0o layers resulting in a magnetic transition , but no indication of superconductivity was found.@xcite these materials are members of a broader pnictide oxide class of compounds the structure and properties of which have been discusses about two decades ago.@xcite the search for superconductivity in pnictide oxides was not successful until very recently where superconductivity was discovered in bati@xmath0sb@xmath0o and ba@xmath6na@xmath7ti@xmath0sb@xmath0o.@xcite the existence of a superconducting state in pnictide oxides at low temperatures is of particular interest since superconductivity is preceded by a density wave transition at about 50 k and the possible coexistence and mutual interaction of both orders has inspired more theoretical and experimental work . in the following sections we present a brief review of the state of the art of synthesis , structure , physical properties , and superconductivity research of ti - based pnictide oxide compounds .

superconductivity in a novel class of layered materials , ti - based pnictide oxides , was recently discovered . these compounds have attracted interest since they combine features of copper oxide and iron pnictide superconductors . here the transition metal ( titanium ) forms two - dimensional tio layers ( anti structure to the cuo planes ) , capped by pnictogen ions ( similar to feas layers ) . the pnictide oxide compounds show a spin or charge density wave phase which coexists with superconductivity in some members of the family . unlike the cuprates , but similar to iron pnictides , the parent compounds of pnictide oxides are metals with specific nesting properties of the fermi surface which leads to the density wave instability . the nature of the superconductivity , coexisting with the density wave order , and the possible competition or mutual interaction between both states is one of the central questions of recent studies . this short review summarizes the current knowledge from an experimental as well as theoretical point of view and discusses some of the open questions and possible future developments .

superconductivity in a novel class of layered materials , ti - based pnictide oxides , was recently discovered . these compounds have attracted interest since they combine features of copper oxide and iron pnictide superconductors . here the transition metal ( titanium ) forms two - dimensional tio layers ( anti structure to the cuo planes ) , capped by pnictogen ions ( similar to feas layers ) . the pnictide oxide compounds show a spin or charge density wave phase which coexists with superconductivity in some members of the family . unlike the cuprates , but similar to iron pnictides , the parent compounds of pnictide oxides are metals with specific nesting properties of the fermi surface which leads to the density wave instability . the nature of the superconductivity , coexisting with the density wave order , and the possible competition or mutual interaction between both states is one of the central questions of recent studies . this short review summarizes the current knowledge from an experimental as well as theoretical point of view and discusses some of the open questions and possible future developments .

1507.02308

i

data on the cosmic microwave background ( cmb ) from the planck satellite @xcite and other experiments are qualitatively consistent with generic expectations from cosmological inflation @xcite . in particular , they are consistent with the prototypical starobinsky model based an @xmath0 extension of minimal einstein gravity @xcite , and are constraining or excluding many other models . as discussed elsewhere in this volume , some still consider alternatives to inflation @xcite , but we are encouraged by the progressive and impressive improvement in experimental precision to explore specific planck - compatible models in more detail . as we discuss , detailed measurements of the cmb provide a window on fundamental physics that is complementary to laboratory experiments , casting light on particle physics at energies far beyond the reach of colliders and possibly giving us insight into string compactifications . run 1 of the lhc revealed the higgs boson @xcite , which is an existence proof for an apparently elementary scalar boson . as such , it may serve as a prototype for the inflaton , and it has been proposed that the higgs could even be the inflaton itself @xcite . this requires a rather large non - minimal gravitational coupling of the higgs field , and seems impossible unless the standard model of particle physics is supplemented , since naive extrapolation of the standard model leads to a negative higgs potential at high scales . at the time of writing the lhc has yet to reveal any new physics beyond the standard model , but there are many reasons to expect new physics , and we consider supersymmetry to be the best - motivated possibility @xcite . the appearance of the higgs boson with a mass @xmath3 gev @xcite sharpens the problem of the naturalness of the electroweak scale , which low - energy supersymmetry could mitigate . moreover , simple supersymmetric models actually predicted correctly the mass of the higgs boson @xcite , and also that its couplings would resemble those in the standard model @xcite - which they do , so far . these are new motivations for supersymmetry provided by run 1 of the lhc , in addition to the rles that supersymmetry could play in grand unified theories and string theory . it is therefore natural to consider supersymmetric models of inflation . supersymmetric versions of inflation were originally proposed in the context of a growing set of problems @xcite besetting the new inflationary theory @xcite based on the one - loop ( coleman - weinberg ) potential for breaking su(5 ) . for example , the vacuum tended to evolve to a minimum different from that containing the standard model @xcite , and quantum fluctuations destabilized the inflationary vacuum @xcite unless the higgs effective quartic self - coupling was small , @xmath4 , whereas its value was fixed by the su(5 ) gauge coupling to be @xmath5 . but the biggest problem for new inflation was the magnitude of density fluctuations @xcite . the new inflationary model based on su(5 ) predicted that they should be @xmath6 , whereas experimentally they are @xmath7 . several of these problems are tied to the magnitude of the effective quartic potential coupling , which must be tuned to @xmath8 to insure acceptable density fluctuations . indeed , in any model of inflation based on an elementary scalar field , its effective potential must have some parameter that is small in natural units where the reduced planck mass @xmath9 gev is set to unity . in a supersymmetric theory , such parameters are renormalized multiplicatively , so the quantum corrections to small values are under control . for this reason , it was suggested that inflation cries out for supersymmetry @xcite . in this framework the magnitude of the self - coupling could be linked to the ratio of supersymmetry breaking to the gut scale rather than to the gut gauge coupling alone @xcite . tension due to fine tuning and the duration of inflation could be further relieved if the inflationary field value were separated from the gut scale and pushed to the planck scale , the scenario of primordial inflation @xcite using a gauge singlet field @xcite that was baptized the inflaton @xcite . primordial supersymmetric inflation made it easy to render natural the fact that the magnitude of the observed scalar density perturbations is @xmath7 @xcite . however , it is clear that any discussion of early - universe cosmology , including inflation , should also incorporate gravity in an essential way , and hence be set in the framework of supergravity @xcite . in general , a simple supergravity theory is characterized by a hermitian function of the matter scalar fields @xmath10 , called the khler potential @xmath11 , that captures its geometry , a holomorphic function of the scalar fields , called the superpotential @xmath12 , that describes their interactions , and another holomorphic function @xmath13 that characterizes their couplings to gauge fields @xmath14 @xcite . in minimal @xmath15 supergravity , the khler metric is flat : k = ^i _ i^ * , where the sum is over all scalar components in the theory . the simplest inflationary theory in minimal supergravity is defined by the superpotential @xcite w = m^2 ( 1 - ) ^2 , [ hrrw ] where @xmath16 is the inflaton and @xmath17 in planck units . however , because inflation in this model is effectively driven by a cubic term in the scalar potential , it leads to a prediction for a scalar perturbation spectrum with tilt , @xmath18 , which is now in serious disagreement with the determination by planck @xcite : @xmath19 . moreover , a generic supergravity theory coupled to matter is not suitable for cosmology , because its effective scalar potential is proportial to @xmath20 , scalars typically pick up masses proportional to @xmath21 , where @xmath22 is the hubble parameter @xcite . though the theory defined by ( [ hrrw ] ) is constructed to avoid this @xmath23 problem , a generic inflationary model is in general plagued by this problem of large masses . in addition , the spontaneous breaking of local supersymmetry introduces additional challenges for constructing a successful supergravity inflationary scenario @xcite , stemming from the introduction of a chiral superfield whose scalar components have weak - scale masses but planck - scale vacuum expectation values ( vevs ) @xcite . the question then arises , which type of supergravity theory to choose for formulating models of inflation ? an attractive way to avoid the @xmath23 problem is provided @xcite by no - scale supergravity @xcite . in the minimal two - field case @xcite useful for inflation , its khler potential can be written in the logarithmic form @xmath24 where @xmath25 and @xmath16 are complex scalar fields and the @xmath26 represent possible additional matter fields problem may also be avoided in theories with a shift symmetry in which the khler potential is a function @xmath27 rather than @xmath28 @xcite . in this case the danergous term arising from @xmath20 does not depend on the combination @xmath29 , which may then be chosen as the inflaton . ] . moreover , no - scale supergravity emerges as the effective four - dimensional low - energy field theory in generic compactifications of string theory @xcite , with @xmath25 being identified as the compactification volume modulus . we therefore consider it to be the best - motivated framework for constructing field - theoretical models of inflation @xcite . a simple version of a no - scale inflationary model is defined by the superpotential @xmath30 @xcite . however , in this model too , inflation is effectively driven by a cubic term in the scalar potential , so that it yields the same prediction @xmath18 as in the minimal model @xcite . the planck 2013 data @xcite , with their confirmation of a tilt in the spectrum of scalar perturbations with @xmath1 and their strengthening of previous upper bounds on the tensor - to - scalar ratio @xmath31 triggered to re - examine no - scale inflation @xcite . as already mentioned , the planck data are highly consistent with the predictions of the starobinsky @xmath0 model @xcite . we were therefore very impressed to discover that the simplest possible wess - zumino superpotential @xcite @xmath32 in conjunction with the simplest no - scale khler potential ( [ nsk ] ) reproduced the starobinsky predictions for suitable choices of @xmath33 and @xmath34 @xcite . subsequently , many other examples of no - scale inflationary models yielding predictions compatible with the planck data have been discovered and studied @xcite . in parallel , the second data release from planck @xcite has sharpened the observational constraints on no - scale models of inflation , and interest in the observability of tensor perturbations in the cmb has been kindled by results from bicep2 @xcite and the prospects for other experiments searching for primordial @xmath35-mode polarization in the cmb . in this article we review these and other recent developments in no - scale inflation , with particular emphasis on the rle of planck data in motivating and constraining no - scale models @xcite . we also address the prospects for tying no - scale models of inflation more closely to string theory and particle physics at accessible collider energies .

no - scale inflation yields naturally predictions similar to those of the starobinsky model based on gravity , with a tilted spectrum of scalar perturbations : , and small values of the tensor - to - scalar perturbation ratio , as favoured by planck and other data on the cosmic microwave background ( cmb ) . detailed measurements of the cmb may provide insights into the embedding of inflation within string theory as well as its links to collider physics .

supersymmetry is the most natural framework for physics above the tev scale , and the corresponding framework for early - universe cosmology , including inflation , is supergravity . no - scale supergravity emerges from generic string compactifications and yields a non - negative potential , and is therefore a plausible framework for constructing models of inflation . no - scale inflation yields naturally predictions similar to those of the starobinsky model based on gravity , with a tilted spectrum of scalar perturbations : , and small values of the tensor - to - scalar perturbation ratio , as favoured by planck and other data on the cosmic microwave background ( cmb ) . detailed measurements of the cmb may provide insights into the embedding of inflation within string theory as well as its links to collider physics . july 2015 kcl - ph - th/2015 - 28 , lcts/2015 - 20 , cern - ph - th/2015 - 144 + act-05 - 15 , mi - th-1521 , umn - th-3442/15 , ftpi - minn-15/32

1507.02308

i

as we have reviewed in this article , no - scale supergravity is an attractive framework for constructing models of inflation , since supersymmetry accommodates naturally the required hierarchy between the scale of inflation and the planck scale @xcite , gravity must be incorporated in any discussion of cosmology , and no - scale supergravity @xcite emerges from generic string compactifications @xcite and yields an effective potential that is positive semi - definite @xcite . we have discussed various no - scale inflationary scenarios , reviewing how they naturally yield an effective potential , and hence predictions for @xmath122 and @xmath31 , that are coincident @xcite with the planck - friendly starobinsky model based on @xmath0 gravity @xcite . moreover , no - scale models achieve this in a technically natural way , via small superpotential couplings rather than surprisingly large non - minimal gravitational couplings as in the starobinsky and higgs inflation models . the no - scale framework is , moreover , more flexible , being able to accommodate models intermediate between the starobinsky model and a quadratic potential suitable for chaotic inflation @xcite , which could yield larger values of @xmath31 that are still compatible with the constraints from planck and other experiments . as in other supersymmetric models of inflation , it is necessary to take into account two - field effects : in the no - scale models we study @xcite , we find that these tend to reduce @xmath31 without generating large non - gaussianity . in principle , no - scale inflation could provide a phenomenological bridge between string theory and collider physics @xcite . in addition to the above - mentioned model - dependence of @xmath31 , the value of @xmath122 is related directly in starobinsky - like models to the number of e - folds during inflation @xcite , which is in turn sensitive to the rate of inflaton decay and thereby the assignment of the inflaton as a modulus or matter field . the pattern of soft supersymmetry breaking is also sensitive to this assignment , and would be measurable at the lhc or in other collider experiments . as we have mentioned , open issues in no - scale inflation include the mechanism for stabilization of the various moduli , including the volume modulus that plays a prominent rle in building models . the inflationary observables are sensitive to the mechanism of modulus stabilization , and therefore may be able to cast some light on this basic issue in string phenomenology . more generally , for the foreseeable future measurements of inflationary observables are likely to take us closer to the string scale than any other experiments , and no - scale inflationary models may be the best platform for exploiting this scientific opportunity .

supersymmetry is the most natural framework for physics above the tev scale , and the corresponding framework for early - universe cosmology , including inflation , is supergravity . no - scale supergravity emerges from generic string compactifications and yields a non - negative potential , and is therefore a plausible framework for constructing models of inflation .

supersymmetry is the most natural framework for physics above the tev scale , and the corresponding framework for early - universe cosmology , including inflation , is supergravity . no - scale supergravity emerges from generic string compactifications and yields a non - negative potential , and is therefore a plausible framework for constructing models of inflation . no - scale inflation yields naturally predictions similar to those of the starobinsky model based on gravity , with a tilted spectrum of scalar perturbations : , and small values of the tensor - to - scalar perturbation ratio , as favoured by planck and other data on the cosmic microwave background ( cmb ) . detailed measurements of the cmb may provide insights into the embedding of inflation within string theory as well as its links to collider physics . july 2015 kcl - ph - th/2015 - 28 , lcts/2015 - 20 , cern - ph - th/2015 - 144 + act-05 - 15 , mi - th-1521 , umn - th-3442/15 , ftpi - minn-15/32

0803.1924

i

the lyman @xmath1 emission line has attracted large attention as a spectral signature for identifying galaxies and securing redshifts at large distances . this emission line , however , is fraught with difficulty . because ly@xmath1 photons are resonantly scattered by neutral hydrogen , they may suffer more dust attenuation than adjacent uv continuum photons ; their escape is also affected by the relative geometries of neutral and ionized interstellar gas , and , last but not least , by the velocity structure of neutral gas . the first two factors have been extensively discussed in the light of iue observations of nearby star - forming galaxies @xcite ( and references therein ) and with model calculations @xcite ( and references therein ) . the crucial role of the velocity structure of neutral gas has been shown by the hst spectra of nearby star - forming galaxies @xcite . similar evidence was offered by the spectra of lyman break galaxies ( lbg ) @xcite . ly@xmath1 photons mainly escape when they are scattered off neutral gas that is offset in velocity from the bulk of the ionized regions . the complexity of the escape of ly@xmath1 emission is also well illustrated by the broad distribution of ly@xmath1 strengths and profile - types observed in the lbg spectroscopic sample of @xcite . the ly@xmath1 transmission mechanisms , especially the resulting emergent line profiles , have since been investigated in increasingly realistic models ( e.g. ) @xcite . an extensive review of all the aspects of the observations of the ly@xmath1 emission line in galaxies has been recently given by @xcite . the complex nature of ly@xmath1 escape was advocated for the disappointing results of earlier searches of distant ly@xmath1 emitters ( e.g. ) @xcite . nonetheless , the ly@xmath1 emission remains the only mean for identifying galaxies when the continuum becomes too faint to be detected , and , following @xcite and @xcite , increasingly deeper and larger surveys have come into a widespread use for detecting galaxies at high redshifts . beyond the redshift of @xmath3 , the increasingly neutral igm is not a complete obstacle to the visibility of ly@xmath1 emission ( e.g. ) @xcite and the density evolution of ly@xmath1 emitters may even help to trace the history of the cosmic re - ionization ( e.g. ) @xcite . although nearby galaxies have played a key role for understanding the factors affecting ly@xmath1 escape , their observations , using space - borne uv spectrographs in pointing mode , were directed to specific and known objects . as a consequence , there is not yet a systematic survey for redshifts smaller than those reachable from the ground . we use here the _ galex _ spectroscopic survey mode for the first systematic search of ly@xmath1 emitting galaxies at low redshift . goals are to understand ( i ) whether the ly@xmath1 escape is related to specific properties of galaxies , ( ii ) whether the ly@xmath1 emission evolves from current epoch to high z as the cosmic star formation rate traced by balmer lines or the uv continuum of galaxies . if so , the average relationship between the massive stellar content of the galaxies and the ly@xmath1 emission would be constant over time ; the ly@xmath1 emission might be used as a tracer of star formation , with an empirical calibration encapsulating the average effects of resonant scattering . if not , there would be an evidence for cosmic evolution of the physical processes , especially galactic winds , expected to play a central role in the ly@xmath1 escape from galaxies .

the _ galex ( galaxy evolution explorer ) _ spectroscopic survey mode , with a resolution of 8 in the fuv ( 1350 - 1750 ) and 20 in the nuv ( 1950 - 2750 ) is used for a systematic search of ly emitting galaxies at low redshift .

the _ galex ( galaxy evolution explorer ) _ spectroscopic survey mode , with a resolution of 8 in the fuv ( 1350 - 1750 ) and 20 in the nuv ( 1950 - 2750 ) is used for a systematic search of ly emitting galaxies at low redshift . this aims at filling a gap between high - redshift surveys and a small set of objects studied in detail in the nearby universe . a blind search of 7018 spectra extracted in 5 deep exposures ( 5.65 sq.deg ) has resulted in 96 ly emitting galaxy candidates in the fuv domain , after accounting for broad - line agns . the ly ews ( equivalent width ) are consistent with stellar population model predictions and show no trends as a function of uv color or uv luminosity , except a possible decrease in the most luminous that may be due to small - number statistics . their distribution in ew is similar to that at z 3 but their fraction among star - forming galaxies is smaller . avoiding uncertain candidates , a sub - sample of 66 objects in the range has been used to build a ly lf ( luminosity function ) . the incompleteness due to objects with significant ly emission but a uv continuum too low for spectral extraction has been evaluated . a comparison with h lf in the same redshift domain is consistent with an average ly/h of 1 in about 15 % of the star - forming galaxies . a comparison with high - redshift ly lfs implies an increase of the ly luminosity density by a factor of about 16 from z 0.3 to z 3 . by comparison with the factor 5 increase of the uv luminosity density in the same redshift range , this suggests an increase of the average ly escape fraction with redshift .

0803.1924

c

a blind search of potential ly@xmath1 emission features has been conducted on 7018 spectra obtained in 5 deep spectroscopic exposures with _ galex_. 96 ly@xmath1 emitting galaxy candidates are identified , after a separation from agns essentially on the basis of the fwhm . they are mostly in the reshift range ( 0.2 @xmath22 0.35 ) . the following properties stand out : \1 ) the ly@xmath1 rest frame equivalent width distribution is comparable with that reported by @xcite for lbgs at @xmath63 . the fraction of galaxies with ly@xmath1 emission ( ew @xmath16 ) seems smaller , 15% against 25% in the lbg sample . \2 ) no trend is found between the ew and the ( fuv @xmath22 nuv ) color , in agreement with a decoupling of the reddening of line and continuum photons in ly@xmath1 resonant scattering . there is no trend either of the ew with the uv luminosity , except a decrease in a sub - sample of ultra - violet luminous galaxies ( uvlgs ) . as at very high - redshifts , small - number statistics might play a role here . a larger fraction of ly@xmath1 emitting galaxies ( ew @xmath64 ) is found among uvlgs . \3 ) a sub - sample of 66 emission features of better quality and strictly in the reshift range ( 0.2 @xmath22 0.35 ) has been used to calculate the space densities of the ly@xmath1 emitting galaxies . a scheme has been presented to correct for a major source of incompleteness , the fact that spectra of objects with significant ew may have not been extracted because their continuum is too weak . \5 ) a comparison of the ly@xmath1 luminosity functions at @xmath65 and @xmath12 shows an evolution beyond that expected from the evolution of the massive stellar content of star - forming galaxies at a significance level of 84% , suggesting a increase of the average ly@xmath1 escape fraction with redshift . _ galex ( galaxy evolution explorer ) _ is a nasa small explorer , launched in april 2003 . we gratefully acknowledge nasa s support for construction , operation , and science analysis for the _ galex _ mission , developed in cooperation with the centre national detudes spatiales of france and the korean ministry of science and technology . this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . ahn , s .- h . , lee , h .- w . , & lee , h. m. 2001 , apj , 554 , 604 ahn , s .- h . , lee , h .- w . , & lee , h. m. 2002 , apj , 567 , 922 ahn , s .- h . , lee , h .- w . , & lee , h. m. 2003 , mnras , 340 , 863 ajiki , m. , mobasher , b. , taniguchi , y. et al . , 2006 , apj , 638 , 596 ando , m. , ohta , k. , iwata , i. et al . , 2004 , apj , 610 , 635 ando , m. , ohta , k. , iwata , i. et al . , 2006 , apj , 645 , 19 arnouts , s. , schiminovich , d. , ilbert , o. et al . , 2005 , apj , 619 , l43 charlot , s. , & fall , s. m. 1993 , apj , 415 , 580 djorgovski , s. , & thompson , d. j. 1992 , in the stellar populations of galaxies , iau symp . b. barbuy & a. renzini , p 337 finkelstein , s. l. , rhoads , j. e. , malhotra , s. , pirzkal , n. , & wang , j. 2007 , apj , 660 , 1023 hopkins , a. m. 2004 , apj , 615 , 209 hopkins , a. m. , & beacom , j. f. 2006 , apj , 651 , 142 hu , e. m. , cowie , l. l. , & mcmahon , r. g. 1998 , apj , 502 , 99 kashikawa , n. , shimasaku , k. , malkan , m. a. et al . 2006 , apj , 648 , 7 kauffmann , g. , heckman , t. m. , tremonti , c. et al . 2003 , mnras , 346 , 1055 kennicutt , r. c. 1998 , ara&a , 36 , 189 kobayashi , m. a. r. , totani , t. , & nagashima , m. 2007 , apj , 670 , 919 pettini , m. , steidel , c. c. , adelberger , k. l. , dickinson , m. , & giavalisco , m. , 2000 , apj , 528 , 96 reddy , n. a. , steidel , c. c. , pettini , m. et al . 2007 , astro - ph/07064091 ryan , r. e. , hathi , n. p. , cohen , s. h. et al . 2007 , apj , 668 , 839 schaerer , d. 2007 , iac winterschool , lecture on primeval galaxies , astro - ph/0706.0139 schaerer , d. & verhamme , a. 2008 , astro - ph/0801.1187 schiminovich , d. , ilbert , o. , arnouts , s. et al . , 2005 , apj , 619 , l47 shapley , a. e. , steidel , c. c. , pettini , m. , & adelberger , k. l. 2003 , apj , 588 , 65 shectman , s. a. , landy , s. d. , oemler , a. et al . , 1996 , apj , 470 , 172 shimasaku , k. , kashikawa , n. , doi , m. et al . 2006 , pasj , 58 , 313 stanway , e. r. , bunker , a. j. , glazebrook , k. et al . 2007 , mnras , 376 , 727 way , m. j. , quintana , h. , infante , d. g. et al . , 2005 , aj , 130 , 2012 weiner , b. j. , phillips , a. c. , faber , s. m. et al . , 2006 , apj , 620 , 595 wyder , t. k. , martin , d. c. , schiminovich , d. et al . , 2007 , apjs , 173 , 293 wolf , c. , meisenheimer , k. , kleinheinrich , m. et al . , 2004 , a&a , 421 , 913 & cdfs-00 & elaiss1 - 00 & groth-00 & ngpdws-00 & sirtffl-00 + exposure time ( s ) & 149315 & 84086 & 281713 & 139598 & 79616 + center of field ra & 53.128 & 9.638 & 214.992 & 219.156 & 259.124 + center of field dec & -27.871 & -43.990 & 52.782 & 35.171 & 59.909 + identified sources & 38697 & 30129 & 43545 & 40619 & 28306 + extracted spectra & 1419 & 925 & 2028 & 1202 & 1444 + emission features & 22 & 9 & 39 & 19 & 7 + used for the lf & 15 & 5 & 29 & 11 & 6 + cdfs & 1348 & 53.2405 & -28.3883 & 43.4 & 1 & 5.43 & 21.35 & 0.615 & 0.217 & 41.87 & + cdfs & 1821 & 53.2585 & -28.3577 & 24.6 & 1 & 3.37 & 21.30 & 0.303 & 0.251 & 41.81 & + cdfs & 2422 & 52.8947 & -28.3395 & 14.4 & 2 & 4.79 & 20.54 & 0.488 & 0.176 & 41.63 & 0.1728(1 ) + cdfs & 3801 & 52.7375 & -28.2794 & 29.7 & 1 & 3.62 & 21.55 & 0.528 & 0.285 & 41.97 & + cdfs & 4927 & 52.9765 & -28.2386 & 102 . & 1 & 8.12 & 21.89 & 0.450 & 0.283 & 42.31 & + cdfs & 5007 & 53.5412 & -28.2554 & 97.7 & 2 & 3.14 & 22.74 & 1.283 & 0.344 & 42.09 & + cdfs & 5448 & 53.0780 & -28.2224 & 149 . & 1 & 11.4 & 21.42 & 0.312 & 0.283 & 42.46 & + cdfs & 6523 & 53.0616 & -28.1865 & 47.4 & 1 & 3.48 & 21.70 & 0.551 & 0.264 & 41.87 & + cdfs & 6535 & 52.9622 & -28.1890 & 34.8 & 1 & 5.16 & 21.01 & 0.386 & 0.216 & 41.85 & + cdfs & 6617 & 53.1743 & -28.1903 & 50.9 & 1 & 17.2 & 20.19 & -0.037 & 0.208 & 42.33 & + cdfs & 7100 & 52.9993 & -28.1644 & 29.1 & 1 & 2.96 & 21.42 & 0.282 & 0.239 & 41.71 & + cdfs & 10526 & 53.5868 & -28.0657 & 24.3 & 1 & 1.75 & 22.11 & 0.940 & 0.361 & 41.89 & + cdfs & 10937 & 53.7850 & -28.0454 & 63.0 & 1 & 5.89 & 21.41 & 0.423 & 0.346 & 42.37 & + cdfs & 11518 & 53.0498 & -28.0250 & 57.7 & 1 & 5.50 & 21.72 & 0.249 & 0.218 & 41.89 & 0.212(2 ) + cdfs & 16104 & 53.2360 & -27.8879 & 23.2 & 2 & 4.35 & 21.14 & 0.544 & 0.374 & 42.32 & 0.365(3 ) + cdfs & 17033 & 52.7601 & -27.8584 & 38.1 & 3 & 3.57 & 21.96 & 0.494 & 0.340 & 42.14 & + cdfs & 18142 & 52.8861 & -27.8344 & 24.4 & 2 & 4.63 & 21.04 & 0.052 & 0.183 & 41.64 & 0.133(2 ) + cdfs & 19355 & 53.7296 & -27.8008 & 28.7 & 1 & 7.49 & 20.56 & 0.783 & 0.314 & 42.38 & + cdfs & 21667 & 53.2803 & -27.7424 & 11.8 & 2 & 2.50 & 20.77 & 0.506 & 0.219 & 41.55 & 0.216(4 ) + cdfs & 21739 & 53.7113 & -27.7293 & 34.8 & 1 & 4.05 & 21.56 & 0.731 & 0.323 & 42.14 & + cdfs & 30899 & 53.3592 & -27.4543 & 78.6 & 1 & 7.29 & 21.63 & 0.502 & 0.352 & 42.48 & + cdfs & 33311 & 53.1045 & -27.2904 & 58.0 & 1 & 8.65 & 21.43 & 0.271 & 0.391 & 42.66 & + elaiss1 & 13715 & 9.6383 & -44.0090 & 21.9 & 3 & 2.93 & 21.64 & 1.308 & 0.213 & 41.59 & + elaiss1 & 16998 & 9.5205 & -43.8745 & 56.9 & 1 & 8.16 & 21.11 & 0.508 & 0.223 & 42.08 & + elaiss1 & 6587 & 9.5590 & -44.2436 & 102 . & 1 & 17.9 & 21.14 & -0.107 & 0.272 & 42.62 & + elaiss1 & 8180 & 9.8839 & -44.1917 & 38.2 & 2 & 10.1 & 20.34 & 0.881 & 0.188 & 42.01 & 0.1862(5 ) + elaiss1 & 21062 & 9.6663 & -43.7225 & 12.5 & 2 & 2.81 & 21.13 & 0.204 & 0.211 & 41.56 & + elaiss1 & 23257 & 9.4752 & -43.6410 & 32.7 & 3 & 5.17 & 21.34 & 0.512 & 0.294 & 42.15 & + elaiss1 & 23425 & 9.3711 & -43.6356 & 21.1 & 2 & 6.49 & 20.87 & 0.387 & 0.300 & 42.27 & + elaiss1 & 16921 & 10.2733 & -43.8748 & 20.3 & 3 & 4.14 & 21.53 & 0.929 & 0.312 & 42.12 & + elaiss1 & 2386 & 10.0078 & -44.4288 & 32.8 & 2 & 2.81 & 21.94 & 0.732 & 0.268 & 41.80 & + groth & 6834 & 215.6564 & 52.4520 & 11.1 & 2 & 2.01 & 21.26 & 0.466 & 0.197 & 41.35 & + groth & 32462 & 215.1704 & 53.1138 & 20.8 & 2 & 1.61 & 21.49 & 0.442 & 0.202 & 41.28 & 0.2004(6 ) + groth & 36896 & 214.9730 & 53.3764 & 29.4 & 1 & 3.29 & 21.14 & 0.373 & 0.199 & 41.57 & + groth & 7430 & 214.4311 & 52.4683 & 104.6 & 1 & 7.67 & 21.80 & -0.101 & 0.211 & 42.00 & 0.2092(7 ) + groth & 5087 & 214.5594 & 52.3956 & 44.6 & 3 & 1.23 & 22.61 & 0.746 & 0.215 & 41.22 & + groth & 34512 & 214.2955 & 53.1980 & 70.2 & 1 & 5.44 & 21.29 & 2.580 & 0.215 & 41.87 & 0.2139(6 ) + groth & 8885 & 215.6107 & 52.5075 & 42.4 & 2 & 2.45 & 21.94 & 0.379 & 0.221 & 41.55 & + groth & 2368 & 214.5933 & 52.3067 & 54.2 & 2 & 1.89 & 22.35 & 0.655 & 0.242 & 41.52 & + groth & 18322 & 214.5216 & 52.7522 & 25.8 & 2 & 2.78 & 21.63 & 0.335 & 0.247 & 41.71 & 0.24438(8 ) + groth & 2682 & 214.7013 & 52.2986 & 19.3 & 3 & 1.52 & 22.03 & 0.370 & 0.244 & 41.44 & + groth & 5715 & 214.2262 & 52.4111 & 27.7 & 1 & 3.59 & 21.51 & 0.507 & 0.250 & 41.83 & 0.24678(8 ) + groth & 19002 & 214.4387 & 52.7719 & 59.9 & 1 & 2.94 & 22.09 & 0.265 & 0.248 & 41.74 & 0.24419(8 ) + groth & 17005 & 215.1805 & 52.7188 & 26.0 & 2 & 2.87 & 21.59 & 0.304 & 0.252 & 41.74 & + groth & 4719 & 214.8114 & 52.3908 & 25.3 & 3 & 1.42 & 22.16 & 0.394 & 0.257 & 41.46 & + groth & 20285 & 215.1330 & 52.7994 & 30.9 & 1 & 4.11 & 21.13 & 0.401 & 0.256 & 41.92 & + groth & 21404 & 215.1861 & 52.8351 & 25.3 & 1 & 2.53 & 21.64 & 0.290 & 0.256 & 41.70 & + groth & 12279 & 214.3008 & 52.5991 & 19.6 & 2 & 2.08 & 21.76 & 0.527 & 0.264 & 41.65 & 0.26113(8 ) + groth & 14069 & 215.3526 & 52.6555 & 29.0 & 2 & 1.80 & 22.28 & 0.463 & 0.260 & 41.57 & + groth & 21024 & 214.7318 & 52.8245 & 41.0 & 2 & 2.01 & 21.13 & -0.026 & 0.269 & 41.65 & 0.2633(6 ) + groth & 36336 & 214.5818 & 53.3393 & 40.3 & 3 & 2.24 & 22.29 & 1.265 & 0.268 & 41.70 & + groth & 37457 & 214.7951 & 53.2660 & 90.7 & 1 & 4.38 & 21.90 & 0.925 & 0.266 & 41.98 & + groth & 3488 & 214.9704 & 52.3502 & 40.4 & 2 & 2.52 & 21.83 & 0.541 & 0.269 & 41.75 & + groth & 37380 & 215.1904 & 53.3248 & 26.1 & 2 & 1.93 & 21.70 & 0.472 & 0.269 & 41.64 & + groth & 3525 & 214.7796 & 52.3522 & 55.2 & 2 & 2.41 & 22.15 & 0.766 & 0.271 & 41.74 & + groth & 29573 & 214.8762 & 53.0349 & 23.9 & 3 & 1.32 & 22.05 & 0.586 & 0.271 & 41.48 & + groth & 31403 & 214.2910 & 53.0867 & 33.5 & 1 & 2.25 & 21.86 & 0.570 & 0.270 & 41.71 & + groth & 33559 & 214.9025 & 53.1601 & 23.0 & 2 & 1.77 & 22.02 & 0.377 & 0.273 & 41.61 & + groth & 17867 & 215.8429 & 52.7425 & 22.0 & 3 & 1.21 & 22.36 & 0.621 & 0.282 & 41.48 & + groth & 17525 & 215.8241 & 52.7135 & 31.9 & 3 & 2.62 & 21.77 & 0.756 & 0.283 & 41.82 & + groth & 9045 & 214.9070 & 52.5070 & 24.5 & 2 & 1.86 & 21.75 & 0.475 & 0.286 & 41.68 & + groth & 15686 & 215.9047 & 52.6719 & 26.6 & 2 & 2.21 & 21.73 & 0.461 & 0.287 & 41.76 & + groth & 13305 & 215.8867 & 52.6237 & 24.6 & 3 & 1.70 & 21.96 & 0.471 & 0.286 & 41.64 & + groth & 21579 & 214.2081 & 52.8388 & 31.1 & 2 & 1.71 & 21.99 & 0.501 & 0.287 & 41.65 & + groth & 28751 & 214.7328 & 52.9926 & 42.5 & 1 & 2.92 & 21.88 & 0.509 & 0.290 & 41.89 & + groth & 23096 & 215.5339 & 52.8738 & 70.4 & 1 & 3.80 & 22.52 & 1.220 & 0.307 & 42.06 & + groth & 29558 & 214.0695 & 53.0259 & 65.7 & 2 & 2.58 & 22.18 & 1.077 & 0.329 & 41.96 & + groth & 19364 & 215.7761 & 52.7797 & 45.3 & 1 & 2.67 & 22.01 & 0.681 & 0.347 & 42.04 & + groth & 5549 & 215.4769 & 52.4065 & 28.3 & 2 & 4.24 & 21.22 & 0.832 & 0.350 & 42.24 & + groth & 10182 & 214.3223 & 52.5384 & 55.7 & 3 & 4.89 & 21.85 & 0.354 & 0.461 & 42.59 & + ngpdws & 28760 & 219.1979 & 35.4351 & 115.0 & 1 & 20.66 & 20.93 & 0.061 & 0.180 & 42.27 & + ngpdws & 23216 & 218.6954 & 35.2844 & 34.0 & 1 & 4.09 & 21.42 & 0.543 & 0.192 & 41.63 & + ngpdws & 32840 & 219.2433 & 35.5977 & 20.9 & 2 & 2.32 & 21.46 & 0.771 & 0.209 & 41.47 & + ngpdws & 11927 & 219.1004 & 34.9935 & 48.9 & 1 & 4.34 & 21.57 & 0.267 & 0.216 & 41.77 & + ngpdws & 19918 & 219.1990 & 35.1757 & 26.2 & 3 & 3.74 & 21.13 & 0.711 & 0.253 & 41.86 & + ngpdws & 23690 & 219.8446 & 35.3075 & 41.2 & 1 & 5.88 & 21.12 & 0.150 & 0.250 & 42.05 & + ngpdws & 28521 & 219.0262 & 35.4586 & 23.9 & 1 & 4.05 & 21.57 & 0.189 & 0.253 & 41.90 & + ngpdws & 35813 & 219.0558 & 35.7291 & 30.4 & 2 & 3.70 & 21.47 & 0.084 & 0.263 & 41.90 & + ngpdws & 33782 & 219.5770 & 35.6305 & 78.2 & 1 & 6.05 & 21.63 & 0.521 & 0.264 & 42.11 & + ngpdws & 10002 & 219.0922 & 34.9421 & 30.8 & 1 & 4.33 & 21.47 & 0.312 & 0.272 & 42.00 & + ngpdws & 6731 & 219.1529 & 34.8428 & 51.7 & 1 & 10.10 & 21.15 & 0.496 & 0.283 & 42.41 & + ngpdws & 2111 & 219.3562 & 34.6855 & 35.3 & 1 & 3.67 & 21.64 & 0.641 & 0.292 & 42.00 & + ngpdws & 30997 & 218.7306 & 35.5246 & 19.4 & 2 & 3.13 & 21.11 & 0.523 & 0.320 & 42.02 & + ngpdws & 1133 & 219.1333 & 34.6415 & 153.0 & 3 & 4.86 & 22.46 & 1.074 & 0.358 & 42.33 & + ngpdws & 27558 & 219.1931 & 35.4176 & 117.0 & 3 & 6.02 & 22.20 & 0.993 & 0.372 & 42.46 & + ngpdws & 10713 & 219.7463 & 34.9603 & 69.3 & 3 & 5.16 & 21.94 & 0.647 & 0.374 & 42.40 & + ngpdws & 6321 & 219.7806 & 34.8359 & 77.2 & 3 & 7.43 & 22.32 & 0.944 & 0.374 & 42.55 & + ngpdws & 35880 & 219.2820 & 35.6919 & 161.0 & 3 & 4.69 & 22.79 & 1.859 & 0.468 & 42.58 & + ngpdws & 4226 & 219.3340 & 34.7577 & 56.0 & 1 & 6.49 & 21.53 & 0.350 & 0.328 & 42.36 & + sirtffl & 14450 & 259.2110 & 59.9642 & 41.8 & 1 & 22.19 & 19.77 & 0.133 & 0.185 & 42.33 & + sirtffl & 14297 & 258.6840 & 59.9474 & 28.4 & 2 & 2.52 & 21.62 & 0.494 & 0.219 & 41.55 & + sirtffl & 14085 & 258.1492 & 59.9468 & 15.8 & 2 & 2.87 & 20.99 & 0.624 & 0.225 & 41.63 & + sirtffl & 10895 & 258.5918 & 59.8333 & 49.5 & 1 & 6.18 & 21.28 & 0.192 & 0.233 & 42.00 & + sirtffl & 958 & 258.8205 & 59.3897 & 30.2 & 2 & 3.45 & 21.03 & 0.547 & 0.235 & 41.76 & + sirtffl & 4246 & 259.8606 & 59.5599 & 49.9 & 2 & 3.58 & 21.57 & 0.556 & 0.237 & 41.78 & + sirtffl & 2856 & 259.3800 & 59.4875 & 33.6 & 2 & 4.72 & 20.94 & 0.610 & 0.302 & 42.14 & +

this aims at filling a gap between high - redshift surveys and a small set of objects studied in detail in the nearby universe . a blind search of 7018 spectra extracted in 5 deep exposures ( 5.65 sq.deg ) a sub - sample of 66 objects in the range has been used to build a ly lf ( luminosity function ) .

the _ galex ( galaxy evolution explorer ) _ spectroscopic survey mode , with a resolution of 8 in the fuv ( 1350 - 1750 ) and 20 in the nuv ( 1950 - 2750 ) is used for a systematic search of ly emitting galaxies at low redshift . this aims at filling a gap between high - redshift surveys and a small set of objects studied in detail in the nearby universe . a blind search of 7018 spectra extracted in 5 deep exposures ( 5.65 sq.deg ) has resulted in 96 ly emitting galaxy candidates in the fuv domain , after accounting for broad - line agns . the ly ews ( equivalent width ) are consistent with stellar population model predictions and show no trends as a function of uv color or uv luminosity , except a possible decrease in the most luminous that may be due to small - number statistics . their distribution in ew is similar to that at z 3 but their fraction among star - forming galaxies is smaller . avoiding uncertain candidates , a sub - sample of 66 objects in the range has been used to build a ly lf ( luminosity function ) . the incompleteness due to objects with significant ly emission but a uv continuum too low for spectral extraction has been evaluated . a comparison with h lf in the same redshift domain is consistent with an average ly/h of 1 in about 15 % of the star - forming galaxies . a comparison with high - redshift ly lfs implies an increase of the ly luminosity density by a factor of about 16 from z 0.3 to z 3 . by comparison with the factor 5 increase of the uv luminosity density in the same redshift range , this suggests an increase of the average ly escape fraction with redshift .

1303.2071

i

the _ sp theory of intelligence _ aims to simplify and integrate ideas in artificial intelligence , mainstream computing , and human perception and cognition , with information compression as a unifying theme . the theory is described in several peer - reviewed articles , and links from there . ] and most fully in @xcite . the main purpose of this article is to describe how the sp theory may be applied to the understanding of natural vision and the development of computer vision , and to discuss associated issues . both of those themes natural vision and artificial vision are discussed together throughout the article , since each one may illuminate the other . in broad terms , the potential benefits of the sp theory in those two areas are the simplification and integration of concepts , deeper insights , better performance ( of artificial systems ) , and the seamless integration of vision with other sensory modalities , and with other aspects of intelligence such as reasoning , planning , problem solving , and unsupervised learning . what is perhaps the main attraction of the theory is the potential for one relatively simple framework to accommodate several different aspects of intelligence , including vision . as a preliminary , the next section describes the theory in outline , with associated ideas .

the _ sp theory of intelligence _ aims to simplify and integrate concepts in computing and cognition , with information compression as a unifying theme . this article discusses how it may be applied to the understanding of natural vision and the development of computer vision . a strength of the sp theory is that it provides for the integration of vision with other sensory modalities and with other aspects of intelligence .

the _ sp theory of intelligence _ aims to simplify and integrate concepts in computing and cognition , with information compression as a unifying theme . this article discusses how it may be applied to the understanding of natural vision and the development of computer vision . the theory , which is described quite fully elsewhere , is described here in outline but with enough detail to ensure that the rest of the article makes sense . low level perceptual features such as edges or corners may be identified by the extraction of redundancy in uniform areas in a manner that is comparable with the run - length encoding technique for information compression . the concept of _ multiple alignment _ in the sp theory may be applied to the recognition of objects , and to scene analysis , with a hierarchy of parts and sub - parts , and at multiple levels of abstraction . the theory has potential for the unsupervised learning of visual objects and classes of objects , and suggests how coherent concepts may be derived from fragments . as in natural vision , both recognition and learning in the sp system is robust in the face of errors of omission , commission and substitution . the theory suggests how , via vision , we may piece together a knowledge of the three - dimensional structure of objects and of our environment , it provides an account of how we may see things that are not objectively present in an image , and how we recognise something despite variations in the size of its retinal image . and it has things to say about the phenomena of lightness constancy and colour constancy , the role of context in recognition , and ambiguities in visual perception . a strength of the sp theory is that it provides for the integration of vision with other sensory modalities and with other aspects of intelligence . _ keywords _ : vision , information compression , artificial intelligence , perception , cognition , representation of knowledge , learning , pattern recognition , natural language processing , reasoning , planning , problem solving .

1303.2071

c

despite some limitations in how the sp theory is currently realised in computer models , it has what i believe are some useful things to say about several aspects of vision : * low level perceptual features such as edges or corners may be identified by the extraction of redundancy in uniform areas in a manner that is analogous to the run - length encoding technique for information compression , and comparable with the effect of lateral inhibition in the visual systems of animals . * the concept of _ multiple alignment _ in the sp theory may be applied to the recognition of objects , and to scene analysis , with a hierarchy of parts and sub - parts , and at multiple levels of abstraction . * the theory has potential for the unsupervised learning of visual objects and classes of objects , and suggests how coherent concepts may be derived from fragments . it provides an account of how we may discover objects via stereo matching and via motion . * as in natural vision , both recognition and learning in the sp system is robust in the face of errors of omission , commission and substitution . * the theory suggests how , via vision , we may piece together a knowledge of the three - dimensional structure of objects and of our environment that is good enough for many practical purposes , despite ambiguities in geometry . * the theory provides an account of how we may see things that are not objectively present in an image , and how we may recognise something despite variations in the size of its retinal image . * the theory has things to say about the phenomena of lightness constancy and colour constancy , about the role of context in recognition , and about ambiguities in visual perception . a strength of the sp theory is that it is not simply a theory of vision . it provides for the integration of vision with other sensory modalities and with other aspects of intelligence such as reasoning , planning , and problem solving . h. b. barlow . sensory mechanisms , the reduction of redundancy , and intelligence . in hmso , editor , _ the mechanisation of thought processes _ , pages 535559 . her majesty s stationery office , london , 1959 . c. farabet , c. couprie , l. najman , and y. lecun . scene parsing with multiscale feature learning , purity trees , and optimal covers . in _ proceedings of the 29th international conference on machine learning , edinburgh , scotland , uk , 2012 _ , 2012 . w. l. gehringer and e. engel . effect of ecological viewing conditions on the ames distorted room illusion . _ journal of experimental psychology : human perception and performance _ , 120 ( 2):0 181185 , 1986 . a. glennerster , s. j. gilson , l. tcheang , and a. j. parker . perception of size in a ` dynamic ames room ' . _ journal of experimental psychology : human perception and performance _ , 30 ( 9):0 490a , 2003 . doi : 10.1167/3.9.490 . bottom - up / top - down image parsing by attribute graph grammar . in _ proceedings of the tenth ieee international conference on computer vision ( iccv 2005 ) , 17 - 21 oct . 2005 _ , volume 2 , pages 17781785 , 2005 . d. marr . _ vision : a computational investigation into the human representation and processing of visual information_. the mit press , london , england , 2010 . this book was originally published in 1982 by w. h. freeman and company . m. j. tarr . rotating objects to recognize them : a case study of the role of viewpoint dependency in the recognition of three - dimensional objects . _ psychonomic bulletin and review _ , 20 ( 1):0 5582 , 1995 . j. g. wolff . learning syntax and meanings through optimization and distributional analysis . in y. levy , i. m. schlesinger , and m. d. s. braine , editors , _ categories and processes in language acquisition _ , pages 179215 . lawrence erlbaum , hillsdale , nj , 1988 . see : http://bit.ly/zigjyc[bit.ly/zigjyc ] . j. g. wolff . _ unifying computing and cognition : the sp theory and its applications_. cognitionresearch.org , menai bridge , 2006 . isbns : 0 - 9550726 - 0 - 3 ( ebook edition ) , 0 - 9550726 - 1 - 1 ( print edition ) . distributors , including amazon.com , are detailed on http://bit.ly/wmb1rs[bit.ly/wmb1rs ] . the publisher and its website was previously cognitionresearch.org.uk .

low level perceptual features such as edges or corners may be identified by the extraction of redundancy in uniform areas in a manner that is comparable with the run - length encoding technique for information compression . the concept of _ multiple alignment _ in the sp theory may be applied to the recognition of objects , and to scene analysis , with a hierarchy of parts and sub - parts , and at multiple levels of abstraction . the theory has potential for the unsupervised learning of visual objects and classes of objects , and suggests how coherent concepts may be derived from fragments . as in natural vision , both recognition and learning in the sp system is robust in the face of errors of omission , commission and substitution . the theory suggests how , via vision , we may piece together a knowledge of the three - dimensional structure of objects and of our environment , it provides an account of how we may see things that are not objectively present in an image , and how we recognise something despite variations in the size of its retinal image . and it has things to say about the phenomena of lightness constancy and colour constancy , the role of context in recognition , and ambiguities in visual perception .

the _ sp theory of intelligence _ aims to simplify and integrate concepts in computing and cognition , with information compression as a unifying theme . this article discusses how it may be applied to the understanding of natural vision and the development of computer vision . the theory , which is described quite fully elsewhere , is described here in outline but with enough detail to ensure that the rest of the article makes sense . low level perceptual features such as edges or corners may be identified by the extraction of redundancy in uniform areas in a manner that is comparable with the run - length encoding technique for information compression . the concept of _ multiple alignment _ in the sp theory may be applied to the recognition of objects , and to scene analysis , with a hierarchy of parts and sub - parts , and at multiple levels of abstraction . the theory has potential for the unsupervised learning of visual objects and classes of objects , and suggests how coherent concepts may be derived from fragments . as in natural vision , both recognition and learning in the sp system is robust in the face of errors of omission , commission and substitution . the theory suggests how , via vision , we may piece together a knowledge of the three - dimensional structure of objects and of our environment , it provides an account of how we may see things that are not objectively present in an image , and how we recognise something despite variations in the size of its retinal image . and it has things to say about the phenomena of lightness constancy and colour constancy , the role of context in recognition , and ambiguities in visual perception . a strength of the sp theory is that it provides for the integration of vision with other sensory modalities and with other aspects of intelligence . _ keywords _ : vision , information compression , artificial intelligence , perception , cognition , representation of knowledge , learning , pattern recognition , natural language processing , reasoning , planning , problem solving .

1108.1252

i

the emission from narrow - line region ( nlr ) of active galactic nucleus ( agn ) is an important tool to study the relation between the activity of the central supermassive black hole ( smbh ) and the growth of its host galaxy in which the smbh resides , both because the nlr emission is mainly resulted from the illumination by the central agn and because the nlr kinematics is believed to be mainly dominated by the gravity of the bulge ( see review in wilson & heckman 1985 and references therein , whittle 1992a , b ; nelson & white 1996 ) . the gravity dominated kinematics motivates a number of previous studies to demonstrate that the line width of the agn s strong [ ] @xmath15007 emission line can be used as a proxy for the stellar velocity dispersion of the bugle ( e.g. , nelson & white 1996 ; nelson 2000 ; boroson 2003 ; komossa & xu 2007 ) . basing upon the tight @xmath2 relationship ( e.g. , tremaine et al . 2002 ; ferrarese & merritt 2000 ; magorrian et al . 1998 ; gebhardt et al . 2000 ; haring & rix 2004 ) , the proxy therefore allows one to easily estimate @xmath3 in a large sample of agns ( e.g. , grupe & mathur 2004 ; wang & lu 2001 ; komossa & xu 2007 ) . it is well known for a long time that the line profiles of the [ ] doublelets show a blue asymmetry with an extended blue wing and a sharp red falloff in a large fraction of agns ( e.g. , heckman et al . 1981 ; whittle 1985 ; wilson & heckman 1985 ; grupe et al 1999 ; tadhunter et al . 2001 ; veron - cetty et al . 2001 ; zamanov et al . 2002 ; komossa & xu 2007 ; xu & komossa 2009 ; greene & ho 2005 ; de roberties & osterbrock 1984 ; storchi - bergmann et al . 1992 ; arribas et al . 1996 ; christopoulou et al . 1997 ) . the blue asymmetry requires a narrow core gaussian profile ( @xmath4 ) with a blueshifted , broad gaussian component ( @xmath5 ) to reproduce the observed asymmetric profiles for both [ ] @xmath6 emission lines . the spectroscopic monitor revealed a variability time scale from one to ten years for the blue wings of the [ ] @xmath0 lines in two type i agns ( izw1 : wang et al . 2005 ; ngc5548 : sergeev et al . 1997 ) , which means that the blue wings are likely emitted from the intermediate - line region located between the traditional blr and nlr . in addition to the blue asymmetry , the redshifts of the [ ] doublelets are often found to be negative compared to the redshifts measured from both stellar absorption features and h@xmath7 emission line ( i.e. , [ ] blueshifts , e.g. , phillips 1976 ; zamanov et al .2002 ; marziani et al . 2003 ; aoki et al . 2005 ; boroson 2005 ; bian et al . 2005 ; komossa et al . although they are rare cases , the objects with strong [ ] blueshifts larger than 100@xmath8 are called `` blue outliers '' . the popular explanation of the observed [ ] emission - line profile is that the material outflow from central agn plays important role in reproducing the observed blue asymmetry and blueshift . with the advent of the high spatial resolution of hubble space telescope ( hst ) , spatially resolved spectroscopic observations of a few nearby seyfert 2 galaxies indicate that the nlrs show complicate kinematics , which could reproduce the observed [ ] line profiles by the radial outflow acceleration ( or deceleration ) and/or jet expansion ( e.g. , crenshaw et al . 2000 ; crenshaw & kraemer 2000 ; ruiz et al . 2001 ; nelson et al . 2000 ; hutchings et al . 1998 ; das et al . 2005 , 2006 , 2007 ; kaiser et al . 2000 ; crenshaw et al . 2010 , schlesinger et al . 2009 ; fischer et al . 2010 ; fischer et al . 2011 ) . recent systematical studies suggested that the blue asymmetry is related with the activity of the central smbh . veron - cetty et al . ( 2001 ) indicated that half of their sample of narrow - line seyfert 1 galaxies ( nls1s ) shows a broad and blueshifted [ ] @xmath15007 component in addition to the unshifted narrow core component . nelson et al . ( 2004 ) found a correlation between the blue asymmetry and eigenvector - i space by studying the [ ] @xmath15007 line profiles of the pg quasars . the quasars associated with larger blue asymmetries tend to be stronger emitters presumably having larger eddington ratios ( @xmath9 , where @xmath10 is the eddington luminosity , see also in xu et al . 2007 ; boroson 2005 ; greene & ho 2005 ; mathur & grupe 2005 ) . similar as the blue asymmetry , the [ ] blueshift is also found to be related with a number of agn properties . some authors claimed that the [ ] blueshift is directly correlated with @xmath9 ( e.g. , boroson 2005 ; bian et al . 2005 ) , although the correlation might not be the truth ( e.g. , aoki et al . marziani et al . ( 2003 ) pointed out that all the `` blue outliers '' have small h@xmath7 line widths ( @xmath11 ) and high @xmath9 ( see also in zamanov et al . 2002 ; komossa et al . 2008 ) . agns are now widely believed to co - evolve with their host galaxies , which is implied by the tight @xmath2 correlation ( see the citations in the first paragraph ) and by the global evolutionary history of the growth of the central smbh that traces the star formation history closely from present to @xmath12 ( e.g. , nandra et al . 2005 ; silverman et al . 2008 ; shankar et al . 2009 ; hasinger et al . 2005 ) . a number of studies recently provided direct evidence supporting the co - evolutionary scenario in which an agn evolves along the eigenvector - i space from a high @xmath9 state to a low @xmath9 state as the circumnuclear stellar population continually ages ( e.g. , wang et al . 2006 ; wang & wei 2008 , 2010 ; kewley et al . 2006 ; wild et al . 2007 ; davis et al . 2007 ) . the results of theoretical simulations indicate a possibility that a major merger between two gas - rich disk galaxies plays important role in the co - evolution of agns and their host galaxies ( e.g. , di matteo et al . 2007 ; hopkins et al . 2007 ; granato et al . detailed analysis even suggests a delay of @xmath13myr for the detectable agn activity after the onset of the star formation activity ( e.g. , wang & wei 2005 ; schawinski et al . 2009 ; hopkins et al . 2005 ; davis et al . 2007 ; wild et al . 2010 ) . the delay might be resulted from the feedback from either the central agn ( e.g. , hopkins et al . 2005 ) or the stellar winds ( e.g. , morman & scoville 1988 ) , and/or resulted from the purely dynamical origin ( hopkins 2011 ) . the outflow origin for both blue asymmetry and blueshift naturally gives us the hint that the [ ] emission - line profile ( and the inferred nlr kinematics ) co - evolves with the stellar population of the host galaxy . we here report a study that is an effort to examine the evolution of the [ ] @xmath15007 emission - line profile . in principle , both broad- and narrow - line agns are needed to be analyzed to give a complete study . although the [ ] line profiles can be easily measured in the spectra of typical type i agns , the host galaxy properties are hard to be determined because of the strong contamination from the central agn s continuum . since our aim is to study the relationship between the line profile and the host galaxy properties , the narrow emission - line galaxies from sloan digital sky survey ( sdss ) are adopted in our study because their spectra allow us to simultaneously measure both [ ] @xmath15007 line profile and stellar population properties in individual object . the high - order dimensionless line shape parameters are adopted by us to describe the line profile in details . the paper is organized as follows . the sample selection is presented in 2 . 3 describes the data reduction , including the stellar component removal , the line profile measurements , and the stellar population age measurements . our analysis and results are shown in 4 . the implications are discussed in the next section . a @xmath14 cold dark matter ( @xmath14cdm ) cosmology with parameters @xmath15 , @xmath16 , and @xmath17 ( spergle et al . 2003 ) is adopted throughout the paper .

the agn - host co - evolution issue is investigated here by focusing on the evolution of the [ ] emission - line profile . in order to simultaneously measure both [ ] line profile and circumnuclear stellar population in individual spectrum , the evolutionary significance revealed here suggests that both nlr kinematics and outflow feedback in agns co - evolve with their host galaxies .

the agn - host co - evolution issue is investigated here by focusing on the evolution of the [ ] emission - line profile . in order to simultaneously measure both [ ] line profile and circumnuclear stellar population in individual spectrum , a large sample of narrow emission - line galaxies is selected from the mpa / jhu sdss dr7 catalog . by requiring that 1 ) the [ ] line signal - to - noise ratio is larger than 30 , 2 ) the [ ] line width is larger than the instrumental resolution by a factor of 2 , our sample finally contains 2,333 seyfert galaxies / liners ( agns ) , 793 transition galaxies , and 190 starforming galaxies . in additional to the commonly used profile parameters ( i.e. , line centroid , relative velocity shift and velocity dispersion ) , two dimensionless shape parameters , skewness and kurtosis , are used to quantify the line shape deviation from a pure gaussian function . we show that the transition galaxies are systematically associated with narrower line widths and weaker [ ] broad wings than the agns , which implies that the kinematics of the emission - line gas is different in the two kinds of objects . by combining the measured host properties and line shape parameters , we find that the agns with stronger blue asymmetries tend to be associated with younger stellar populations . however , the similar trend is not identified in the transition galaxies . the failure is likely resulted from a selection effect in which the transition galaxies are systematically associated with younger stellar populations than the agns . the evolutionary significance revealed here suggests that both nlr kinematics and outflow feedback in agns co - evolve with their host galaxies .

1108.1252

c

we systematically examined the evolutionary issue of the [ ] @xmath0 emission - line profile by using a large sample of narrow emission - line galaxies selected from the mpa / jhu sdss dr7 value - added catalog . the sample is separated into three sub - samples ( i.e. , star - forming galaxies , transition galaxies and seyfert galaxies / liners ) basing upon the line ratios given in the catalog . two shape parameters , skewness ( @xmath45 ) and kurtosis ( @xmath47 ) , are additionally used to quantify the profile deviation from a pure gaussian . our analysis indicates that a ) the transition galaxies are systematically associated with narrower line widths and with weaker [ ] broad wings than the agns ; b ) the agns with stronger blue asymmetries tend to be associated with younger stellar populations . the evolutionary significance of the [ ] line profile suggests a co - evolution of the outflow feedback and the agn s host galaxy . we would like to thank the anonymous referees for his / her constructive comments in improving the paper . this study was supported by the national science foundation of china ( under grant 10803008 ) , and by the national basic research program of china ( grant 2009cb824800 ) . this study uses the sdss archive data that was created and distributed by the alfred p. sloan foundation .

we show that the transition galaxies are systematically associated with narrower line widths and weaker [ ] broad wings than the agns , which implies that the kinematics of the emission - line gas is different in the two kinds of objects . by combining the measured host properties and line shape parameters , we find that the agns with stronger blue asymmetries tend to be associated with younger stellar populations the failure is likely resulted from a selection effect in which the transition galaxies are systematically associated with younger stellar populations than the agns .

the agn - host co - evolution issue is investigated here by focusing on the evolution of the [ ] emission - line profile . in order to simultaneously measure both [ ] line profile and circumnuclear stellar population in individual spectrum , a large sample of narrow emission - line galaxies is selected from the mpa / jhu sdss dr7 catalog . by requiring that 1 ) the [ ] line signal - to - noise ratio is larger than 30 , 2 ) the [ ] line width is larger than the instrumental resolution by a factor of 2 , our sample finally contains 2,333 seyfert galaxies / liners ( agns ) , 793 transition galaxies , and 190 starforming galaxies . in additional to the commonly used profile parameters ( i.e. , line centroid , relative velocity shift and velocity dispersion ) , two dimensionless shape parameters , skewness and kurtosis , are used to quantify the line shape deviation from a pure gaussian function . we show that the transition galaxies are systematically associated with narrower line widths and weaker [ ] broad wings than the agns , which implies that the kinematics of the emission - line gas is different in the two kinds of objects . by combining the measured host properties and line shape parameters , we find that the agns with stronger blue asymmetries tend to be associated with younger stellar populations . however , the similar trend is not identified in the transition galaxies . the failure is likely resulted from a selection effect in which the transition galaxies are systematically associated with younger stellar populations than the agns . the evolutionary significance revealed here suggests that both nlr kinematics and outflow feedback in agns co - evolve with their host galaxies .

physics9912023

i

the aim of this work is to develop the framework for the description of low - energy positron annihilation on molecules , and to analyse its two main mechanisms : direct and resonant annihilation . there are a number of remarkable phenomena associated with this process : very large annihilation rates @xcite , high sensitivity of the rates to small changes in the molecular structure @xcite , large ionization - fragmentation cross sections for organic molecules at sub - ps - threshold positron energies @xcite , and rapid increase of the fragmentation and annihilation rates towards small positron energies @xcite . in spite of decades of study , there is no consistent physical picture or even general understanding of these processes , and there have been very few calculations @xcite , which leaves too much room for speculations @xcite . my main objective is to consider real mechanisms of positron annihilation on molecules , describe their characteristic features , make estimates of the corresponding annihilation rates , and formulate the terms in which positron - molecule annihilation should be described and analysed . in recent work @xcite , iwata _ _ describe new experiments to study positron annihilation on molecules . some of these experiments test specific features of the annihilation processes described in the present paper . though some aspects of the experimental work are discussed here , futher details and comparison with theory and various models of positron annihilation can be found in ref . @xcite . the annihilation rate @xmath5 for positrons in a molecular or atomic gas is usually expressed in terms of a dimensionless parameter @xmath0 : @xmath6 where @xmath7 is the classical radius of the electron , @xmath8 is the non - relativistic spin - averaged rate of electron - positron annihilation into two @xmath9 quanta , and @xmath10 is the number density of molecules @xcite . equation ( [ eq : zeff ] ) implies that @xmath0 is the effective number of target electrons contributing to the annihilation process . in terms of the annihilation cross section @xmath11 the rate is @xmath12 , so by comparison with eq . ( [ eq : zeff ] ) , we have @xmath13 where @xmath14 is the positron velocity . accordingly , the spin - averaged cross section of annihilation of a non - relativistic positron on a single electron corresponds to @xmath15 , see e.g. @xcite . if the annihilation occurs during binary positron - molecule collisions , as in the experiments of the san diego group @xcite who use a positron trap and work at low gas densities , the parameter @xmath0 is independent of the density . it characterizes the annihilation of a positron on a single molecule . one could expect that @xmath0 is comparable to the number of electrons @xmath16 in an atom or molecule . moreover , low - energy positrons do not penetrate deep into the atom , and annihilate most probably with the valence electrons only . however , even for hydrogen @xmath17 at low energies @xcite . this is a manifestation of correlation effects . the most important of them is polarization of the atom by the positron and , as a result , an attractive @xmath18 positron - atom potential , @xmath19 being the atomic dipole polarizability . an additional short - range contribution to the positron - atom attraction comes from virtual ps formation , i.e. , hopping , or rather , tunneling of an electron between the atomic ion and the positron . the electron density on the positron is also enhanced due to the coulomb attraction between them . these effects make atomic @xmath0 large , e.g. , @xmath20 for room temperature positrons on xe @xcite . even compared with this large number , annihilation rates for low - energy ( room temperature ) positrons on polyatomic molecules are huge . they increase very rapidly with the molecular size , and depend strongly on the chemical composition of the molecules , see fig . [ fig : zeffmol ] . this has been known for quite a while , after early measurements for ccl@xmath21 , @xmath22 @xcite , butane , @xmath23 @xcite , and @xmath0 ranging between @xmath24 and @xmath25 for large alkanes c@xmath26h@xmath27 , @xmath28416 @xcite ( see also @xcite ) . the largest @xmath0 values measured so far are @xmath29 for antracene c@xmath30h@xmath31 @xcite and @xmath32 for sebacic acid dimethyl ester c@xmath33h@xmath34o@xmath21 @xcite . thus , while @xmath0 up to five orders of magnitude greater than @xmath16 have been observed , the physical processes responsible for these anomalously large annihilation rates have not been really understood . in other words , if the observed @xmath0 are parametrically large , compared to the number of available electrons , then what are the parameters that determine large annihilation rates for positrons on molecules ? in this work i consider two basic mechanisms of positron - molecule annihilation . the first mechanism is _ direct annihilation _ of the incoming positron with one of the molecular electrons . the contribution of this mechanism to the annihilation rate is proportional to the number of valence electrons available for annihilation . it can be enhanced by the positron - molecule interaction which distorts the positron wave . in particular , the positron density in the vicinity of the molecule increases greatly if a low - lying virtual state ( @xmath35 ) or a weakly bound level ( @xmath36 ) exists for the @xmath37-wave positron . in this case @xmath38 for small positron energies @xmath39 @xcite . this type of enhancement is responsible for large @xmath0 values observed in heavier noble gas atoms , where successively lower virtual levels exist for the positron ( @xmath40 , 90.1 and 401 for ar , kr and xe , respectively @xcite ) . this understanding is confirmed by the temperature dependences of the annihilation rates measured for the noble gases in @xcite . note that for room - temperature positrons , @xmath41 , even for @xmath42 the size of the enhancement due to virtual / weakly bound states is limited . the second mechanism is _ resonant annihilation_. by this i mean a two - stage process . the positron is first captured into a feshbach - type resonance , where positron attachment is accompanied by excitation of some molecular degrees of freedom . such process is well known for electrons @xcite . the positron in the quasi bound state then annihilates with a molecular electron . enhancement of annihilation due to a single resonance was considered theoretically in @xcite . the possibility of forming such resonances by excitation of the vibrational degrees of freedom of molecules was proposed by surko _ @xcite to explain high annihilation rates and their strong dependence on the molecular size observed for alkanes . it was also considered in relation to the problem of fragmentation of molecules by positron annihilation @xcite . however , its contribution to the annihilation have never been properly evaluated . to make this mechanism work for low - energy positrons one must assumed that positrons can form bound states with large neutral molecules , i.e. , the positron affinity of the molecule is positive , @xmath43 @xcite . the capture is then possible if the energy of the incoming positron is in resonance with the vibrationally excited state of the positron - molecule complex @xcite . the density of the vibrational excitation spectrum of this complex can be high , even if the excitation energy supplied by positron binding , @xmath44 , is only few tenths of an ev ( it is reasonable to assume that the presence of the positron does not change the vibrational spectrum of the molecule by too much ) . for positrons with thermal maxwellian energy distribution the contribution of the resonant annihilation mechanism averaged over a number of resonances @xmath45 is observed . the magnitude of @xmath45 is determined by three parameters of the positron - molecule resonant states : their annihilation width @xmath46 , the autodetachment width @xmath47 , which also determines the probability of positron capture , and the level density @xmath48 of the positron - molecule resonant states populated in positron capture . the magnitude of @xmath46 for positron - molecule bound states is comparable to the spin - averaged annihilation width of the ps atom ( @xmath49 s ) . note that @xmath46 does not increase with the size of the molecule , because the increase in the number of electrons is accompanied by thinning of the positron density in the ( quasi)bound positron - molecule state . it turns out ( see sec . [ sec : anmech ] ) that for @xmath50 the magnitude of @xmath45 is simply proportional to @xmath48 . this density increases rapidly with the size of the molecule , @xmath51 , where @xmath52 is the number of vibrational modes , @xmath53 is the effective number of vibrational quanta excited in positron capture , and @xmath54 is a typical molecular vibrational frequency . thus , the resonant annihilation mechanism can explain the rapid increase of @xmath0 with the size of the molecule shown in fig . [ fig : zeffmol ] . moreover , my estimates show that for thermal positrons @xmath45 up to @xmath55 could be observed . a necessary condition for the resonant annihilation to occur is the existence of positron - molecule bound states . until recently there was almost no positive information about the possibility of positron binding to neutral atomic species . the experimental results and their interpretation by surko _ @xcite could be viewed as the strongest , albeit indirect , evidence of positron binding to large molecules . this situation has changed now . many - body theory calculations of dzuba _ et al . _ @xcite indicated strongly that positrons can be bound by mg , zn , cd , and hg and , possibly , many other atoms . recently the variational calculations of ryzhikh and mitroy proved rigorously that positrons form bound states with li atoms , and demonstrated that bound states also exist for na , be , mg , zn , cu and ag @xcite . molecules are much larger potential wells for the positron , and it seems natural that many of them should be capable of binding positrons . ideas about different mechanisms in positron - molecule annihilation have been discussed earlier in a number of theoretical @xcite and experimental @xcite works . however , there is a need to re - examine this question using a unified approach to the annihilation mechanisms , and define clearly the physical variables which determine the observed annihilation rates . the latter is especially important for the present work which aims to provide understanding of a whole variety of phenomena , including the origins of the high values of @xmath0 for molecules and their dependence on the chemical composition and positron energy .

the aim of this work is to identify the mechanisms responsible for very large rates and other peculiarities observed in low - energy positron annihilation on molecules . the two mechanisms considered are : ( i ) direct annihilation of the incoming positron with one of the molecular electrons . averaged over some energy interval , e.g. , due to thermal positron energy distribution , is proportional to the level density of the positron - molecule complex , which is basically determined by the spectrum of molecular vibrational states populated in the positron capture . it is highly sensitive to molecular structure and shows a characteristic behaviour of at small positron energies .

the aim of this work is to identify the mechanisms responsible for very large rates and other peculiarities observed in low - energy positron annihilation on molecules . the two mechanisms considered are : ( i ) direct annihilation of the incoming positron with one of the molecular electrons . this mechanism dominates for atoms and small molecules . i show that its contribution to the annihilation rate can be related to the positron elastic scattering cross section . this mechanism is characterized by strong energy dependence of at small positron energies and high values ( up to ) for room temperature positrons , if a low - lying virtual level or a weakly bound state exists for the positron . ( ii ) resonant annihilation , which takes place when the positron undergoes resonant capture into a vibrationally excited quasibound state of the positron - molecule complex . this mechanism dominates for larger molecules capable of forming bound states with the positron . for this mechanism averaged over some energy interval , e.g. , due to thermal positron energy distribution , is proportional to the level density of the positron - molecule complex , which is basically determined by the spectrum of molecular vibrational states populated in the positron capture . the resonant mechanism can produce very large annihilation rates corresponding to . it is highly sensitive to molecular structure and shows a characteristic behaviour of at small positron energies . the theory is used to analyse calculated and measured for a number of atoms and molecules .

physics9912023

r

if low - energy positron scattering is dominated by the presence of a virtual or weakly bound state at @xmath172 , the corresponding cross section has the form ( for scattering by a short - range potential @xcite ) @xmath173 where @xmath174 . according to eq . ( [ eq : zdir1 ] ) a similar maximum should appear in the momentum dependence of the annihilation rate . its magnitude at @xmath175 can be arbitrarily large if @xmath176 ( @xmath177 ) , which corresponds to a level at zero energy . however , for nonzero momenta the maximal cross section is finite , @xmath178 , which corresponds to the unitarity limit for the @xmath37-wave cross section . real atomic and molecular targets have nonzero electric dipole polarizabilities @xmath19 , which give rise to the long - range polarization potential @xmath179 for the positron . its effect is taken into account by the modified effective - range formula for the @xmath37-wave phase shift @xcite , @xmath180^{-1}~ , \\ \sigma _ { \rm el}=\frac{4\pi a^2 } { \left [ 1-(\pi \alpha k/3a)-(4\alpha k^2/3 ) \ln \left ( \frac{c}{4}\sqrt{\alpha } k \right ) \right]^2+a^2k^2 } ~ , \label{eq : mersig}\end{aligned}\ ] ] the latter formula being valid when the scattering length is large and the @xmath37-wave scattering dominates at small @xmath181 . in equations ( [ eq : mer ] ) and ( [ eq : mersig ] ) @xmath182 is a dimensionless positive constant . note that for @xmath183 , eq . ( [ eq : csvirt ] ) is immediately recovered . the polarization potential modifies the behaviour of the cross section at low energies . for example , it leads to a more rapid decrease of the cross section for @xmath116 , @xmath184 $ ] . however , this does not change the estimates of the maximal values of @xmath0 that could be produced in direct annihilation . to illustrate the relation between direct annihilation and elastic scattering , and the enhancement of both due to the presence of a low - lying virtual level , let us compare the behaviour of @xmath0 and @xmath104 for ar and kr . the results shown in fig . [ fig : zandcs ] were obtained within the polarized - orbital method @xcite , which takes into account the polarization of the target by the positron . these calculations yield large negative values of the scattering length for ar , kr and xe ( see table [ tab : ar ] ) , indicating the presence of positron - atom virtual levels formed due to strong positron - atom attraction . the increase of @xmath185 correlates with the increase of the dipole polarizability in these atoms . similar values of @xmath111 have been obtained in the many - body theory calculations of dzuba _ et al . figure [ fig : zandcs ] shows that both @xmath104 and @xmath0 are enhanced at low momenta due to the presence of the virtual @xmath37 levels . this effect is stronger for kr , which has a greater absolute value of the positron scattering length . as illustrated by fig . [ fig : zandcs]a for kr , eq . ( [ eq : mersig ] ) provides a good description of the cross section at small @xmath181 . the visible difference between @xmath0 and @xmath104 in fig . [ fig : zandcs ] is due to the background given by the energy - independent term @xmath186 in eq . ( [ eq : zdir1 ] ) . figure [ fig : zdir ] provides a direct comparison between @xmath0 and the right - hand side of eq . ( [ eq : zdir1 ] ) , and shows that this relation is valid at low positron energies . the comparison is based on the polarized - orbital method results for the noble - gas atoms @xcite , and the values of @xmath0 and @xmath104 obtained for the ethylene molecule ( c@xmath187h@xmath21 ) by the schwinger multichannel method @xcite . in this comparison i have considered @xmath63 and the pre - factor @xmath188 in eq . ( [ eq : zdir1 ] ) as fitting parameters . their values are listed in table [ tab : ar ] together with the values of @xmath111 obtained in those calculations . note that the theoretical results used to produce this plot are not necessarily `` exact '' or accurate ( although , experimental data confirm that they are reasonable @xcite ) . it follows from the derivation that eq . ( [ eq : zdir1 ] ) holds for any calculation , as long as the same wave function is used in the scattering and annihilation calculations @xcite . in agreement with the estimates made in sec . [ subsec : dir ] , fig . [ fig : zdir ] shows that direct annihilation is indeed strongly enhanced by the presence of low - lying virtual levels . nevertheless , even for targets with very large scattering lengths , such as xe or c@xmath187h@xmath21 , the annihilation rates do not exceed @xmath189 for room - temperature positron momenta ( 0.05 a.u . ) . direct annihilation is the only annihilation mechanism for atoms and molecules which do not form bound states with positrons . it will also dominate for small molecules which do form a weakly bound state with the positron , but whose vibrational frequencies are high . in this case the energy @xmath190 is simply insufficient for the excitation of the resonant quasibound states at low impact positron energies @xmath4 . for large molecules the difference between the resonant and direct mechanisms is probably most obvious when one compares the experimental values of @xmath0 for alkanes and perfluorinated alkanes shown in fig . [ fig : zeffmol ] . the large annihilation rates of the alkane molecules with more than two carbon atoms can not be explained by direct annihilation . they also display a very rapid increase with the size of the molecule , which is typical of resonant annihilation . on the other hand , the @xmath0 values of the perfluorinated alkanes remain comparatively small , in spite of their softer vibrational spectra . thus , one is lead to conclude that the resonant mechanism is switched off for them . the latter is explained by the very weak attraction between the positron and fluorine atoms @xcite , insufficient to provide positron - molecule binding . let us examine the effect of fluorination on @xmath0 for the lightest molecule of the series , methane . the experimental data at room temperature are : @xmath191 , 715 , 411 , 127 , and 38 , for ch@xmath21 , ch@xmath192f , ch@xmath187f@xmath187 , chf@xmath192 , and cf@xmath21 , respectively ( data from @xcite normalized to the given value for methane ) . these values are small enough to be accounted for by the direct mechanism . within its framework the increase and subsequent drop of @xmath0 could be explained by the existence of a loosely bound state for the positron on methane , which turns into a virtual level as the number of substitute fluorine atoms increases @xcite . in terms of @xmath193 parameter this would mean that @xmath193 is small and positive for ch@xmath21 , and then goes through zero , and becomes negative upon fluorination . accordingly , both the cross section and the annihilation rate peak for the molecule with the smallest absolute value of @xmath193 , namely ch@xmath192f . this picture is considered in ref . @xcite in more detail using the zero - range potential model for positron - molecule interaction . besides having a larger value of @xmath0 , the molecule with a smaller @xmath194 ( i.e. , larger @xmath185 ) should have a more rapid dependence of the annihilation rate on the positron energy , cf . figure [ fig : zdir ] . if the experiment is done with thermal positrons this should manifest in a stronger temperature dependence of the maxwellian average of @xmath195 @xmath196 on the positron temperature @xmath197 . the overbar is usually omitted , as it is clear from the context whether one is dealing with @xmath195 at a specific positron momentum , or with a thermal average @xmath198 . the temperature dependences of the annihilation rates for methane and fluoromethane measured in ref . @xcite are shown in fig . [ fig : ch4ch3f ] . also shown are low - temperature theoretical fits obtained using eqs . ( [ eq : zdir1 ] ) , ( [ eq : mersig ] ) and ( [ eq : zt ] ) . their parameters are given in the caption . the dipole polarizability of ch@xmath192f @xmath199 a.u . is close to that of methane , @xmath200 a.u . , and i use the latter for both molecules . the constant @xmath182 appears in eqs . ( [ eq : mer ] ) and ( [ eq : mersig ] ) under the logarithm , and the result is not very sensitive to it , so @xmath201 has been chosen . the value of the characteristic radius @xmath202 a.u . is similar to those for noble gas atoms and ethylene ( table [ tab : ar ] ) , and the pre - factor @xmath203 is between those for noble gas atoms and c@xmath187h@xmath21 . of course , the number of independent parameters ( @xmath111 , @xmath182 , @xmath63 and @xmath204 ) is too large to enable their unique determination from the experimental data . however , the fits clearly demonstrate that very different @xmath205 curves can be obtained _ only _ due to different @xmath193 values ( @xmath206 and 0.01 , for ch@xmath21 and ch@xmath192f , respectively . these values imply that both molecules have bound states with the positron . the binding energy for ch@xmath21 is @xmath207 a.u.@xmath208 ev , and the binding energy corresponding to @xmath209 is just 1 mev . there is a large uncertainty in the latter value , because measurements performed at and above room temperature , @xmath210 ev , are not really sensitive to such small @xmath193 . this can be seen , e.g. , from eq . ( [ eq : csvirt ] ) , which becomes @xmath193-independent for @xmath211 . zero - range model calculations presented in ref . @xcite show that the last three members of the fluoromethane sequence have negative @xmath193 , corresponding to virtual levels with increasing energies . this causes the decrease of their @xmath0 values . as seen in fig . [ fig : ch4ch3f ] , equation ( [ eq : zdir1 ] ) for the direct annihilation combined with the modified effective range formula ( [ eq : mersig ] ) works well in the low - energy part of the graph . however , the data for methane clearly show an abrupt departure from this law at higher @xmath197 , and the formation of some kind of a plateau in @xmath205 . in principle , one could think that this is due to contributions of higher partial waves , not included in @xmath104 , eq . ( [ eq : mersig ] ) . however , their contribution has been included via the @xmath63 term of eq . ( [ eq : zdir1 ] ) . also , the contributions of higher partial waves to @xmath0 emerge as @xmath212 , which is a manifestation of the wigner threshold law @xcite . for thermally averaged rates this corresponds to @xmath213 . thus , it can not be responsible for this sudden feature . on the other hand , if the methane molecule forms a bound state with the positron the system can also have vibrationally excited positron - molecule resonant states . the positron bound state on ch@xmath21 must belong to the @xmath214 symmetry type of the molecule . since the positron @xmath37 wave dominates at low energies , its capture into the @xmath214 state can result in the excitation of @xmath214 vibrational modes of the molecule . the frequency of this mode for methane is @xmath215 @xmath216 ev . assuming that the positron binding does not change this frequency much , the lowest vibrationally excited positron - molecule resonance will occur at @xmath217 ev . it is easy to estimate the contribution of a single narrow vibrational resonance located at positron energy @xmath218 to the thermally averaged @xmath0 @xcite , @xmath219 the latter formula valid for @xmath220 , which implies that the resonance has a capture width greater than 1 @xmath85ev . figure [ fig : ch4ch3f ] shows the effect of the lowest vibrational @xmath214 resonance at @xmath221 ev on @xmath0 for methane ( chain curve ) . its onset is indeed quite rapid , due to the exponent in eq . ( [ eq : singres ] ) , which makes @xmath222 very small for @xmath223 . to fit the experimental data the density @xmath224 is chosen to be 25% of @xmath225 . one could expect that for a weakly bound state ( @xmath226 ev ) , where the positron spends most of its time outside the molecule , its density on the electrons is reduced below that of ps ( binding energy 6.8 ev ) @xcite . equation ( [ eq : resres ] ) derived in sec . [ subsec : res ] shows that the annihilation rate due to positron capture into resonances is determined by the level density of these quasibound vibrationally excited states of the positron - molecule complex . this density depends on the excitation energy available , as defined by the positron kinetic energy and positron affinity , @xmath44 , and also on the structure of the molecular vibrational spectrum . suppose that the molecule possesses a particular symmetry , which is true for most of the molecules where positron annihilation has been studied so far @xcite . the electronic ground state wave function of the molecule is usually nondegenerate and invariant under all symmetry transformations . let us call this symmetry type @xmath227 . depending on the actual symmetry of the molecule this can be @xmath214 , @xmath228 , or @xmath229 . if the positron can be bound by such molecule , the electron - positron part of the wave function of the positron - molecule complex will also be fully symmetric , i.e. , of the @xmath227 symmetry type . consider now the capture of a continuous spectrum positron into the bound positron - molecule state . at low positron energies this process is dominated by the incident positron @xmath37 wave , higher partial waves being suppressed as @xmath230 , compared to the @xmath37 wave [ cf . ( [ eq : gamcth ] ) ] . as a result , the electron - positron part of the wave function of the initial ( molecule and the @xmath37-wave positron ) and final ( bound positron - molecule complex ) states of the capture process are characterized by the same full molecular symmetry @xmath227 . this imposes a selection rule on the nuclear vibrations which can be excited during the capture process . they must also belong to the @xmath227 symmetry type . therefore , the selection rule limits the spectrum of possible vibrationally excited resonances which could in principle be formed . it allows arbitrary excitations and combinations of the @xmath227 modes . it also allows overtones and combinations of the other symmetry types , provided such excitations contain the @xmath227 symmetry type , i.e. , the ( symmetric ) product of the symmetry types involved contains @xmath227 among its irreducible representations @xcite . this does not mean that all such vibrations will contribute to the density factor @xmath48 in eq . ( [ eq : resres ] ) for @xmath0 . some of them may have extremely weak coupling to the electron - positron degrees of freedom , with capture widths much smaller than 1 @xmath85ev . in this case they will be effectively decoupled from the positron capture channel , and hence , will not contribute to @xmath0 . of course , this can only be found out by doing detailed calculations for specific molecules . nevertheless , it is instructive to compare eq . ( [ eq : resres ] ) with experimental data . this comparison enables one to extract the effective mean spacing @xmath126 between the positron - molecule resonances . for experiments with thermal positrons eq . ( [ eq : resres ] ) must be averaged over the maxwellian positron momenta distribution , @xmath231 let us use the ps value , @xmath232 , to estimate the electron - positron density , and apply eq . ( [ eq : zrest ] ) to simple symmetric molecules with @xmath233 , where resonant annihilation must be the dominant mechanism . the effective spacings @xmath234 ( in @xmath235 ) obtained from the experimental @xmath0 values measured with room - temperature positrons @xcite are listed in table [ tab : vibfreq ] . they are compared with the low frequency vibrational modes of the @xmath227 symmetry type of these molecules taken from ref . @xcite . as discussed above , vibrations of the @xmath227 symmetry type also occur in overtones and combinations of other modes . however , their frequencies scale with the size and chemical composition of the molecule in a way similar to the @xmath227 modes , and the @xmath227 mode frequencies listed in the table are representative of the lower vibrational modes on the whole . for molecules with moderate @xmath0 at the top of the table , such as ccl@xmath21 , the effective resonance spacing @xmath126 is comparable to the frequencies of single modes . with the increase of the size of the molecule ( alkanes ) , or masses of the constituents ( e.g. , cbr@xmath21 ) , the vibrational modes are softened , and the number of low - frequency modes increases . at the same time one can expect that the positron binding energy increases for these molecules . these effects , and especially the increase of the number of modes , facilitate multimode excitations , whose density is much greater that the level density of the individual modes . accordingly , we see that @xmath126 becomes much smaller that the frequencies of the individual modes at the bottom of the table . in the simplest model this effect can be estimated as follows . suppose the vibrational modes in question are characterized by some typical frequency @xmath54 , and the molecule has @xmath52 such modes . suppose , the positron binding energy is @xmath236 , where @xmath10 is the number of vibrational quanta excited due to positron binding . if we neglect the small kinetic energy of the positron , @xmath237 , the total number of various vibrational excitations at energy @xmath238 is given by @xmath239 $ ] ( number of ways to distribute @xmath10 vibrational quanta among @xmath52 modes ) . for large molecules @xmath240 remains finite , whereas @xmath52 increases linearly with the size of the molecule , the total number of vibrational modes being @xmath241 , where @xmath242 is the number of atoms . therefore , the number of vibrational excitations available , and the density of the resonant vibrational spectrum , increase as @xmath243 . such rapid increase is indeed observed for alkanes and aromatic hydrocarbons , see fig . [ fig : zeffmol ] . the effective number of vibrational modes excited in the capture process , @xmath244 and 8.2 , respectively , is compatible with the positron binding energy of few tens of an electron volt . for example , if i use the lowest @xmath228 mode frequency of hexane ( table [ tab : vibfreq ] ) , the positron affinity is @xmath245 ev . this number looks reasonable , compared with positron binding energies on single atoms , e.g. , @xmath246 , 0.15 , and 0.38 , for be , cu and mg , respectively @xcite . apart from the rapid growth , @xmath0 for alkanes shows clear signs of saturation , when the number of carbon atoms becomes greater than 8 or 10 . apparently , this takes place well before the unitarity limit derived in sec . [ subsec : res ] is reached . this behaviour can be understood if we recall that eq . ( [ eq : resres ] ) is valid only when the capture width @xmath47 is greater than the annihilation width @xmath46 . with the increase of the number of vibrational modes their coupling to the electron - positron degrees of freedom decreases . this coupling is represented by @xmath47 , and for small capture widths , @xmath247 , @xmath45 from eq . ( [ eq : zres ] ) is estimated as @xmath248 where eq . ( [ eq : gama ] ) is used together with @xmath249 , in atomic units . the decrease of @xmath47 is a simple consequence of sum rules , because the total strength of positron coupling is distributed among larger number of possible vibrational excitations . in this regime @xmath47 is proportional to @xmath126 , and the increase of @xmath45 related to the increase of the density of vibrational excitation spectrum stops . the relation @xmath250 which characterizes this regime is well known in neutron capture into compound resonances @xcite . it takes place in complex atomic spectra , e.g. , in rare - earths , where the oscillator strengths are distributed among very large numbers of transitions @xcite . it also emerges in the unimolecular reaction treatment of dissociative electron attachment @xcite , where it is responsible for very large lifetimes ( i.e. , small state widths ) of transient molecular anions . let us now look at the energy dependence of the resonant annihilation rate . at very small positron energies @xmath45 must be constant ( see discussion at the end of sec . [ subsec : res ] ) . however , as soon as the @xmath37-wave capture width becomes greater that 1 @xmath85ev , the corresponding annihilation rate shows a @xmath251 dependence on positron energy , as predicted by eq . ( [ eq : resres ] ) . for a thermally averaged rate this is described by eq . ( [ eq : zrest ] ) . figure [ fig : c4h10 ] presents a comparison between the @xmath252 law and the experimental temperature dependence of @xmath0 for c@xmath21h@xmath31 @xcite . this molecule has @xmath253 . within the present theoretical framework this large value must be due to the resonant annihilation process . the theory and experiment agree well at low temperatures . one may notice that the measured @xmath0 show a slightly steeper rise towards small @xmath197 . however , the difference is not large , both in relative and absolute terms . it could be explained by a direct contribution @xmath96 in eq . ( [ eq : result ] ) , which peaks sharply at small energies , if the positron - molecule scattering length is large ( see sec . [ subsec : illdir ] ) . in spite of the dominance of the resonant contribution , @xmath254 for butane , the addition of @xmath125 at small positron energies would still be noticeable . a more pronounced feature of the experimental data , which is not accounted for by eq . ( [ eq : zrest ] ) , is the plateau observed at higher temperatures , @xmath255 ev , where @xmath0 goes well above the @xmath252 curve . to find its possible origins let us first take a closer look at eq . ( [ eq : zrest ] ) and its predecessor , eq . ( [ eq : resres ] ) . for small impact positron energies @xmath4 the vibrational excitation energy is given by @xmath237 . accordingly , the resonance density @xmath48 in eq . ( [ eq : resres ] ) , and the mean spacing @xmath126 in eq . ( [ eq : zrest ] ) are approximately constant . as the positron energy , or temperature , increase , the resonance density factor should also increase , since @xmath48 is a strong function of the excitation energy for multimode vibrational spectra . therefore , the decrease of @xmath45 should be slower than @xmath168 , or @xmath252 . moreover , the density factor may even produce a rise in the energy dependence of @xmath45 . besides this , contributions of higher positron partial waves which emerge as @xmath197 , @xmath256 , etc . , at small @xmath197 , may also contribute to @xmath45 in the plateau region . it might even seem that these effects could lead to a rapid increase of @xmath45 with positron energy . however , there is an effect that suppresses the increase of resonant annihilation . throughout the paper i have assumed that the positron - molecule resonances have only two decay channels , annihilation and detachment , the latter being the reverse of positron capture . when the positron energy rises above the threshold of molecular vibrational excitations , the resonances can also decay into the ` positron @xmath66 vibrationally excited molecule ' channels . in this situation the total width of a resonance will be given by @xmath257 , where @xmath258 is the decay width due to positron detachment accompanied by the vibrational excitation of the molecule . this leads to a modification of eq . ( [ eq : resres ] ) , which now reads @xmath259 this equation shows that as soon as the positron energy exceeds another inelastic vibrational - excitation threshold , the factor in brackets drops , thereby reducing the resonant annihilation contribution . such downward step - like structures at vibrational thresholds are well known in dissociative electron attachment experiments ( see , e.g. , refs . when the positron energy is well above the lowest inelastic vibrational threshold the `` elastic '' width @xmath47 will become much smaller than the `` inelastic '' width @xmath260 , due to a large number of open inelastic vibrational - excitation scattering channels , and due to a kinematic increase of @xmath260 above the respective thresholds . this will strongly suppress the resonant annihilation contribution ( [ eq : zgv ] ) with respect to that of eq . ( [ eq : resres ] ) at larger positron energies . one may speculate that it is precisely the increase of @xmath258 that counteracts the rise of @xmath48 , and prevents rapid growth of @xmath261 with positron energies . it may also be true that a similar mechanisms is behind the dramatic drop of the dissociative attachment cross sections for projectile energies above few lower vibrationally inelastic thresholds @xcite .

this mechanism dominates for atoms and small molecules . ( ii ) resonant annihilation , which takes place when the positron undergoes resonant capture into a vibrationally excited quasibound state of the positron - molecule complex . this mechanism dominates for larger molecules capable of forming bound states with the positron . for this mechanism the theory is used to analyse calculated and measured for a number of atoms and molecules .

the aim of this work is to identify the mechanisms responsible for very large rates and other peculiarities observed in low - energy positron annihilation on molecules . the two mechanisms considered are : ( i ) direct annihilation of the incoming positron with one of the molecular electrons . this mechanism dominates for atoms and small molecules . i show that its contribution to the annihilation rate can be related to the positron elastic scattering cross section . this mechanism is characterized by strong energy dependence of at small positron energies and high values ( up to ) for room temperature positrons , if a low - lying virtual level or a weakly bound state exists for the positron . ( ii ) resonant annihilation , which takes place when the positron undergoes resonant capture into a vibrationally excited quasibound state of the positron - molecule complex . this mechanism dominates for larger molecules capable of forming bound states with the positron . for this mechanism averaged over some energy interval , e.g. , due to thermal positron energy distribution , is proportional to the level density of the positron - molecule complex , which is basically determined by the spectrum of molecular vibrational states populated in the positron capture . the resonant mechanism can produce very large annihilation rates corresponding to . it is highly sensitive to molecular structure and shows a characteristic behaviour of at small positron energies . the theory is used to analyse calculated and measured for a number of atoms and molecules .

physics9912023

i

in this work i have considered two possible mechanisms of low - energy positron annihilation in binary collisions with molecules . the first mechanisms is direct annihilation . it describes positron annihilation with atoms and small molecules , as well as molecules which do not form bound states with the positron . the annihilation rate due to this mechanism has been related to the positron elastic scattering properties . in particular , it is enhanced when the positron has a low - lying virtual @xmath37-type level or a weakly bound state at @xmath172 . for zero - energy positrons the direct annihilation rate is inversely proportional to @xmath262 . small @xmath193 , together with the dipole polarizability of the target , also determine the rapid energy dependence of @xmath0 at small positron energies . estimates show that for room - temperature positrons @xmath0 of up to @xmath1 can be produced due the virtual / weakly bound state enhancement . the second mechanism is resonant annihilation . it is operational when the positron forms temporary bound states with the molecule . as a necessary condition , the positron affinity of the molecule must be positive . the positron capture is a resonant process , whereby the energy of the positron is transferred into vibrational excitations of the positron - molecule complex . the contribution of this mechanisms to the annihilation rate is proportional to the level density of the positron - molecule resonances @xmath263 . these resonances are characterized by the capture width @xmath47 and annihilation width @xmath264ev . for @xmath265 its contribution is independent of @xmath47 , and is basically determined by the density @xmath263 . the resonant mechanism can give very large annihilation rates ( up to @xmath55 ) . through its dependence on the vibrational excitation spectrum of the positron - molecule complex , this mechanism shows high sensitivity to the chemical composition of the target , and the size of the molecule . both are essential features of the experimental data @xcite . the difference between the two mechanisms is illustrated most clearly by comparison of the annihilation rates of alkanes and perfluoroalkanes . for example , c@xmath266h@xmath30 has @xmath267 , whereas for c@xmath266f@xmath30 , @xmath0 is only 630 . the present theory attributes this huge difference to the fact that perfluorocarbons do not form bound states with the positrons , and hence , the resonant annihilation is switched off for them . on the other hand , this mechanism is behind the the high @xmath0 values of alkanes . the experimental group at san diego has performed a number of measurements on protonated and deuterated molecules to test the sensitivity of @xmath0 to the molecular vibrational modes @xcite . for example , their data for benzene show that a replacement of a single hydrogen atom with deuterium changes the annihilation rate from @xmath268 for c@xmath266h@xmath266 to @xmath269 for c@xmath266h@xmath270d . on the other hand , the data on fully protonated vs fully deuterated alkanes shows very little difference between the two cases . such behaviour is natural for smaller alkanes , e.g. , methane , where direct annihilation is the dominant mechanism . however , observed for large alkanes , it can not be readily interpreted by means of eq . ( [ eq : resres ] ) or alike . it is possible that the vibrational excitations are dominated by low - lying c@xmath271c modes which are weakly affected by deuteration . on the other hand , deuteration may also influence positron coupling to the molecular vibrations , which will most likely lead to a reduction of @xmath47 in eq . ( [ eq : zres ] ) . if the system is in the regime where @xmath272 , this effect may offset the decrease of the vibrational spacings . in spite of these difficulties , which could only be resolved by doing calculations for specific molecules , the present theory offers a consistent description of positron - molecule annihilation in real terms , through some well defined parameters which characterize the system . it clearly identifies the two basic mechanisms of positron annihilation and discusses their specific features . it also shows that studies of positron annihilation on molecules may give a unique insight into the physics of molecular reactions which go through formation of vibrationally excited intermediate states . such processes are very likely to be responsible for large dissociative electron attachment cross sections observed for molecules such as sf@xmath266 . they are also of key importance for the whole class of chemical reactions , namely , for unimolecular reactions ( see , e.g. , @xcite ) . this work was strongly stimulated by the vast experimental data of the san diego group , and i very much appreciate numerous discussions with its members , especially c. surko and k. iwata . i am thankful to my colleagues at the university of new south wales , v. flambaum , a. gribakina , m. kuchiev , and o. sushkov for their encouragement and useful discussions . my thanks also go to s. buckman for the information on vibrational excitations and dissociative attachment . support of my work by the australian research council is gratefully acknowledged . e. p. da silva , j. s. e. germane , and m. a. p. lima , phys . 77 * , 1028 ( 1996 ) . the @xmath228 symmetry ( `` @xmath37 wave '' ) dominates in both @xmath104 and @xmath0 at low positron energies , and i use @xmath273 to extract the @xmath37 wave phase shift and amplitude @xmath106 necessary for implementation of eq . ( [ eq : zdir1 ] ) . in this paper the word ` molecules ' is often used interchangeably with ` atoms ' , or ` atoms or molecules ' . however , there are specific phenomena , e.g. , low - energy positron capture ( sec . [ subsec : res ] ) , which involve vibrational degrees of freedom , and hence , apply to molecules only . the energy of positrons at room temperature , @xmath274 mev , is too small to excite any electronic degrees of freedom . the formation of ps is also impossible if we consider molecules with ionization potentials greater than the ps binding energy of 6.8 ev . g. g. ryzhikh and j. mitroy , phys . lett . * 79 * , 4124 ( 1997 ) . b * 31 * , l401 ( 1998 ) ; * 31 * , 4459 ( 1998 ) ; * 31 * , 5013 ( 1998 ) ; * 32 * , 1375 ( 1999 ) ; g. g. ryzhikh , j. mitroy , and k. varga , j. phys . b * 31 * , 3965 ( 1998 ) . at low positron energy annihilation and emission are the only decay channels of the resonances . at higher energies positron emission accompanied by the vibrational ( and then electronic ) excitation of the molecule becomes possible , see sec . [ subsec : illres ] . r. p. mceachran , d. l. morgan , a. g. ryman , and a. d. stauffer , j. phys . b * 10 * , 663 ( 1977 ) ; * 11 * , 951 ( 1978 ) ; r. p. mceachran , a. g. ryman , and a. d. stauffer , j. phys . b * 11 * , 551 ( 1978 ) ; * 12 * , 1031 ( 1979 ) ; r. p. mceachran , a. d. stauffer , and l. e. m. campbell , _ ibid _ * 13 * , 1281 ( 1980 ) . the most accurate theoretical data on positron scattering and annihilation are available for hydrogen . to avoid cluttering the plot the corresponding results are not presented in fig . [ fig : zdir ] . for hydrogen eq . ( [ eq : zdir1 ] ) provides a good fit of @xmath96 [ j. w. humberston , adv . at . phys . * 15 * , 101 ( 1979 ) ] with @xmath275 a.u . , @xmath276 a.u . , when variational scattering phase shifts are used to obtain @xmath104 and @xmath106 [ a. k. bhatia _ et al . _ , rev . a * 3 * , 1328 ( 1971 ) ; * 9 * , 219 ( 1974 ) ; d. register and r. t. poe , phys . a * 51 * , 431 ( 1975 ) ] . experimental data for a variety of molecules show that a non - zero dipole moment of the molecule does not have any direct effect on @xmath0 , ref . for example , @xmath277 , 1090 , and 1600 , for h@xmath1870 , no@xmath187 , and nh@xmath192 , whereas their dipole moments are 1.85 , 0.32 , and 1.47 debye , respectively . there also seems to be no correlation between @xmath0 values of ch@xmath192f , ch@xmath187f@xmath187 , chf@xmath192 , quoted in the text , and their respective dipole moments , 1.85 , 1.97 , and 1.65 debye . the contribution of a particular resonance to @xmath0 is given by the breit - wigner formula , cf . terms with @xmath131 in eq . ( [ eq : zeff1 ] ) . for the purpose of thermal averaging , the contribution of the @xmath73th resonance can be approximated by the @xmath95-function , @xmath278 , without any loss of accuracy . numerical calculations of positron - atom bound states show that for atoms with ionization potentials greater than 6.8 ev and positron affinities in the range @xmath279@xmath280 a.u . ( zn , be , cu , and ag ) the annihilation rates are 2030% that of ps , see g. ryzhikh and j. mitroy , j. phys . b * 31 * , 5013 ( 1998 ) ; j. mitroy and g. ryzhikh , j. phys . b * 32 * , 1375 ( 1999 ) .

this mechanism is characterized by strong energy dependence of at small positron energies and high values ( up to ) for room temperature positrons , if a low - lying virtual level or a weakly bound state exists for the positron . the resonant mechanism can produce very large annihilation rates corresponding to .

the aim of this work is to identify the mechanisms responsible for very large rates and other peculiarities observed in low - energy positron annihilation on molecules . the two mechanisms considered are : ( i ) direct annihilation of the incoming positron with one of the molecular electrons . this mechanism dominates for atoms and small molecules . i show that its contribution to the annihilation rate can be related to the positron elastic scattering cross section . this mechanism is characterized by strong energy dependence of at small positron energies and high values ( up to ) for room temperature positrons , if a low - lying virtual level or a weakly bound state exists for the positron . ( ii ) resonant annihilation , which takes place when the positron undergoes resonant capture into a vibrationally excited quasibound state of the positron - molecule complex . this mechanism dominates for larger molecules capable of forming bound states with the positron . for this mechanism averaged over some energy interval , e.g. , due to thermal positron energy distribution , is proportional to the level density of the positron - molecule complex , which is basically determined by the spectrum of molecular vibrational states populated in the positron capture . the resonant mechanism can produce very large annihilation rates corresponding to . it is highly sensitive to molecular structure and shows a characteristic behaviour of at small positron energies . the theory is used to analyse calculated and measured for a number of atoms and molecules .

cond-mat9903146

i

quantum corrections to the classical drude formula for the electrical conductivity give rise to singular terms in low - dimensional systems@xcite . there are two types of such terms . the first is known as the weak localization correction ( wl ) and arises as a result of the quantum interference of electron waves in disordered systems . the second is a consequence of the enhancement of the electron - electron interaction in a disordered system and is usually referred to as electron - electron interaction correction ( eei ) . in two dimensions , in particular , the correction to the conductivity is logarithmic for both the wl and eei correction . the argument of the logarithm contains the ratio of two length scales . the first is the mean free path , @xmath0 , which sets the microscopic scale , beyond which the system behaves diffusively . the second length scale differs in the two cases . for wl it is @xmath1 , the scale over which inelastic scattering starts to destroy the interference effects . for eei it is usually given by the thermal length @xmath2 . in a diffusive system , all length scales correspond to characteristic times : the elastic scattering time @xmath3 , the dephasing time @xmath4 , and the thermal time @xmath5 . in general , dephasing occurs either as a result of the interaction of the system with the external environment or as a consequence of the internal electron interactions . for example , it is known that an ac - field suppresses the wl . on the other hand , while it is clear that inelastic scattering contributes to dephasing , the exact way this happens is by far less obvious as witnessed by the recent hot debate in the literature @xcite . natural questions to ask are : how does the dephasing time @xmath6 that enters the wl correction and cuts off the logarithmic singularity depend on inelastic scattering and on the external environment ? does dephasing also affect the eei correction ? the two issues need to be addressed together if one wants to understand the experimental data in detail . although one can find in the literature discussions of both these issues , there seems to exist no unified discussion of them . it is one of the aims of the present paper to fill this gap . it was first noted by schmid@xcite that the inelastic quasiparticle scattering time is enhanced in the presence of disorder . the dephasing time , which controls the wl correction was initially assumed to be identical to the inelastic quasiparticle scattering time in a disordered fermi - liquid @xcite . according to this analysis , the inverse dephasing time was assumed to be @xmath7 in 2d , thus predicting a violation of the fermi - liquid behavior at low temperatures . however , altshuler , aronov , and khmelnitsky@xcite ( hereafter referred to as aak ) , by means of a semi - classical path - integral approach to the wl correction , were able to calculate the dephasing time directly and predicted an inverse dephasing time proportional to @xmath8 , in contrast to ref.@xcite . some time later fukuyama and abrahams@xcite ( hereafter indicated as fa ) , re - examined the problem in terms of standard diagrams and calculated the `` mass '' term that develops in the particle - particle propagator . they found the same result as ref.@xcite . the origin of the discrepancy of the aak and fa results lies in a genuine ambiguity in the definition of the dephasing time itself . a review of the attempts to clarify this issue made at the time@xcite may be found in @xcite . the issue was further complicated from the fact that a dephasing time also appears in the particle - hole channel@xcite . the mass term in the particle - hole propagator turned out to coincide with that found by fa in the particle - particle propagator . more recently inelastic scattering and dephasing have been addressed from a general point of view by stern et al @xcite and in connection with disordered mesoscopic systems by various groups@xcite , in all cases confirming the aak result . furthermore , during the last couple of years , various experimental groups have observed a saturation of the dephasing time at low temperatures @xcite . usually this saturation has been related to heating effects or to the presence of magnetic moments . in ref.@xcite , however , these possibilities have been excluded experimentally , and the observed saturation seems to be in contrast to the available theories . if the observed saturation of the dephasing time is due to an intrinsic mechanism of disordered electron systems , this will have dramatic consequences on the localization theory , such as preventing an insulating ground state . the above consideration led to a fresh re - examination of the theory whose historical development has been sketched above . in particular , such an intrinsic mechanism has been claimed to be discovered in ref.@xcite . however in refs.@xcite this new theoretical result has been questioned and at the same time in ref.@xcite a conventional mechanism has been suggested as a possible explanation of the experimentally observed saturation of the dephasing time . the authors of ref.@xcite concluded that there is no need to revise the existing theory of the dephasing time in wl . while we completely agree with ref.@xcite on this latter point , we think that the interpretation of the experiments is not yet settled and , especially , the effect of dephasing on the eei correction is not clear . in this paper we discuss dephasing in the particle - hole channel , and in parallel we clarify the reason for the discrepancy in the aak and fa calculations . the difference between the results may be traced back to a different definition of the dephasing time . in the fa case , the dephasing time is assumed to be the mass of the particle - particle propagator as due to the self - energy corrections . in this type of corrections , one does not include diagrams which connect the upper and the lower electron lines entering the particle - particle propagator . in the aak approach these diagrams , i.e. the vertex corrections , are taken into account . the inclusion of these vertex diagrams in the diagrammatic approach of fa leads to the aak result@xcite . in the particle - hole channel , on the other hand , we find that vertex corrections are negligible and the dephasing is entirely determined by the self - energy . to see this we will adopt a real time - formulation based on the keldysh technique which allows us to discuss wl and eei corrections in a unified way . furthermore , in the real - time formulation non - linear effects , for example those due to an external field , can be incorporated more easily . in order to address the issue of how dephasing arises in the particle - particle and in the particle - hole channels , it is instructive to start considering the situation of an external field . this analysis , besides providing a relatively simple physical situation to analyse has also a genuine experimental interest . for example , there exists no satisfactory theoretical explanation for the non - linear field effects observed in refs.@xcite . to this end we will devote a substantial part of our analysis to the nonlinear effects on wl and eei corrections for which we shall find an unexpected difference in their dependence on a static electric field . the plan of the paper is the following . in the next section , by means of the keldysh formalism , we derive an expression for the additional current in a disordered conductor due to both the wl and eei corrections . the formulae obtained are valid in the presence of an arbitrary time - dependent external field . this result allows us , in section iii , to discuss the wl and eei corrections in the presence of both a dc and an ac electric field . we show that , in the case of a dc field , the eei correction is suppressed , in contrast to what happens for the case of wl correction . an ac field , on the other hand , suppresses both the wl and eei correction , but with a different dephasing time . in section iv , we will review the fa calculation of the inelastic scattering time in two dimensions and show how the aak result may be obtained from it . in section v the path integral approach to the dephasing time of aak is briefly outlined and connection is made with the diagrammatic analysis . special attention is paid to how the cancellation of the infrared singularity occurs . we extend this approach to a calculation of the dephasing time in the particle - hole channel . finally , section vi is devoted to some discussion of the experimental results . in appendix a we give technical details concerning the calculation of the dephasing time in the particle - hole channel .

we discuss in a unifying way both weak localization and interaction effects in disordered systems . this allows us to show how dephasing arises both in the particle - particle channel ( weak localization ) and in the particle - hole channel ( interaction effect ) . we find that the latter may be suppressed by a static electric field , in contrast to weak localization . we show that different dephasing times appear in the particle - particle and particle - hole channels . finally we comment on recent experiments .

the calculation of the dephasing time in electron systems is presented . by means of the keldysh formalism we discuss in a unifying way both weak localization and interaction effects in disordered systems . this allows us to show how dephasing arises both in the particle - particle channel ( weak localization ) and in the particle - hole channel ( interaction effect ) . first we discuss dephasing by an external field . besides reviewing previous work on how an external oscillating field suppresses the weak localization correction , we derive a new expression for the effect of a field on the interaction correction . we find that the latter may be suppressed by a static electric field , in contrast to weak localization . we then consider dephasing due to inelastic scattering . the ambiguities involved in the definition of the dephasing time are clarified by directly comparing the diagrammatic approach with the path - integral approach . we show that different dephasing times appear in the particle - particle and particle - hole channels . finally we comment on recent experiments .

1605.01504

r

in its ground electronic state c@xmath1 has a fairly strong bond @xcite . the equilibrium bond distance of the state at 1.2425 is short for a double bond ( considerably shorter than the c = c bond of ethylene at @xmath151(c = c ) = 1.331 ) , but long for a triple bond ( in c@xmath1h@xmath1 @xmath151(cc ) = 1.203 ) . this also means that the dissociation energy of the state is large , in fact more than 50,000 @xmath4 . compared to this , the energy differences among the several feasible asymptotes comprised by the low - lying @xmath21p , @xmath22d , and @xmath22s states of the c atom are relatively minor . furthermore , the structure of the molecular orbitals ( mo ) of c@xmath1 is such that a large number of low - energy singlet , triplet , and quintet valence states are feasible and many of them are part of experimentally measurable rovibronic transitions ( see table 1 ) . in the state the leading valence electron configuration is ( core)@xmath152 . by promoting electrons from the weakly antibonding @xmath153 and the strongly bonding @xmath154 mos and populating the @xmath155 mo a large number of electronic states arise . fortunately , for obtaining proper , temperature - dependent ideal - gas thermochemical quantities up to about 4,000 k , it is sufficient to consider 9 electronic states , four singlet , four triplet , and one quintet states ( see table 4 ) . as mentioned already , all these lowest - energy electronic states correlate with the c(@xmath21p ) + c(@xmath21p ) separated - atom limit . not too surprisingly for such a simple molecule , a large number of electronic structure computations are available for c@xmath1 in the literature @xcite . there are several issues which make the electronic structure computations extremely challenging for c@xmath1 . first , there is a quasi - degeneracy of the fully occupied @xmath156 and the empty @xmath157 mos , explaining some of the unusual characteristics of the excited electronic states of c@xmath1 . second , the existence of several low - lying excited electronic states leads to the occurrence of a considerable number of avoided crossings among the pecs as the cc distance is varied . third , as pointed out by @xcite based on full configuration interaction ( fci ) computations , at least in the cases of the x , b , and b@xmath26 states , methods based on an unrestricted hartree fock ( uhf ) reference provide correct but methods based on a restricted hf ( rhf ) reference provide incorrect results . fourth , one must account for the strong multireference character of the electronic states and the near degeneracies changing rapidly along the cc distance . fifth , rather large atom - centered , fixed - exponent gaussian basis sets are required for the correct and converged description of the valence states . these difficulties explain why this deceptively simple diatomic molecule is still one of the favorites of developers of modern wavefunction - based electronic structure techniques @xcite . using ci methods , 27 bound valence states of c@xmath1 were computed by @xcite . @xcite obtained results for all 62 electronic states in the valence manifold , including weakly bound and repulsive ones . @xcite obtained results for rydberg states , as well . electronic states with @xmath158 values up to 75,000 @xmath4 ( this is in fact the f @xmath11 state ) have been studied but for the present investigation the energy cut - off value was chosen to be 35,000 @xmath4 . this limits the number of singlet , triplet , and quintet states to 4 , 4 , and 1 , respectively , 9 states altogether . none of the higher - lying states will be considered in what follows . note that rkr potential curves are given for several singlet , triplet , and quintet states in @xcite . in this study , the so - called @xmath159 values obtained for the electronic states define directly the lowest measurable term energies of the states ( thus , they may not necessarily correspond to @xmath160 ) . it is not that simple to determine the @xmath158 values of the excited electronic states of c@xmath1 , as these are not measurable quantities . this can only be achieved if the zero - point vibrational energy ( zpve ) of all the states is determined . however , since all states are coupled in the duo computations , these do not come directly from our joint marvel and duo analysis . in particular , for the singlet @xmath161 and @xmath162 electronic states there are no transitions to @xmath160 upper rovibronic states . llrrrclcl [ tab : vib_singletfirst ] x @xmath126 & 1 & 1829.15 & 1827.4849(2 ) & 1827.486(5 ) + & 2 & 3630.35 & 3626.6835(2 ) & 3626.681(10 ) + & 3 & 5402.78 & 5396.6892(4 ) & 5396.686(9 ) + & 4 & 7145.40 & 7136.3507(6 ) & 7136.350(6 ) + & 5 & 8856.84 & 8844.1241(11 ) & 8844.124(7 ) + & 6 & 10536.37 & 10517.9659(39 ) & 10517.950(7 ) + & 7 & 12178.69 & 12154.9615(29 ) & 12154.961(6 ) + & 8 & 13783.76 & 13751.3944(38 ) & 13751.393(3 ) + & 9 & 15346.69 & 15302.8952(46 ) & 15302.893(7 ) + b@xmath163 & 1 & & 1420.4850(4 ) & 1420.488(9 ) + & 2 & & 2840.0048(4 ) & + & 3 & & 4261.0686(4 ) & 4261.071(1 ) + & 4 & & 5681.5113(6 ) & + e @xmath126 & 1 & & & 1592.316(200 ) + lrrrllrrr [ tab : vib_singletsecond ] a @xmath164 & 1 & 1 & 1584.008(4 ) & & b @xmath165 & 1 & 2 & 1384.440(2 ) + & 2 & 1 & 3143.805(5 ) & & & 2 & 2 & 2746.010(9 ) + & 3 & 1 & 4679.323(6 ) & & & 3 & 2 & 2746.010(9 ) + & 4 & 1 & 6190.503(7 ) & & & 4 & 2 & 5400.804(8 ) + & 5 & 1 & 7677.273(4 ) & & & 5 & 2 & 6694.148(10 ) + & 6 & 1 & 9139.523(9 ) & & & 6 & 2 & 7964.836(3 ) + & 7 & 1 & 10577.184(13 ) & & & 7 & 2 & 9214.047(3 ) + & 8 & & & & & 8 & 3 & 10446.668(5 ) + & 9 & 1 & 13378.377(1 ) & & & + & 10 & 1 & 14741.688(1 ) & & & + & 11 & 1 & 16079.978(7 ) & & & + & 12 & 1 & 17393.116(8 ) & & & + & 13 & 1 & 18680.944(7 ) & & & + & 14 & 1 & 19943.297(7 ) & & & + & 15 & 1 & 21179.968(7 ) & & & + & 16 & 1 & 22390.754(7 ) & & & + lrrr [ tab : vib_triplet ] a @xmath166 & 1 & 1617.985(10 ) + & 2 & 3212.620(9 ) + & 3 & 4783.940(5 ) + & 4 & 6331.973(1 ) + & 5 & 7855.893(100 ) + & 7 & 10835.820(1 ) + & 8 & 12290.393(1 ) + & 9 & 13721.623(5 ) + & 10 & 15129.564(1 ) + & 11 & 16514.369(1 ) + b @xmath167 & 1 & 1448.103(8 ) + & 2 & 2874.028(2 ) + & 3 & 4277.927(1 ) + c @xmath168 & 1 & 2031.833(8 ) + & 2 & 4034.776(7 ) + & 3 & 6007.745(8 ) + & 5 & 9859.060(1 ) + & 6 & 11734.338(10 ) + & 7 & 13573.601(1 ) + d @xmath24 & 1 & 1753.500(7 ) + & 2 & 3469.636(10 ) + & 3 & 5145.247(6 ) + & 4 & 6776.153(1 ) + & 5 & 8356.139(7 ) + & 6 & 9880.362(7 ) + & 7 & 11337.658(1 ) + & 8 & 12722.024(1 ) + & 9 & 14025.567(1 ) + & 10 & 15245.388(2 ) + figure [ fig : marvelels ] shows all marvel term values below 35,000 @xmath4 for four singlet and four triplet states , where @xmath169 @xmath4 has been subtracted from the computed energies to make the figure clearer : this means that near - horizontal sequences of levels for a particular electronic state are all associated with something one could call a single vibrational level . figure [ fig : marvelels ] shows that the largest total angular momentum quantum numbers , @xmath170 , are 74 , 75 , 86 , and 70 for the , , , and states , respectively . as expected , as the vibrational excitation increases , the @xmath171 value usually decreases . finally , note that the coverage of rovibronic levels up to 35,000 @xmath4 from experiment is not complete ; assuming rigid rotation , data up to about @xmath172 is needed to have full coverage of the energy levels required during the thermochemical analysis . this coverage is provided in this study by duo energy levels ( _ vide infra _ ) . due to the strength of the cc bond in all the electronic states studied , the vibrational fundamental is substantial in almost all the bound electronic states of c@xmath1 . in fact , for the ground electronic state the harmonic wavenumber is close to 2,000 @xmath4 , a high value for a relatively heavy molecule . thus , the number of vibrational states is not that high , despite the large dissociation energy . in particular , @xcite computed 57 , 54 , 49 , and 36 bound vibrational levels for the , , , and b@xmath26 @xmath124 states , respectively . the number of vibrational levels characterized by our marvel analysis is considerably smaller , only 9 , 16 , 8 , and 3 , respectively . the vibrational energies presented for the triplet electronic states given in table 7 can not be compared easily with existing literature values , since the marvel values are for a specific spin component of a rovibronic energy level . the largest `` vibrational fundamental '' ( @xmath160 ) corresponding to the electronic states studied here is that of the c @xmath168 state , at 2031.833 @xmath4 . consequently , this state must have the strongest cc bond . the rotational constant of c@xmath1 for the state is relatively small , about 1.81 @xmath4 . this results in a large number of rotational states for each vibrational level . as part of this study , duo results were obtained up to @xmath172 . they served to check whether a marvel energy level is viable or not as well as they were generated to help the thermochemical analysis of this study ( _ vide infra _ ) . the lowest missing marvel energy level is at 7,800 @xmath4 ; up to this energy the coverage is complete . as figure [ fig : marvelrovib ] shows , as the energy increases there are more and more experimentally unknown energy levels . the coverage drops below 10% at about 30,000 @xmath4 . it is interesting to note how close some of the rovibrational energy differences are to each other . take the state as an example . the @xmath173 energy difference for @xmath160 is 1617.985 @xmath4 . the highly similar energy differences for the different spin components ( @xmath174 ) , ( @xmath175 ) , ( @xmath176 ) , ( @xmath177 ) , and ( @xmath178 ) , are 1618.063 , 1617.941 , 1617.985 , 1617.902 , and 1617.831 , respectively . the reason behind this observation is that each spin component of each vibrational level of the state has a slightly different effective value for their rotational constant due to both electronic and vibrational effects , and these energy differences include rotational energies . the first - principles duo energies , where such interactions are taken explicitly into account , results in similar energy differences .

this well - determined energy difference should facilitate observations of singlet triplet intercombination lines which are thought to occur in the interstellar medium and comets . the large number of highly accurate and clearly labeled transitions that can be derived by combining marvel energy levels with computed temperature - dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements .

the carbon dimer , thec molecule , is ubiquitous in astronomical environments . experimental - quality rovibronic energy levels are reported forc , based on rovibronic transitions measured for and among its singlet , triplet , and quintet electronic states , reported in 42 publications . the determination utilizes the measured active rotational - vibrational energy levels ( marvel ) technique . the 23,343 transitions measured experimentally and validated within this study determine 5,699 rovibronic energy levels , 1,325 , 4,309 , and 65 levels for the singlet , triplet , and quintet states investigated , respectively . the marvel analysis provides rovibronic energies for six singlet , six triplet , and two quintet electronic states . for example , the lowest measurable energy level of the state , corresponding to the total angular momentum quantum number and the spin - multiplet component , is 603.817(5 ) . this well - determined energy difference should facilitate observations of singlet triplet intercombination lines which are thought to occur in the interstellar medium and comets . the large number of highly accurate and clearly labeled transitions that can be derived by combining marvel energy levels with computed temperature - dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements . the experimental rovibronic energy levels , augmented , where needed , with _ ab initio _ variational ones based on empirically adjusted and spin - orbit coupled potential energy curves obtained using the duo code , are used to obtain a highly accurate partition function , and related thermodynamic data , forc up to 4,000 k. llll singlet & phillips & & + & mulliken & & + & _ herzberg f _ & f & + & bernath b & & + & bernath b & b & + & _ deslandres dazambuja _ & & + & _ messerle krauss _ & c & + & freymark & & + & _ goodwin cool a _ & 1 a & + & _ goodwin cool b _ & 1 b & + triplet & ballik ramsay & & + & swan & & + & fox herzberg & e & + & _ herzberg f _ & f & + & _ herzberg g _ & g & + & krechkivska schmidt & 4 a & + & duck & & + & _ kable schmidt _ & e & + quintet & radi bornhauser & & + intercombination & triplet - singlet & & + & quintet - triplet & & + & singlet - triplet & & + + [ tab : bands ] c showing the bands considered in this work . the dashed lines represent observed but unnamed intercombination bands.,height=604 ]

1605.01504

i

this study utilizes the marvel technique to accurately determine close to 6,000 experimental rovibronic energies of @xmath0c@xmath1 for six singlet , six triplet , and two quintet electronic states , including the eight lowest valence states which gives coverage up to 35 000 @xmath4 . we survey all available laboratory high - resolution spectroscopic studies to provide input data for this process , resulting in 23,343 transitions connecting the 14 electronic states . while there are many spectroscopic studies available , in fact 42 were analyzed to yield the transitions analyzed , and there has been significant recent activity including the identification of several new band systems , there are also surprising gaps . for example , there is a detailed , fully rovibronically - resolved study of the deslandres dazambuja ( @xmath5 ) band system for @xmath125c@xmath1 @xcite , but even a century after the original observation of this band @xcite there is no available high - resolution study for @xmath0c@xmath1 . the recent observation of singlet triplet intercombination bands by @xcite helped us to achieve to link all rovibronic levels of @xmath0c@xmath1 into a single huge component within its experimental spectroscopic network ; thus , individual intercombination lines can now be predicted accurately using the results of our study . this is a significant step towrd the astronomical detection of these transitions @xcite . to further aid this work and other astronomical studies involving c@xmath1 , a full rovibronic line list for @xmath0c@xmath1 is currently being constructed using the variational code duo by @xcite , as part of the exomol project @xcite . as to now , the full set of marvel results comprising a file of validated transition frequencies and a file containing the resulting rovibronic energy levels are given in the supplementary information to this paper . the highly accurate but limited set of experimental ( marvel ) energy levels augmented with the much less accurate but much more complete set of duo energy levels has been used to compute ideal - gas thermochemical functions for @xmath0c@xmath1 up to 4,000 k. the accuracy of the partition function is better than 0.1% even at the highest temperatures , considerably exceeding the accuracy of all previous studies . this assures that the accuracy of the present isobaric heat capacity of @xmath0c@xmath1 is significantly better than that of any previous study .

experimental - quality rovibronic energy levels are reported forc , based on rovibronic transitions measured for and among its singlet , triplet , and quintet electronic states , reported in 42 publications . the 23,343 transitions measured experimentally and validated within this study determine 5,699 rovibronic energy levels , 1,325 , 4,309 , and 65 levels for the singlet , triplet , and quintet states investigated , respectively . the marvel analysis provides rovibronic energies for six singlet , six triplet , and two quintet electronic states . the experimental rovibronic energy levels , augmented , where needed , with _ ab initio _ variational ones based on empirically adjusted and spin - orbit coupled potential energy curves obtained using the duo code , are used to obtain a highly accurate partition function , and related thermodynamic data , forc up to 4,000 k. llll singlet & phillips & & + & mulliken & & + & _ herzberg f _ & f & + & bernath b & & + & bernath b & b & + & _ deslandres dazambuja _ & & + & _ messerle krauss _ & c & + & freymark & & + & _ goodwin cool a _ & 1 a & + & _ goodwin cool b _ & 1 b & + triplet & ballik ramsay & & + & swan & & + & fox herzberg & e & + & _ herzberg f _ & f & + & _ herzberg g _ & g & + & krechkivska schmidt & 4 a & + & duck & & + & _ kable schmidt _ & e & + quintet & radi bornhauser & & + intercombination & triplet - singlet & & + & quintet - triplet & & + & singlet - triplet & & + + [ tab : bands ] c showing the bands considered in this work .

the carbon dimer , thec molecule , is ubiquitous in astronomical environments . experimental - quality rovibronic energy levels are reported forc , based on rovibronic transitions measured for and among its singlet , triplet , and quintet electronic states , reported in 42 publications . the determination utilizes the measured active rotational - vibrational energy levels ( marvel ) technique . the 23,343 transitions measured experimentally and validated within this study determine 5,699 rovibronic energy levels , 1,325 , 4,309 , and 65 levels for the singlet , triplet , and quintet states investigated , respectively . the marvel analysis provides rovibronic energies for six singlet , six triplet , and two quintet electronic states . for example , the lowest measurable energy level of the state , corresponding to the total angular momentum quantum number and the spin - multiplet component , is 603.817(5 ) . this well - determined energy difference should facilitate observations of singlet triplet intercombination lines which are thought to occur in the interstellar medium and comets . the large number of highly accurate and clearly labeled transitions that can be derived by combining marvel energy levels with computed temperature - dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements . the experimental rovibronic energy levels , augmented , where needed , with _ ab initio _ variational ones based on empirically adjusted and spin - orbit coupled potential energy curves obtained using the duo code , are used to obtain a highly accurate partition function , and related thermodynamic data , forc up to 4,000 k. llll singlet & phillips & & + & mulliken & & + & _ herzberg f _ & f & + & bernath b & & + & bernath b & b & + & _ deslandres dazambuja _ & & + & _ messerle krauss _ & c & + & freymark & & + & _ goodwin cool a _ & 1 a & + & _ goodwin cool b _ & 1 b & + triplet & ballik ramsay & & + & swan & & + & fox herzberg & e & + & _ herzberg f _ & f & + & _ herzberg g _ & g & + & krechkivska schmidt & 4 a & + & duck & & + & _ kable schmidt _ & e & + quintet & radi bornhauser & & + intercombination & triplet - singlet & & + & quintet - triplet & & + & singlet - triplet & & + + [ tab : bands ] c showing the bands considered in this work . the dashed lines represent observed but unnamed intercombination bands.,height=604 ]

1207.3070

i

in cataclysmic variable stars ( cvs ) , a white dwarf primary star accretes matter by way of roche lobe overflow from a binary companion , which resembles a main - sequence star . the variety of cv behaviors leads to a complicated taxonomy @xcite . many cvs undergo dwarf nova outbursts , thought to be caused by accretion disk instabilities which greatly increase the rate at which matter moves inward in the disk . other cvs , called novalike variables , remain in a bright state for years at a time . in still others , called am her stars or polars , the matter that is transferred becomes entrained in a strong white - dwarf magnetic field , and is funneled directly onto the white dwarf s magnetic pole . the main driver of cv evolution is thought to be a gradual loss of orbital angular momentum . this causes the roche critical lobe of the secondary star to shrink , leading to a shortening of the orbital period @xmath0 , and driving mass transfer on long ( gyr ) timescales . the mechanisms by which angular momentum is lost are not fully understood . it is often supposed that magnetic braking of the secondary star predominates at longer periods ( @xmath1 3 hr ) , and that magnetic braking becomes inefficient at short period , so that gravitational radiation predominates . around @xmath0 = 70 min , the secondary becomes degenerate and its radius begins to _ increase _ with mass , leading to a slow _ increase _ in the orbital radius . this turnaround is often called the _ period bounce _ , even though it is thought to take place very slowly . the histogram of cv orbital periods shows a significant dip at roughly 2 hr @xmath2 3 hr , known as the _ gap _ @xcite . this is often explained as follows . as the secondary loses mass , its thermal timescale increases to become comparable to the time for the orbit to evolve , with the result that the secondary exceeds its equilibrium radius . at about three hours , the secondary becomes fully convective , reducing the efficiency of magnetic braking . as the orbital evolution slows , the secondary detaches from its roche lobe , shutting down mass transfer . the detached system continues to evolve to shorter periods , crossing the gap and eventually re - establishing contact with the roche lobe near @xmath3 hr . while the mechanism by which this happens is somewhat speculative , @xcite shows that a discontinuity in the secondary stars radii occurs across the gap . in a steady state , the number of stars with a given @xmath0 should be inversely proportional ( roughly ) to @xmath4 , the rate at which the period changes . if @xmath4 really is very slow at short periods , then there should be a large population of short - period cvs , and the gradual turnaround at the period bounce around 70 minutes should lead to a ` spike ' in the distribution @xcite . efforts to confront theories such as this with observation have often been frustrated , because the sample of known cvs is incomplete in ways that are difficult to quantify . the discovery channels for cvs include the following : ( 1 ) dwarf nova outbursts are conspicuous they last for days or weeks and typically have amplitudes of several magnitudes . ( 2 ) nearly all cvs have unusual colors compared to normal stars , most conspicuously ultraviolet excesses arising from accretion processes or ( in some cases ) the underlying white dwarf . ( 3 ) with the exception of some novalike variables and dwarf novae near the peak of outburst , nearly all cvs show emission lines , especially in the balmer sequence ; these can be strong enough to be noticed in surveys such as iphas @xcite . ( 4 ) a great many other cvs have been discovered as optical counterparts of x - ray sources . ( 5 ) cvs at minimum light can be rather faint ( @xmath5 ) , and a small handful have turned up in proper motion surveys . new , large samples of cvs with consistent selection criteria are potentially useful for clarifying issues such as the space density and orbital period distribution of these objects . because the colors of cvs overlap those of quasars , the sloan digital sky survey ( sdss ) turned up a large number of spectroscopically confirmed cvs ( @xcite ; hereafter referred to as szkodyi - viii ) . @xcite compiled orbital periods for 137 of these ; with the sdss sample , they were finally able to discern the long - predicted period spike . like the sdss , the catalina real time survey ( crts ; * ? ? ? * ) has discovered many new cvs . while the sdss cvs were originally selected by color they were chosen for spectroscopy largely because their colors overlap those of quasars the crts selects entirely by variability . briefly , the crts surveys most of the accessible sky at galactic latitudes @xmath6 and declination @xmath7 every lunation , using a 0.7 m schmidt telescope in the catalina mountains near tucson , arizona . they search for variability using a master catalog that reaches to @xmath8 . objects that show abrupt outbursts of @xmath9 mag amplitude lasting less than few weeks are classified as likely cvs , making the crts a prolific source of dwarf novae in particular . the crts maintains a catalog of `` confirmed / likely '' cvs on the world wide web . we downloaded this catalog on 2012 march 7 , when it contained 584 objects , and used this data set for the present analysis . the crts cv sample is of great interest because of its depth and selection criteria , so it is a natural choice for follow - up studies similar to @xcite . @xcite describe high - speed photometry of 20 objects , mostly from the crts , and give orbital periods for 15 , including two eclipsing dwarf novae and two superhumpers . only two of their sample had periods longer than the 2 - 3 hour period gap . the period distribution of their sample also showed the spike just above the turnaround . in addition , they found that dwarf novae with more recorded outbursts tended to have longer orbital periods than those with fewer outbursts . here , we report on followup spectroscopy and photometry of the crts cvs listed in table [ tab : star_info ] . most of the crts cvs are too faint for us to follow up , so we selected this sample based largely on apparent brightness . operational considerations , such as the ease with which observations could be interleaved other programs , the nearness of the target to opposition at midnight , and ( for radial velocity targets ) the strength and tractability of emission and absorption spectra also entered into target selection . we find spectroscopic periods for 8 objects , one of which was independently measured by @xcite . in addition , we obtained exploratory spectra of 28 others , largely to assess their feasibility for radial - velocity studies . we also obtained standardized magnitudes for 37 objects ( 17 of which also have spectra ) . _ plan of this paper . _ we describe our equipment and techniques in section [ sec : techniques ] . table [ tab : spectro_summary ] summarizes all of our spectroscopy . in section [ sec : explore ] we describe the spectra of the 28 objects for which we have only a only a quick spectrum . the eight objects for which we have radial velocity time series are discussed in section [ sec : rvs ] ; table [ tab : velocities ] gives the velocities , and table [ tab : parameters ] lists parameters for sinusoidal fits to the velocity time series . table [ tab : photometry ] gives magnitudes and colors of objects for which we have standardized photometry . finally , in section [ sec : statistics ] we consider how the crts cv samples overlaps with other lists of cvs , discuss the apparent selection biases of crts and the implications for the cv population in general .

the catalina real time survey ( crts ) has found over 500 cataclysmic variable ( cv ) candidates , most of which were previously unknown . we report here on followup spectroscopy of 36 of the brighter objects . one object appears to be a flare star , while another has a spectrum consistent with a cv but lies , intriguingly , at the center of a small nebulosity . we measured orbital periods for eight of the cvs , and estimated distances for two based on the spectra of their secondary stars . most of our new orbital periods are shortward of the so - called period gap from roughly 2 to 3 hours . by considering the cross - identifications between the catalina objects and other catalogs such as the sloan digital sky survey we speculate that this is a consequence of the survey cadence .

the catalina real time survey ( crts ) has found over 500 cataclysmic variable ( cv ) candidates , most of which were previously unknown . we report here on followup spectroscopy of 36 of the brighter objects . nearly all the spectra are typical of cvs at minimum light . one object appears to be a flare star , while another has a spectrum consistent with a cv but lies , intriguingly , at the center of a small nebulosity . we measured orbital periods for eight of the cvs , and estimated distances for two based on the spectra of their secondary stars . in addition to the spectra , we obtained direct imaging for an overlapping sample of 37 objects , for which we give magnitudes and colors . most of our new orbital periods are shortward of the so - called period gap from roughly 2 to 3 hours . by considering the cross - identifications between the catalina objects and other catalogs such as the sloan digital sky survey , we argue that a large number of cataclysmic variables remain uncatalogued . by comparing the crts sample to lists of previously - known cvs that crts does not recover , we find that the crts is biased toward large outburst amplitudes ( and hence shorter orbital periods ) . we speculate that this is a consequence of the survey cadence .

nucl-ex0002006

i

beginning in the 1970 s significant advances in the understanding of nuclear multifragmentation were made possible with the advent of high statistics inclusive experiments . typically , only one intermediate mass fragment ( @xmath0 ) was detected per event . from these inclusive studies came the first evidence that intermediate mass fragments ( imfs ) were associated with a simultaneous multi - body breakup of a system which had undergone expansion . a study of the fragment mass yield distribution obtained in an inclusive gas jet experiment conducted at fermilab contained the first indication that nuclear multifragmentation might be related to critical phenomena normally observed in macroscopic systems @xcite . the purdue group was the first to make the suggestion that the observed power law in the fragment yield distribution might result from a system whose excitation energy was comparable to its total binding energy @xcite . the exponent of the power law was @xmath1 , within the range expected for a system near its critical point . the presence of the power law and the value of the exponent , coupled with the strong similarity of the nuclear and van der waals potentials , led the purdue group to suggest that multifragmentation of nuclei might be analogous to a fluid undergoing a continuous phase transition from a liquid to a gas . furthermore , the fisher droplet model ( fmd ) @xcite-@xcite , used to describe condensation in a fluid system near its critical point , after modification for nuclear physics effects , was capable of describing the isotopic yields of 50 fragments with one set of parameters @xcite , @xcite . the temperature of the system was determined to be about 5 mev @xcite , a reasonable value considering that the average binding energy per nucleon in a nucleus is approximately 8 mev . the success of this approach reinforced the notion that multifragmentation was both a thermal process and that it was related to critical phenomena . with the advent of exclusive experiments capable of detecting all of the charged reaction products , the possibility of studying multifragmentation on an event - by - event basis became a reality . high statistics exclusive experiments in which the fragmenting system is characterized according to its nucleon number and excitation energy permit both the correlation of dynamical and statistical information and the study of fluctuations in experimental observables . fluctuations are central to all critical phenomena , and indeed , such fluctuations are apparent in exclusive multifragmentation data . in this paper , the focus will be on the statistical signals of multifragmentation data observed in the eos experiment @xcite-@xcite . comparisons will be made with two other systems , one of which exhibits critical behavior and one of which does not . much of the pioneering work in understanding the statistical aspects of multifragmentation has been performed by campi @xcite-@xcite and mekjian @xcite-@xcite . both efforts have compared multifragmentation data to model systems in order to gain some insight into the nuclear breakup process . in this paper , many of the ideas suggested by these authors are followed and applied to both the eos data and the model systems in order to demonstrate which of the many suggested signals are useful for the identification of critical behavior . a major goal of this paper is to present a comprehensive review of several methods proposed for detecting signals of critical phenomena in multifragmentation . it is tempting to compare the experimental data to dynamical models that attempt to describe nuclear multifragmentation . however , the task of modeling multifragmentation from the initial collision phase of the reaction to freeze - out has proven to be a daunting task . models that adequately describe the initial stage of the reaction @xcite-@xcite do not satisfactorily describe the fragment formation stage , in either statistical or dynamical aspects . likewise , the most successful models in describing the statistical properties of nuclear multifragmentation @xcite-@xcite , assume thermodynamic equilibrium , yet fail to adequately match the dynamical features of the data . molecular dynamical approaches , which have enjoyed considerable success in describing critical behavior in classical systems @xcite-@xcite , have not been conclusive in describing nuclear multifragmentation and at times have yielded contradictory results @xcite , @xcite . later studies suggested flaws in the application of molecular dynamical models to nuclear multifragmentation , therefore calling into question the conclusions drawn from the earlier studies @xcite . the most striking of the early theoretical efforts came from campi s analysis of a few hundred completely reconstructed emulsion multifragmentation events @xcite and the comparison of these data to clusters generated from a percolation calculation @xcite , @xcite . in this series of papers it was shown that the fragment distributions from multifragmentation bore a striking similarity to the cluster distributions from percolation lattices . this analysis provided strong evidence that multifragmentation was a statistical process which appeared to be related to critical phenomena . in this analysis another estimate of the exponent @xmath2 was made which agreed with the first measurements from the purdue group and several later analyses of various fragment distributions . in the early 1990 s the aladin group from gsi performed several multifragmentation experiments @xcite-@xcite . of particular importance was the `` rise and fall '' of multifragmentation . in one analysis the aladin group plotted the `` rise and fall '' curve of the production of imfs versus an observable related to the excitation energy of the reaction for several multifragmenting systems . with the appropriate scaling the data collapsed to a single curve suggesting that the multifragmenting systems retained no memory of the reaction entrance channel . this is expected for an equilibrated system . the results of some statistical analyses of multifragmentation data could be interpreted to suggest that multifragmentation is a sequential decay @xcite in contrast to the phase transition picture . the same sort of statistical analysis has also been applied to explicitly simultaneous models @xcite and produced results that were similar to those of multifragmentation data . thus those signals could be interpreted as evidence for either sequential or simultaneous multifragmentation @xcite . this last effort puts into focus the main question in this work : what type of analysis of the statistical aspects of a cluster distribution can provide the most insight into the nature of the mechanism which created the clusters ? specifically , can those systems which contain critical behavior be distinguished from those which do not ? it will be argued that this question has two answers . analysis of the _ insensitive _ features of the cluster distribution can not make the above mentioned distinction @xcite . however , an analysis of the _ sensitive _ features of the cluster distribution will be shown to provide deeper insight into the cluster production mechanism . this type of analysis has been previously reported for clusters resulting from nuclear multifragmentation @xcite-@xcite . note that the more generic term _ cluster _ will be used to refer to any composite of constituents , whether these be molecules of a fluid , nuclear fragments or percolation clusters . the method employed to address the above question is as follows . the same analysis is performed on the cluster distributions produced by three different systems . in one case , clusters are generated by randomly partitioning an integer . such one - dimensional partitioning does not posses critical behavior indicative of a continuous phase transition . in the second case , three - dimensional bond building percolation is used to produce clusters . percolation is well - known mathematical construct that possesses a continuous phase transition , _ i.e. _ a critical point . finally , the cluster distributions resulting from the multifragmentation of gold nuclei are analyzed . although it is not known , a priori , whether the nuclear multifragmentation bears any relation to critical phenomena , it will be seen that the analysis presented in this work yields suggestive results . this paper is organized as follows . in section ii a description of each system is presented . in section iii the fisher droplet model is reviewed . in section iv - a the insensitive signatures of the cluster distributions for all systems are examined . in section iv - b the sensitive signatures are examined . sections v and vi present possible corrections to the analysis of the multifragmentation data . finally , section vii discusses the conclusions reached upon the completion of the analyses in sections iv and v. throughout this paper the term _ continuous phase transition _ will be used instead of _ second order phase transition _ , the latter from the outdated ehrenfest theory of phase transitions @xcite .

the cluster distributions of different systems are examined to search for signatures of a continuous phase transition . in a system known to possess such a phase transition , both sensitive and insensitive signatures are present ; while in systems known not to possess such a phase transition , only insensitive signatures are present . it is shown that nuclear multifragmentation results in cluster distributions belonging to the former category , suggesting that the fragments are the result of a continuous phase transition .

the cluster distributions of different systems are examined to search for signatures of a continuous phase transition . in a system known to possess such a phase transition , both sensitive and insensitive signatures are present ; while in systems known not to possess such a phase transition , only insensitive signatures are present . it is shown that nuclear multifragmentation results in cluster distributions belonging to the former category , suggesting that the fragments are the result of a continuous phase transition . + pacs number(s ) : 25.70 pq , 64.60.ak , 24.60.ky , 05.70.jk

1006.1271

i

dilute magnetic semiconductors , such as ( ga , mn)as , form a class of materials with many outstanding properties@xcite and functionalities.@xcite a number of these result from the complex structure of the valence band , which hosts holes mediating magnetic order between spins localized on transition metal impurities . the strong force which lies behind this mechanism is the carrier - mediated exchange interaction . it gives the low - lying energy states of such a system the character of spin waves , which contribute to both its equilibrium ( e.g. spontaneous magnetization and curie temperature ) and nonequilibrium magnetic properties ( ferromagnetic resonance and relaxation).@xcite at the same time , it allows us to replace the atomic quantum - mechanical description of the system with the classical , continuous micromagnetic theory , where it appears in form of exchange stiffness.@xcite quite generally , micromagnetic properties of any ferromagnet are determined by the magnitudes of the exchange stiffness and magnetocrystalline anisotropy.@xcite the first describes the exchange energy associated with nonuniform distributions of local directions of magnetization . the other is the energy needed to change the total magnetization direction with respect to the crystal axes , which involves the competing crystal - field and spin - orbit interactions . while the main part of the exchange energy is isotropic , a consequence of its electrostatic origin , the relativistic spin - orbit coupling can create its small anisotropy , namely the dependence on the crystalline orientation of magnetization . in zinc - blende bulk crystals and thin layers with broken space inversion symmetries , it leads to many interesting effects , related to the anisotropic@xcite and dzyaloshinskii - moriya@xcite exchange , which have not been hitherto studied in ( ga , mn)as . since the total spin is no longer conserved , they are indispensable when considering any usage of spins for information storage and processing . the spin - wave spectrum and the isotropic exchange stiffness in bulk ( ga , mn)as were computed by knig , jungwirth and macdonald,@xcite and by brey and gmez - santos@xcite within the @xmath0 zener model employing the six - band @xmath2 hamiltonian,@xcite which neglects the inversion asymmetry specific to the zinc - blende lattice . it was found that the actual magnitude of the exchange stiffness is much greater when one takes into account the complex structure of the valence band , as compared to the case of a simple parabolic band.@xcite this , as well as the highly anisotropic fermi surface , were shown to explain@xcite why the mean - field approximation@xcite is so accurate in ( ga , mn)as . it was also found that the values of exchange and anisotropy energies obtained within the same formalism describe quantitatively@xcite the width of stripe domains in films with perpendicular magnetic anisotropy . more recently , bouzerar@xcite employed a self - consistent local random - phase approximation in order to evaluate the spectral density of spin - wave excitations in ga@xmath3mn@xmath4as . the magnitudes of spin - spin exchange integrals @xmath5 were obtained from first principles computations within the local spin - density approximation ( lsda ) and tight - binding linear muffin - tin orbital approach neglecting the spin - orbit interaction . the theory allows to treat disorder and thermal fluctuations , and shows that the calculated spectral density has well - defined maxima up to about one half of the relevant debye wave vector @xmath6 , where @xmath7 is the lattice constant . this made it possible to determine the spin - wave dispersion @xmath8 in the range @xmath9 , from which the magnitude of spin - wave stiffness was obtained.@xcite experimentally , potashnik _ et al._@xcite analyzed the temperature dependence of magnetization in a series of ga@xmath3mn@xmath10as samples , which provided the values of spin - wave stiffness from the @xmath11 bloch law . in later experiments , the stiffness was determined by examining spin precession modes excited by optical pulses@xcite and under ferromagnetic resonance conditions.@xcite the values obtained for some films with thickness greater than 120 nm , either as - grown@xcite or annealed,@xcite are in good agreement with those predicted by bouzerar.@xcite however , the values for thinner films@xcite or another series of annealed samples@xcite were about three times smaller . similarly small magnitudes of spin - wave stiffness were found by analyzing the domain structure of annealed ga@xmath12mn@xmath13as.@xcite the experimental works@xcite demonstrate that spectral positions of spin - wave resonances are strongly affected by the character of spin pinning at the sample borders . the same effect is caused by magnetic anisotropy changes along the growth direction , particularly strong at the film interface and surface.@xcite therefore , theoretical predictions concerning spin - wave excitations in both thick and thin layers may provide a useful guide to better understanding of magnetization dynamics in real samples . in this paper we investigate spin waves and related micromagnetic constants in ferromagnetic ( ga , mn)as , as described by the @xmath0 zener model.@xcite the validity of this model is supported by photoemission experiments@xcite and _ ab initio _ computations , in which the inaccuracies of the lsda are partly reduced by self - interaction.@xcite furthermore , the magnitude of low - temperature quantum corrections to conductivity indicates that in the concentration range relevant to ferromagnetism , the density of states assumes values expected for valence band holes.@xcite the carrier band is formed from @xmath14-type - like states of the gaas semiconductor structure , which are mostly built from the anion @xmath15 orbitals , but has a rather large @xmath16 component as the result of a strong @xmath17 interaction . we describe it by the @xmath1 tight - binding approximation for thin layers and , by applying periodic boundary conditions , for bulk crystals.@xcite our analysis of the anomalous hall effect in ( ga , mn)as in refs . and provides a thorough comparison of this method with other band structure models.@xcite one of its advantages is that it captures the inversion asymmetry of the zinc - blende lattice , which produces the dresselhaus spin splitting of the conduction band,@xcite and additionally the structure inversion asymmetry in thin layers , which creates the bychkov - rashba spin splitting.@xcite the growth - induced biaxial strain is included by changing the atoms arrangement , according to the strain tensor values : @xmath18 and @xmath19 , where @xmath20 is the strain - induced change of the lattice constant , and @xmath21 is the ratio of elastic moduli . also , the on - site energies of the @xmath16 orbitals depend linearly on the strain tensor values.@xcite the @xmath17 exchange coupling is modelled using the virtual crystal and mean - field approximations , while taking into account the appropriate weights of ga and as orbitals in the wavefunctions close to the center of the brillouin zone.@xcite in this way , spin polarization of individual mn moments is replaced by a molecular field , which creates a @xmath22-dependent zeeman - like splitting of the host bands . for heavy holes in the @xmath23 point it is given by @xmath24 , where @xmath25 is the fraction of cation site density @xmath26 substituted by mn forming a spin @xmath27 , and @xmath28 mevnm@xmath29 is the @xmath0 exchange integral.@xcite the validity of this approach can be questioned if the magnetic ions produce bound states,@xcite but the metallic character of the carrier states of interest here means that this does not occur due to many - body screening . at the same time we neglect the effect of this screening on potentials produced by magnetization fluctuations , which is justified as long as @xmath30 is smaller than the fermi energy , so that spin and charge density fluctuations are decoupled . a part of mn atoms form unintentional defects such as interstitials ( which can passivate single substitutional spins ) and antisites . both being double donors , they significantly lower the hole density , which can be partly remedied by removing the interstitials by post - growth annealing . the paper is arranged as follows . in sec . [ sec : theoreticalmodel ] we use the proposed variational - perturbation calculus to describe the system of lattice spins interacting via hole carriers , and its spin - wave excitations . in the micromagnetic theory , the system is described by the set of constants related to magnetocrystalline anisotropy and exchange energy . section [ sec : exchange ] provides quantitative results on the spin - wave stiffness expressed as the dimensionless parameter @xmath31 , comparing it between the @xmath2 and @xmath1 tight - binding models . in sec . [ subsec : magntemp ] we derive the spin - wave contribution to magnetization and curie temperature . section [ sec : experimental ] compares our theory to related experimental findings.@xcite the last section of the paper contains the summary of our work .

the collective behavior of spins in a dilute magnetic semiconductor is determined by their mutual interactions and influenced by the underlying crystal structure . hence , we begin with the atomic quantum - mechanical description of this system using the proposed variational - perturbation calculus , and then turn to the emerging macroscopic picture employing phenomenological constants . within this framework we also derive and discuss the spin - wave contribution to magnetization and curie temperature .

the collective behavior of spins in a dilute magnetic semiconductor is determined by their mutual interactions and influenced by the underlying crystal structure . hence , we begin with the atomic quantum - mechanical description of this system using the proposed variational - perturbation calculus , and then turn to the emerging macroscopic picture employing phenomenological constants . within this framework we study spin waves and exchange stiffness in the zener model of ( ga , mn)as , its thin layers and bulk crystals described by the tight - binding approximation . analyzing the anisotropic part of exchange , we find that the dzyaloshinskii - moriya interaction may lead to a cycloidal spin arrangement and uniaxial in - plane anisotropy of diagonal directions in thin layers , resulting in a surface - like anisotropy in thicker films . we also derive and discuss the spin - wave contribution to magnetization and curie temperature . our theory reconstructs the values of stiffness determined from the temperature dependence of magnetization , but reproduces only partly those obtained from analyzing precession modes in ( ga , mn)as thin films .

1006.1271

i

we have investigated spin waves and exchange stiffness in thin layers and bulk crystals of ferromagnetic ( ga , mn)as described by the @xmath1 tight - binding computational scheme . using the proposed variational - perturbation calculus , we have described the analyzed systems and their spin - wave excitations . their properties have been expressed by the phenomenological parameters of micromagnetic theory . we have noticed that the strength of ferromagnetic order described by the isotropic exchange stiffness is significantly amplified by the @xmath14-like character of carrier wave functions , as compared to the simple parabolic band model . furthermore , we have found various effects reflecting the tendency of the spin - orbit interaction to pervade every aspect of carrier dynamics . they produce the relativistic corrections to spin - waves given by the anisotropic exchange stiffness tensor and the asymmetric dzyaloshinskii - moriya coefficient . the latter accounts for the cycloidal spin arrangement and the accompanying uniaxial in - plane anisotropy of diagonal ( [ 110]/@xmath218 $ ] ) directions in thin layers , which can result in a surface - like anisotropy in thicker films . quantitative results on the stiffness constant have been provided in form of a normalized parameter , which assumes the value @xmath359 over a wide range of mn and hole concentrations in ( ga , mn)as . they agree with the previous @xmath2 calculations@xcite but predict significantly smaller values of spin - wave stiffness than those resulting from _ ab initio _ computations.@xcite the above theories have been applied to analyze the related experimental data on the stiffness parameter and the temperature dependence of magnetization . our basic theoretical model has not managed to reconstruct all stiffness values obtained by various experimental methods . in all cases we have reconstructed the entire range of magnetization dependence on temperature . at low temperatures , it can be understood within the the modified bloch law@xcite employing the values of spin - wave stiffness calculated by our model . at higher temperatures , the mean - field theory becomes justifiable owing to thermal decoherence and the long range character of spin - spin interactions . at the same time , we have reproduced only partly the stiffness values obtained from analyzing precession modes in ( ga , mn)as thin films . our results may allow to separate bulk and surface effects , as well as bring to light the pining phenomena and the role of inhomogeneities in experiments examining precession modes in slabs of carrier - controlled ferromagnetic semiconductors . a.w . acknowledges support by the president of polish academy of sciences and ec network semispinnet ( pitn - ga-2008 - 215368 ) , and t.d . acknowledges support from the european research council within the `` ideas '' 7th framework programme of the ec ( fundms advanced grant ) .

we study spin waves and exchange stiffness in the zener model of ( ga , mn)as , its thin layers and bulk crystals described by the tight - binding approximation . analyzing the anisotropic part of exchange , we find that the dzyaloshinskii - moriya interaction may lead to a cycloidal spin arrangement and uniaxial in - plane anisotropy of diagonal directions in thin layers , resulting in a surface - like anisotropy in thicker films . our theory reconstructs the values of stiffness determined from the temperature dependence of magnetization , but reproduces only partly those obtained from analyzing precession modes in ( ga , mn)as thin films .

the collective behavior of spins in a dilute magnetic semiconductor is determined by their mutual interactions and influenced by the underlying crystal structure . hence , we begin with the atomic quantum - mechanical description of this system using the proposed variational - perturbation calculus , and then turn to the emerging macroscopic picture employing phenomenological constants . within this framework we study spin waves and exchange stiffness in the zener model of ( ga , mn)as , its thin layers and bulk crystals described by the tight - binding approximation . analyzing the anisotropic part of exchange , we find that the dzyaloshinskii - moriya interaction may lead to a cycloidal spin arrangement and uniaxial in - plane anisotropy of diagonal directions in thin layers , resulting in a surface - like anisotropy in thicker films . we also derive and discuss the spin - wave contribution to magnetization and curie temperature . our theory reconstructs the values of stiffness determined from the temperature dependence of magnetization , but reproduces only partly those obtained from analyzing precession modes in ( ga , mn)as thin films .

1109.0154

i

the coma cluster which was observed with the x - ray imaging spectrometer ( xis ) onboard suzaku , was analyzed by the x - ray satellite in six pointings , centered on the x - ray peak and offset by west , , , , and . because of its low background , suzaku is the most sensitive x - ray satellite for observing k@xmath1 lines of fe in the intracluster medium . after obtaining accurate measurements of fe lines , we studied the temperature structure of the intracluster medium , searched for possible bulk - motions , and measured the fe abundance in the cluster . the spectra of each extracted region were well fitted by the single - temperature apec model , and the two- or three- temperature apec model did not improve @xmath2 . the temperatures derived from the observed ratios of k@xmath1 lines of h - like and he - like fe agree well with those from spectral fittings with the single - temperature apec model . because this line ratio is a strong function of plasma temperature , the observed consistency supports the accuracy of temperature measurements with suzaku , and constrains the temperature structure of icm . the observed values of the central energy of the he - like fe line of the center , , and offset regions are constant within 500 @xmath318 , which corresponds to the calibration error . because relative bulk velocities in the coma cluster are smaller than the sound velocity of the intracluster medium , 1500 km s @xmath3 , we can verify the derived total mass in a cluster on the basis of the hydrostatic icm equilibrium inside the offset region . significant bulk velocities were also not found in the offset region , which corresponds to the ngc 4839 subcluster . the results on the temperature and velocity structure suggest that the core of the coma cluster is in a fairly relaxed state . this is consistent with models in which the non - thermal electrons relevant to the radio halo are accelerated by the intracluster turbulence rather than large - scale shocks . this is also consistent with the fact that numerical simulations show that the turbulence motion is developed in the late phase of mergers . the observed fe abundance of the intracluster medium is almost constant at 0.4 solar inside the offset region , and decreases with radius . the central abundance is slightly lower than that of other clusters or groups . this indicates that central regions of the gas were mixed well during the past merger growth of the cluster . + _ acknowledgements . _ we wish to thank the referee for his / her suggestions on the paper . the authors are grateful to all members of suzaku for their contributions in instrument preparation , spacecraft operation , software development , and in - orbit instrumental calibration . to analyze the data , we used the isas analysis servers provided by isas / c - soda . n. o. acknowledges support by the ministry of education , culture , sports , science and technology of japan , grant - in - aid for scientific research no . cls was supported in part by nasa suzaku grants nnx08az99 g , nnx09ah25 g , and nnx09ah74 g .

the coma cluster was observed with an x - ray imaging spectrometer ( xis ) onboard suzaku in six pointings , including the central x - ray peak region , the 14 west offset region , 30 and 34 north - west offset regions , and 44 and 60 south - west offset regions . the observed spectra were well - represented by a single - temperature model , and two- or three- temperature model did not improve substantially . the central energy of fe lines at the 44 offset region around the ngc 4839 subcluster is also consistent with those within the 34 region . these results on the temperature and velocity structure suggest that the core of the cluster is in a relaxed state , and non - thermal electrons relevant to the radio halo are accelerated by intracluster turbulence rather than large - scale shocks . fe abundance is almost constant at 0.4 solar within the 34 region , and decreases with radius . this value is slightly lower than those of other clusters , which means the gas have been mixed well during a past merger associated with the growth of the cluster .

the coma cluster was observed with an x - ray imaging spectrometer ( xis ) onboard suzaku in six pointings , including the central x - ray peak region , the 14 west offset region , 30 and 34 north - west offset regions , and 44 and 60 south - west offset regions . owing to its lower background level , suzaku has better sensitivity to fe k lines than other satellites . using precise fe line measurements , we studied the temperature structure , possible bulk motions , and iron abundance distributions in the intracluster medium ( icm ) . the observed spectra were well - represented by a single - temperature model , and two- or three- temperature model did not improve substantially . the temperature , derived from k line ratios of h - like and he - like fe , agree with those derived from the single - temperature model . because the line ratio is a steep function of temperature , the consistency supports the accuracy of temperature measurements conducted with suzaku . within the 34 region , the redshift derived from the central energy of the he - like fe line is consistent with that from optical observations , within a calibration error of 18 ev or 818 km s in the line of sight . this value is smaller than the sound velocity of icm , which is 1500 km s . the central energy of fe lines at the 44 offset region around the ngc 4839 subcluster is also consistent with those within the 34 region . these results on the temperature and velocity structure suggest that the core of the cluster is in a relaxed state , and non - thermal electrons relevant to the radio halo are accelerated by intracluster turbulence rather than large - scale shocks . fe abundance is almost constant at 0.4 solar within the 34 region , and decreases with radius . this value is slightly lower than those of other clusters , which means the gas have been mixed well during a past merger associated with the growth of the cluster .

1408.4134

i

let @xmath13 or @xmath3 denote a compact , connected , orientable surface of genus @xmath14 , where @xmath1 . a simple closed curve on @xmath13 is _ essential _ if does not bound a disk in @xmath13 . the complex of curves , introduced by harvey @xcite , is the simplicial complex , @xmath15 , whose vertices ( or @xmath16-skeleton ) , @xmath17 , are isotopy classes of essential simple closed curves ; and , whose edges of the @xmath4-skeleton , @xmath18 , connect vertices that have disjoint representatives . for the remainder of this note , `` curve '' will mean `` simple closed curve '' . by declaring that each edge of @xmath18 has length @xmath4 , we endow @xmath17 with a metric . specifically , an _ edge path _ is a sequence of vertices @xmath19 such that @xmath20 . a _ geodesic path _ joining @xmath7 and @xmath8 is a shortest edge - path . the _ distance _ , @xmath6 , between arbitrary vertices is the length of a geodesic path . since it is known that the complex of curves is connected , which was stated by harvey @xcite and followed from a previous argument of lickorish @xcite , the value @xmath6 is well - defined for all vertex pairs . we note that if @xmath21 , there is a vertex @xmath22 and curve representatives in @xmath13 , @xmath23 , @xmath24 and @xmath25 , such that @xmath26 and @xmath27 . the generic situation ( when some component of @xmath28 has euler characteristic less than zero ) is that there are infinitely many isotopically distinct choices for @xmath29 and , thus , infinitely many possible geodesics for distance @xmath30 . in this case , the existence of infinitely many geodesics at distance @xmath30 forces infinitely many geodesics for all distances . it is this infinite local pathology which makes finding an effective distance computing algorithm challenging . the curve complex was first introduced by harvey @xcite . its coarse geometric properties were first studied extensively by masur minsky @xcite . the complex of curves has proved a useful tool for the study of hyperbolic @xmath31-manifolds , mapping class groups and teichmller theory . in particular , in @xcite , it was established that teichmller space is quasi - isometric to the complex of curves and is therefore @xmath32-hyperbolic . here , @xmath32-hyperbolic means that geodesic triangles in @xmath18 are @xmath32-thin : any edge is contained in the @xmath32-neighborhood of the union of the other two edges . in @xcite , aougab established uniform hyperbolicity@xmath32 can be chosen independent of genus ( for @xmath1 ) . in spite of this considerable advancement in understanding the coarse geometry of the complex of curves , the development of tools intended to explicitly compute distance has been difficult . in 2002 , jason leasure proved the existence of an algorithm to compute the distance between two vertices of @xmath17 ( @xcite , corollary 3.2.6 ) . later , other algorithms were discovered by shackleton @xcite and webb @xcite , but none of these algorithms were studied seriously from the viewpoint of doing explicit computations , and all seem unsuitable for that purpose . recently birman , margalit and the second author @xcite have given a new algorithm_the efficient geodesic algorithm_and we have developed an implementation of it called the _ metric in the curve complex _ applications of micc we will present in this note include : * establishing that the minimal geometric intersection number for vertices of @xmath33 with distance four is @xmath12 , * listing of all vertex pairs ( up to an action of an element of the mapping class group ) of @xmath33 with distance four and having minimally positioned representatives with intersection number at most @xmath34 , and * producing an explicit example of two vertices of @xmath35 that have distance four and intersection number @xmath36 the key idea in @xcite is the introduction of a new class of geodesics , _ efficient geodesics_. they are not the same as the ` tight geodesics ' that have dominated almost all published work on the curve complex following their introduction in @xcite , however they share with tight geodesics the nice property that there are finitely many efficient geodesics between any two fixed vertices in @xmath15 . for convenience , for a pair of curves , @xmath37 , we will refer to a component of @xmath38 as a _ segment_. we will use a slightly weaked definition for efficient geodesic than that given in @xcite . [ d : ie ] let @xmath39 with @xmath40 . an oriented path @xmath41 , in @xmath17 is _ initially efficient _ if there are representatives @xmath42 , @xmath43 and @xmath44 such that @xmath45 for any segment @xmath46 . we say @xmath47 is _ efficient _ if @xmath48 is initially efficient for each @xmath49 and the oriented path @xmath50 is also initially efficient . the efficient path algorithm is a consequence of the following . ( theorem 1.1 of @xcite ) [ t : simplify ] let @xmath51 , and let @xmath7 and @xmath8 be two vertices of @xmath52 with @xmath40 . there exists an efficient geodesic from @xmath7 to @xmath8 , and in fact there are finitely many . when @xmath53 , notice that an efficient geodesic @xmath54 yields an oppositely oriented efficient geodesic , @xmath55 . that is , distance @xmath31 vertices have non - oriented efficient geodesics . thus , for corresponding representatives @xmath56 , we have that @xmath57 ( respectively @xmath58 ) will intersect segments of @xmath59 ( respectively of @xmath60 ) at most once . from this observation , we will establish the following test for distance @xmath61 which micc implements . [ theorem : bmm test](*distance @xmath61 test * ) let @xmath62 be vertices with @xmath40 . let @xmath63 be the collection of all vertices such that the following hold : 1 . for @xmath64 , we have @xmath65 ; and 2 . for @xmath64 , there exist representatives @xmath66 of @xmath67 respectively , such that for each segment @xmath68 we have @xmath69 . then @xmath70 if and only if @xmath71 for all @xmath64 . moreover , the collection @xmath72 is finite . [ remark on z ] keeping with our previous observation regarding non - oriented efficient geodesics at distance @xmath31 , we can flip the roles of @xmath7 and @xmath8 . thus , the test can also be stated in terms of @xmath73 for @xmath74 where : * if @xmath74 then @xmath75 . * if @xmath74 , there exists representatives , @xmath23 , @xmath24 and @xmath76 such that for all segments , @xmath77 , we have @xmath78 . before giving the proof of the distance @xmath61 test , we recall a useful concept and its implications . let @xmath79 be a pair of curves such that @xmath80 is minimal with respect to isotopies of @xmath81 . that is , @xmath82 and @xmath81 are _ minimally positioned_. determining when @xmath83 and @xmath84 are minimally positioned is straightforward due to the bigon criterion ( propostion 1.7 , @xcite)no disc component of @xmath85 has exactly two segments of @xmath38 in its boundary . we say @xmath82 and @xmath81 ( or @xmath86 ) is a _ filling pair _ if @xmath87 is a collection of @xmath30-discs . it is readily seen that a pair is filling on @xmath13 if and only if their corresponding vertices in @xmath17 are at least distance @xmath31 apart . when a minimally positioned pair of curves is not filling but still intersects , some component of @xmath87 contains an essential curve . thus , the corresponding vertices are distance @xmath30 apart . algorithmically determining whether a minimally positioned pair is filling , or not , requires simple tools coming from classical topology . for @xmath26 , let @xmath88 be a regular neighborhood . the genus of this neighborhood , @xmath89 , can be algorithmically computed as discussed in [ sec : genus ] . ( for an oriented surface @xmath90 with boundary , recall @xmath91 , where @xmath92 is the euler characteristic and @xmath93 . ) if @xmath94 , then a component of @xmath95 contains an essential curve of @xmath3 and the vertices that @xmath82 and @xmath81 represent are distance @xmath30 apart . if @xmath96 , those vertices are distance at least @xmath31 apart . we will see in [ sec : genus ] that this _ filling calculation _ can be readily implemented . however , if one is handed a nice enough presentation of @xmath83 and @xmath84 in @xmath13 , determining whether they are a filling pair can be done by inspection . for example , we will do such filling determinations in example [ example : hempel ] . we now give the proof of distance @xmath61 test . * proof : * from the above discussion we see that the assumption , @xmath40 , translates into considering only minimally positioned filling pairs in @xmath13 . to determine whether the associated vertices in @xmath17 of a filling pair are at distance @xmath61 , we need only determine that they are not at distance 3 . thus , suppose @xmath82 and @xmath81 represent classes @xmath7 and @xmath8 such that @xmath40 . assume there exists a length @xmath31 path @xmath97 . from theorem [ t : simplify ] , we can further assume that this path is initially efficient . in particular , for representative @xmath98 of the vertices of this path , respectively , we can assume @xmath99 intersects segments of @xmath100 at most once . thus , @xmath101 is an element of the set @xmath72 . but , since @xmath102 , we need only establish that @xmath103 for all @xmath64 to contradict the assumption that there was a distance @xmath31 path . the fact that the set @xmath72 is finite is due to @xmath104 being a collection of @xmath30-discs and representatives of any vertex of @xmath72 having bounded intersection with any such @xmath30-disc component . the stated test for @xmath61 follows . [ example : hempel ] we consider an example of a pair of curves , @xmath82 and @xmath81 , on a genus @xmath30 surface which represent classes that are distance @xmath10 apart . ( see figure [ fig : hempel example ] . ) this is an example of j. hempel and appears in the lecture notes @xcite . these notes assert distance @xmath10 for the pair without proof . as an application of the distance @xmath105 test , we now give a proof establishing distance @xmath10 for hempel s example . @xmath106 at 140 100 @xmath81 at 165 119 @xmath81 at 363 244 @xmath107 at 97 280 @xmath108 at 380 276 in figure [ fig : hempel example ] , the surface @xmath109 is represented as a rectangular region minus two discs . the gray sides of the rectangle are identified , left - to - right and top - to - bottom , to form a torus minus two discs . the genus @xmath30 surface is obtained by identifying the two oriented red boundary curves , and the resulting single curve is @xmath81 ( the identification is initiated by lining up the six colored dots on the @xmath110 curves ) . these identifications induce identifications of the endpoints of the dark blue arcs , so as to form the curve @xmath82 . by inspection , one can see that @xmath111 is a minimally positioned filling pair . we now apply the distance @xmath61 test . we wish to find curves , @xmath112 , that represent vertices , @xmath64 . such a @xmath112 will be in the complement of @xmath82 , intersecting any segment of @xmath113 at most once . three such @xmath114 can be immediately identified . this is because the complement of @xmath115 in @xmath109 is a collection of some number of @xmath10-gon regions and one single @xmath12-gon region . the boundary of any one of these regions is an alternating joining of segments in @xmath82 and @xmath81 . thus , any @xmath10-gon boundary has two segments in @xmath81 ; and , the boundary of the single @xmath12-gon has @xmath116 segments in @xmath81 . requiring that any @xmath112 intersect segments of @xmath81 at most once forces it to either not intersect a @xmath10-gon , or intersect each of the two @xmath81 segments of a @xmath10-gon once . however , there six different ways a @xmath112 can exit / enter the @xmath12-gon , giving us three possible @xmath114 that intersect the @xmath12-gon region once . in figure [ fig : hempel example ] , the dashed green and purple curves @xmath112 and @xmath117 illustrate two of the three curves generated by the exit / enter possibilities . it is readily apparent that both @xmath118 and @xmath119 is a collection of @xmath30-discs , none of which are bigons . thus , the corresponding vertex pairs are at least distance @xmath31 apart . the remaining possibilities for a @xmath107 can be dealt with in a similar straightforward manner ( theoretically , there are also @xmath120 that intersect the @xmath12-gon region @xmath30 and @xmath31 times ) . @xmath121 the @xmath72-calculation above illustrates the primary computing capabilities of the micc software package @xcite . micc is a computational tool that can determine whether the distance between two vertices in @xmath122 is @xmath30 , @xmath31 , or @xmath61 . its input is readily produced from any representation of two curves on a closed surface . it has functionality that can be used to search for new curve pairs or manipulate existing examples . its output can be used to construct geodesic paths between curves of short distances . as such , micc is an additional tool scholars can utilize in answering a number of basic questions about the local pathology of the complex of curves . as an illustration , we consider the relationship between distance and minimal intersection number . it is known that the theoretical minimal intersection number for a filling pair on a @xmath3 is @xmath123 due to the euler characteristic of the surface . for @xmath11 , this theoretical minimum is not realizable and the realizable minimum is in fact @xmath10 . recent work of aougab and huang @xcite has given a construction for realizing the theoretical minimum for @xmath124 . additionally , they show that all such minimum filling pairs are distance @xmath31 . for fixed @xmath1 , using his uniform hyperbolicity result , aougab proved that the theoretical minimum intersection number grows exponentially as a function of distance ( theorem 1.2 , @xcite ) . also , aougab and taylor @xcite give a recipe for producing filling pairs at a given distance whose intersection numbers are close to the minimum in an asymptotic sense ; see their paper for the precise statement . ido , jang and kobayashi @xcite also have a construction for producing filling pairs of a prescribed distance . the arguments in these last three citations employs the high power machinery of masur and minsky , including the _ bounded geodesic image theorem _ @xcite . thus , the growth bounds and constructed examples inherit a `` coarse geometry '' quality , which so far in the literature has not been used to produce the exact minimal intersection number with accompanying filling pairs for a specified distance and genus . in contrast , micc can be used to find explicitly all minimum intersecting filling pairs of distance @xmath10 . using the distance @xmath61 test , we give a `` proof of concept '' calculation that constructs all minimum intersecting distance @xmath10 filling pairs in @xmath125 up to homeomorphism . we can next use micc to calculate distance for curve pairs of increasing intersection number starting at this minimum . the result of this calculation is the following theorem . [ theorem : dwh - g2-d4-i12 ] the minimal intersection for a filling pair , @xmath126 , representing vertices @xmath127 , respectively , with @xmath128 is @xmath12 . combining this theorem with the distance @xmath61 test we obtain a partial test for distance four . [ corollary : dwh - g2-d4-i12 ] let @xmath70 for two vertices in @xmath129 . let @xmath130 be curves in minimal position representing @xmath7 and @xmath8 , respectively . let @xmath131 be a curve . if 1 . @xmath132 and @xmath133 , or 2 . @xmath134 and @xmath135 , then @xmath128 . the proof of concept calculation for theorem [ theorem : dwh - g2-d4-i12 ] involves finding all solutions to an integer linear programing problem so as to identify all potential candidates for minimally intersecting distance four curve pairs . however , such a comprehensive search is not necessarily needed to find examples of distance @xmath61 pairs . utilizing all of the functionality of micc , one can `` experiment '' with different curve pairs in a search distance four pairs . remark [ remark : experiment ] discusses how such experimentation led to the discovery of the first known filling pair representing distance @xmath10 vertices in @xmath136 . in particular , we have the following result : [ theorem : dwh - g3-d4-i29 ] the minimal intersection number for a pair of filling curves in @xmath137 that represent distance @xmath10 vertices in @xmath136 is less than or equal to @xmath36 . the outline for our paper is as follows . in [ sec : dwh ] , we discuss a method of representing a filling pair on @xmath138 . in [ sec : dwh - g2-d4-i12 ] , we give the proof of theorem [ theorem : dwh - g2-d4-i12 ] . in particular , the proof can be viewed as giving a general strategy for calculating theoretical minimal intersections of distance @xmath10 filling pairs for any higher genus . this strategy employed in a limited manner allowed us to verify that the explicit example given in @xcite ( cf . 2 ) of a distance @xmath10 vertex pair in @xmath129 establishes theorem [ theorem : dwh - g2-d4-i12 ] . we finish [ sec : dwh - g2-d4-i12 ] with an analysis of a genus @xmath31 distance @xmath10 pair establishing theorem [ theorem : dwh - g3-d4-i29 ] . finally , in [ sec : micc commands ] , we discuss the complete functionality of micc . to make this discussion concrete , we illustrate the range of micc commands with a running example . at the end of this manuscript , we attach the current known _ spectrum _ of pairs of distance @xmath10 or greater in @xmath129 with up to @xmath139 intersections . the full distance @xmath10 or greater spectrum in @xmath129 with up to @xmath34 intersections is available at @xcite . _ an expository remark_throughout we will continue to use @xmath83 and @xmath84 as representatives of @xmath7 and @xmath8 , respectively . similarly , indexed @xmath140 curves will be used as representatives of indexed @xmath141 vertices . this is meant to be consistent with the notation used in @xcite . for all other curves in the surface , we will use various `` flavors '' of @xmath107 , and @xmath142 will denote the corresponding vertex . we will always assume that any pairing of curves are in minimal position .

the complex of curves of a closed orientable surface of genus is the simplicial complex whose vertices , , are isotopy classes of essential simple closed curves in . two vertices co - bound an edge of the-skeleton , , if there are disjoint representatives in . thus , the distance between two vertices , , corresponds to the length of a geodesic a shortest edge - path between and in . in , birman , margalit and the second author introduced the concept of _ efficient geodesics _ in and used them to give a new algorithm for computing the distance between vertices . in this note , we introduce the software package micc ( _ metric in the curve complex _ ) , a partial implementation of the efficient geodesic algorithm . in particular , up to an action of an element of the mapping class group , we give a calculation which produces all distance vertex pairs for that intersect times , the minimal number of intersections needed for this distance and genus .

the complex of curves of a closed orientable surface of genus is the simplicial complex whose vertices , , are isotopy classes of essential simple closed curves in . two vertices co - bound an edge of the-skeleton , , if there are disjoint representatives in . a metric is obtained on by assigning unit length to each edge of . thus , the distance between two vertices , , corresponds to the length of a geodesic a shortest edge - path between and in . in , birman , margalit and the second author introduced the concept of _ efficient geodesics _ in and used them to give a new algorithm for computing the distance between vertices . in this note , we introduce the software package micc ( _ metric in the curve complex _ ) , a partial implementation of the efficient geodesic algorithm . we discuss the mathematics underlying micc and give applications . in particular , up to an action of an element of the mapping class group , we give a calculation which produces all distance vertex pairs for that intersect times , the minimal number of intersections needed for this distance and genus .

1004.3492

c

we have revisited the control landscape for several classes of canonical quantum control problems , in particular pure - state transfer and unitary gate optimization problems . although the pure - state transfer fidelity as a function over the unitary group only has two types of critical points , corresponding to either the global minimum @xmath19 or the global maximum @xmath117 , detailed analysis shows that the class of critical points for the actual optimization problem over functions in @xmath0 is strictly larger than the set of kinematic critical points . in particular , for any bilinear control system @xmath175 and any fixed target time @xmath17 , there exist pairs of initial and target states , such that some @xmath427 is a critical point of the system , and we can achieve any value of the fidelity between @xmath19 and @xmath117 for such critical points . moreover , while these critical points are not expected to be attractive in most cases , we have presented examples of systems with attractive suboptimal critical points , showing that traps _ do _ exist for such problems , and the fidelity at these traps can take many values , unlike the fidelity for kinematic critical points , which is limited to 0 or 1 for pure - state optimization problems . for the problem of unitary operator optimization we demonstrated that there are indeed no traps when we consider the fidelity as a functional over the unitary group . although there are critical manifolds on which the fidelity takes values between @xmath428 ( global minimum ) and @xmath429 ( global maximum ) , all of these critical points are indeed saddle points , but the situation changes when the analysis is restricted to the special unitary group @xmath57 . this case may appear artificial but it is actually highly relevant for quantum control , as many quantum control problems involve control hamiltonians that have zero - trace , and hence we have no global phase control . although the system may be @xmath2 controllable when @xmath319=0 $ ] , if the target time is fixed , so is the global phase . perhaps surprisingly , there are more critical points in this case than for @xmath2 , and some of these are attractive critical points at which the fidelity assumes values @xmath430 , i.e. , traps . more careful analysis shows that these traps correspond to solutions @xmath431 , where @xmath320 is a root of unity , which immediately shows that these solutions have fidelity @xmath430 , according to the standard definition of the fidelity . nonetheless , these solutions are perfectly adequate for most practical purposes as we usually do not care about the global phase of an operator , and this problem can be avoided entirely simply by modifying the performance index to reflect the fact that we do not care about the global phase . optimizating over the projective unitary group @xmath317 there are indeed no traps , at least on the group . again , the situation is more complicated for actual optimization problem over controls in @xmath0 . not only are there critical points @xmath8 for which the fidelity assumes critical values other than those permitted over @xmath2 or @xmath57 , but examples again show that the hessian at these critical points can be negative definite , implying that they are locally attractive on any finite - dimensional subspace and therefore traps . the results can even be extended to the case where the target time @xmath17 is variable , again proving the existence of traps . the specific examples of traps constructed prove a theoretical point about the existence of traps , but they are not of particular interest in their own right . unfortunately , due to the difficulty of exactly calculating the hessian for complex systems with time - varying controls , it is difficult to _ prove _ the existence of traps for more interesting cases . therefore we turned to numerical simulations to investigate any evidence for the existence of trapping regions in practice . for a three - qubit gate optimization problem we studied the simulation results suggests that there are genuine traps , i.e. , attractive critical points for which the fidelity is below a certain threshold . although such traps do not appear to be very common in the example considered we observed trapping in about 42 out of 1000 cases , they do complicate the control landscape and obstruct convergence to a global extremum , and perhaps even more importantly , trapped runs can be extremely time - consuming , which suggests that it is important to consider the possibility of trapping in the algorithm design , to ensure that trapped runs are quickly identified and terminated . furthermore , the example considered was a rather simple system of dimension @xmath432 with six independently variable controls . it is quite plausible that the number of traps and the likelihood of a local optimization algorithm converging to these increases with the system dimension or complexity . this is an important issue of practical concern that requires a systematic further analysis . we would like to thank thomas schulte - herbrggen , robert zeier and john v. leahy for helpful discussions and suggestions . sgs acknowledges funding from epsrc arf grant ep / d07192x/1 , the epsrc qip interdisciplinary research collaboration ( irc ) , hitachi and nsf grant phy05 - 51164 . pdf acknowledges funding from epsrc and hitachi ( case / cna/07/47 ) .

the control landscape for various canonical quantum control problems is considered . for the class of pure - state transfer problems , analysis of the fidelity as a functional over the unitary group reveals no suboptimal attractive critical points ( traps ) . for the actual optimization problem over controls in , however , there are critical points for which the fidelity can assume any value in , critical points for which the second order analysis is inconclusive , and traps . for the class of unitary operator optimization problems analysis of the fidelity over the unitary group again , the set of critical points for the actual optimization problem for controls in is larger and includes traps , some of which remain traps even when the target time is allowed to vary . ,

the control landscape for various canonical quantum control problems is considered . for the class of pure - state transfer problems , analysis of the fidelity as a functional over the unitary group reveals no suboptimal attractive critical points ( traps ) . for the actual optimization problem over controls in , however , there are critical points for which the fidelity can assume any value in , critical points for which the second order analysis is inconclusive , and traps . for the class of unitary operator optimization problems analysis of the fidelity over the unitary group shows that while there are no traps over , traps already emerge when the domain is restricted to the special unitary group . the traps on the group can be eliminated by modifying the performance index , corresponding to optimization over the projective unitary group . however , again , the set of critical points for the actual optimization problem for controls in is larger and includes traps , some of which remain traps even when the target time is allowed to vary . ,

1408.6505

i

quantum optimal control theory ( oct ) provides a basis to explore applied field tuning of quantum system dynamics @xcite . recent successes include achieving control of electrons in quantum dots through time - varying gate voltages @xcite , controlling electronic correlations in molecules @xcite , manipulating the dynamics of quantum many - body systems @xcite , cooling ultracold atomic gases @xcite , eliciting quantum revivals @xcite , and generating adiabatic time evolution @xcite . optimal control experiments ( oce ) have found growing success even for complex systems , especially through the use of closed - loop learning algorithms @xcite combined with femtosecond laser pulse shaping technology @xcite . for example , these advances have enabled vibrational control of population inversion in bose - einstein condensates @xcite , strong - field ionization of silver atoms @xcite , and coherent energy transfer in light - harvesting complexes @xcite . underlying these achievements is the question of why desirable quantum controls can evidently be found with only modest search effort over the vast space of possible control fields . an important factor in addressing this question is the favorable control landscape _ topology _ , which results upon satisfaction of certain physical assumptions @xcite . the present paper considers a second contributing factor based on the landscape _ structure _ ( i.e. , non - topological features ) reflected in the behavior of the evolving controls during the optimization process . + the dynamics of a closed quantum system interacting with an applied field is described by the time - dependent schrdinger equation @xmath3 where @xmath4 is the time - dependent hamiltonian and @xmath5 is the corresponding evolution operator ( propagator ) with @xmath6 . here @xmath7 is the time at which the objective is optimized . treating the interaction within the dipole approximation , the time - dependent hamiltonian is given by @xmath8 where @xmath9 is the field - free hamiltonian , @xmath10 is the dipole moment operator and @xmath11 is the time - dependent control field . + through eq . ( [ tdse ] ) , a control field can be mapped to a value of a cost functional @xmath12 $ ] , which may be either the expectation value @xmath13 of an observable @xmath14 or the cost functional @xmath15 for creating a target unitary transformation @xmath16 ( see eqs . ( [ trpo ] ) and ( [ wcost ] ) , respectively ) . the functional relationship between @xmath12 $ ] and the control field @xmath11 can be cast in terms of a _ quantum control landscape _ , where each point @xmath12 $ ] on the landscape corresponds to a particular control field @xmath11 , @xmath6 . finding successive control fields that eventually lead to an optimal value of the cost functional entails climbing the landscape . we will refer to ` climbing ' as moving towards the target value of @xmath17 , regardless of whether the cost functional is to be maximized or minimized . using a local search algorithm to climb ( e.g. , the gradient algorithm utilized in this work ) results in smooth paths up the landscape @xmath18 $ ] that can be parametrized by the continuous variable @xmath19 . every such path up the landscape is associated with a trajectory @xmath20 through _ control space_. thus , starting with an initial control field @xmath21 that produces a low value of the cost functional , the goal is to find the final control field @xmath22 that yields a high ( optimal ) value of the cost functional at @xmath23 . + many recent studies have considered the _ topology _ of quantum control landscapes @xcite . the control landscape topology is specified by the character of the critical points where @xmath24 , @xmath25 $ ] . a critical point at a suboptimal value of @xmath17 where the hessian @xmath26 is negative semi - definite would indicate a ( second order ) trap capable of halting an effort attempting to reach the top of the landscape . the landscape topology has been analyzed for closed quantum systems with @xmath27 states under the assumptions of : ( i ) controllability , such that any unitary evolution matrix @xmath28 can be generated by at least one control field at some sufficiently large time @xmath7 , ( ii ) surjectivity , whereby the set of functions @xmath29 , @xmath30 are linearly independent over @xmath31 $ ] , and ( iii ) full accessibility , allowing for free access to any control field . upon satisfaction of these assumptions , the quantum control landscape can be shown to contain only trap - free intermediate value critical saddle submanifolds ( when they exist for a particular application ) @xcite along with the absolute minimum and absolute maximum submanifolds . thus , the landscape topology is very favorable to performing oces or oct simulations , which is an important factor in explaining the evident ease of locating optimal control fields . + beyond issues of topology , the _ structure _ of the quantum control landscape away from the critical points could greatly influence the nature of a control trajectory winding its way to an optimal field . if landscape structure is highly gnarled , this circumstance could call for complex control trajectories , although the trap free topology assures that the path ( e.g. , guided by a gradient ascent algorithm ) will lead to an optimal solution . the encountered landscape structure upon climbing may be examined by quantifying the linearity of the control trajectories @xcite . a predilection towards nearly straight trajectories is indicative of very simple control landscape structural features . prior experimental work aiming to maximize second harmonic generation found that all of the sampled control trajectories were strikingly close to being straight @xcite . recent theoretical work has also supported the presence of simple landscape structure by examining the linearity of control trajectories in simulations over the state - to - state transition probability landscape @xcite . + in this work , we extend the state - to - state transition probability quantum control landscape structure analysis to consider two additional landscapes : @xmath32 and @xmath33 where @xmath34 denotes the frobenius norm . the quantum ensemble control landscape @xmath13 allows for controlling arbitrary observables and consideration of systems which are initially in mixed states @xmath35 , and the unitary transformation landscape @xmath15 is relevant to the prospect of creating logic gates for quantum information processing @xcite . both landscapes can contain critical saddle submanifolds @xcite , which are not present in the simpler state - to - state transition probability landscape . thus , we aim to assess the influence of these saddle submanifolds on landscape structure . specifically , we will show that encountering saddle submanifolds at intermediate heights on the landscape can drive control trajectories away from straight paths . this phenomenon is sketched in figure [ sketch ] . the trajectory on the right takes a rather straight path up the landscape , while the trajectory on the left is initially attracted to the saddle point , thus altering its direct nature . nevertheless , we will show in numerical simulations that the trajectories leading to optimal controls are generally still close to being straight , despite the presence of saddles . lastly , we will derive a mathematical criterion showing that the gradient of the cost functional must be an eigenfunction of the hessian in order to achieve a perfectly straight gradient - based control trajectory . + the remainder of the paper is organized as follows . the linearity measure @xmath2 of a control trajectory is defined in section 2 . section 3 gives the gradient - based search algorithm used in this work to identify control fields that optimize arbitrary observables or achieve unitary transformations , respectively , through @xmath13 or @xmath15 . the presence of landscape saddle submanifolds is examined , and a metric is outlined that gives the distance from any point on a trajectory to a particular saddle submanifold . in section 4 , a derivation is presented specifying the hessian - gradient eigen - relation for straight control trajectories . section 5 provides numerical results on the statistical behavior of @xmath2 over a large ensemble of landscape trajectories for @xmath13 and @xmath15 . we also illustrate satisfaction of the hessian - gradient eigen - relation for nearly straight control trajectories . concluding remarks are furnished in section 6 .

the control of quantum system dynamics is generally performed by seeking a suitable applied field . the physical objective as a functional of the field forms the quantum control landscape , whose _ topology _ , under certain conditions , has been shown to contain no critical point suboptimal traps , thereby enabling effective searches for fields that give the global maximum of the objective . a value of would indicate an exactly straight trajectory to the optimal observable value . again , nearly straight trajectories predominate , and we demonstrate that can take values approaching 1.0 with high precision . however , the interplay of optimization trajectories with critical saddle submanifolds is found to influence landscape structure . a fundamental relationship necessary for perfectly straight gradient - based control trajectories is derived , wherein the gradient on the quantum control landscape must be an eigenfunction of the hessian . this relation is an indicator of landscape structure and may provide a means to identify physical conditions when control trajectories can achieve perfect linearity .

the control of quantum system dynamics is generally performed by seeking a suitable applied field . the physical objective as a functional of the field forms the quantum control landscape , whose _ topology _ , under certain conditions , has been shown to contain no critical point suboptimal traps , thereby enabling effective searches for fields that give the global maximum of the objective . this paper addresses the _ structure _ of the landscape as a complement to topological critical point features . recent work showed that landscape structure is highly favorable for optimization of state - to - state transition probabilities , in that gradient - based control trajectories to the global maximum value are nearly straight paths . the landscape structure is codified in the metric , defined as the ratio of the length of the control trajectory to the euclidean distance between the initial and optimal controls . a value of would indicate an exactly straight trajectory to the optimal observable value . this paper extends the state - to - state transition probability results to the quantum ensemble and unitary transformation control landscapes . again , nearly straight trajectories predominate , and we demonstrate that can take values approaching 1.0 with high precision . however , the interplay of optimization trajectories with critical saddle submanifolds is found to influence landscape structure . a fundamental relationship necessary for perfectly straight gradient - based control trajectories is derived , wherein the gradient on the quantum control landscape must be an eigenfunction of the hessian . this relation is an indicator of landscape structure and may provide a means to identify physical conditions when control trajectories can achieve perfect linearity . the collective favorable landscape topology and structure provide a foundation to understand why optimal quantum control can be readily achieved .

astro-ph9804012

i

a galaxy can be well described by an ecosystem . there is an intimate relationship , much like a symbiosis , between the discrete components of the galaxy such as stars , and its interstellar medium ( ism ) . the ism provides the foundation for the birth of a new generation of stars , while at the same time it is enriched by the remains of the older generations and their byproducts during their life cycle . hence , it is natural to expect that the understanding of formation and evolution of galaxies is closely related to the understanding of their ism . the ism of the milky way has been found to have many components . magnetic fields and cosmic ray gas compose the relativistic fluid , while the gaseous phase consists of both ionized and neutral components . the hot ionized medium observable in uv and x - ray has a temperature above @xmath8 k and is composed of hot coronal gas heated by supernova shocks . a good portion of the energy of the ism resides in this component . the warm ionized medium ( e.g. hii , planetary nebulae ) is visible in @xmath9 , uv , and optical , and has a temperature as high as @xmath10 k. the neutral atomic gas appears to have both cold ( @xmath11 k ; e.g. hi clouds ) and warm ( 100 k @xmath12 8000 k ) components . molecular clouds compose the self - gravitating gaseous phase . finally the ism ( with the exception of its hot phase ) is filled with dust , particles typically a few tenth of microns in size and visible through their infrared radiation . since the peak emission of each component arises in different wavebands , multi - wavelength observations from radio to @xmath13-rays are needed to probe the ism . diffuse x - ray emission from our galaxy is a powerful diagnostic of the hot phase of the ism . it is our purpose here to use this tool to probe the processes that contribute to its energetics and dynamics . the first detection of the x - ray emission from the galactic disk was achieved by the pioneering rocket experiment of bleach et al . they detected excess emission associated with a narrow disk component of angular size @xmath14 . since then , x - ray emission from the galactic plane and in particular the ridge ( the narrow region centered on the galactic mid - plane extending approximately to @xmath15 in longitude and @xmath16 in latitude ) has been measured in the past with several satellites ( e.g. _ heao-1 _ [ 2 - 50 kev ] : worrall et . 1982 ; _ exosat _ [ 2 - 6 kev ] : warwick et al . 1985 ; _ tenma _ [ 2 - 11 kev ] : koyama et al . 1986 ; _ ginga _ [ 2 - 16 kev ] : yamasaki et al . 1997 ; _ asca _ [ 0.5 - 10 kev ] : kaneda et al . 1997 ) . the presence of the @xmath17 kev iron line in the spectrum discovered with _ tenma _ has motivated the idea that part of the emission below 10 kev is due to a hot optically thin plasma of temperature @xmath7 kev . because of its high spectral resolution , _ asca _ has provided the most accurate measurement of the spectrum of the emission to date . the presence of mg , si , and fe k - lines in the spectrum obtained by _ asca _ suggests that at least part of the emission is of thermal origin . close examination of _ asca _ data has also revealed that unresolved , discrete sources are not responsible for the bulk of the emission ( yamauchi et al . 1996 ; kaneda 1997 ) . the most recent investigation of the diffuse emission from the scutum arm region with _ asca _ ( kaneda et al . 1997 ) has concluded that the emission below 10 kev has both soft ( @xmath18 kev ) and hard ( @xmath19 kev ) thermal components . if indeed the super hot gas ( @xmath20 kev ) exists in an extended form in the ism , it is not clear how to explain its confinement to the galactic disk since its temperature exceeds the gravitational potential of the disk by at least an order of magnitude ( townes 1989 ) . unfortunately , the two - temperature model does not produce a good fit to the data above 10 kev indicating the presence of additional component(s ) at higher energies . indeed , a hard power law tail has been detected in the hard x - ray / soft @xmath13-ray band from observations of the ridge with _ ginga _ and the balloon experiment _ welcome-1 _ ( yamasaki et al . 1997 ) , and _ osse _ ( skibo et al . 1997 ) . in this paper , we present the results from _ rxte _ measurement of the diffuse x - ray emission from the galactic ridge in the 3 - 35 kev band . observations in the hard x - ray / soft @xmath13-ray band have usually been complicated by the presence of numerous variable discrete sources , and the fact that the instruments generally have large fields of view and no imaging capabilities , or have imaging capability but no diffuse emission sensitivity . the combination of these factors makes the separation of emission between diffuse and compact sources a difficult task . the advantage of _ rxte _ over previous missions is its small field of view ( @xmath21 fwhm ) combined with its wide energy bandpass ( 2 - 60 kev for the pca ) , allowing for the subtraction of the contribution of discrete sources from the diffuse emission spectrum in the hard x - ray band . in addition to reporting on the detection of a hard power law tail in the _ rxte _ data , we also offer an alternative interpretation for the origin of the emission below 10 kev ( i.e. instead of a super hot plasma of temperature @xmath7 kev ) . in agreement with previous studies , our results indicate that the emission is most likely of diffuse origin as opposed to the superposition of discrete sources . however , we present a model in which the x - ray emission is the superposition of both thermal ( modelled by a raymond - smith plasma ) and possibly non - thermal ( modelled by a power law ) components . we discuss the origin of the thermal component in terms of a population of snrs residing in the disk . the origin of the power law component remains uncertain . by comparing the spectrum of the diffuse emission in hard x - rays ( _ rxte _ ) and soft @xmath13-rays ( _ osse _ ) , we find indications that the emission in the two bands are related . we discuss its origin in terms of both discrete hard x - ray sources and radiation mechanisms such as non - thermal bremsstrahlung from cosmic ray electrons and protons , and inverse compton scattering . the plan of this paper is as follows . in 2 , we describe the observations . in 3 , we present the results of our spatial and spectral analysis of the data . 4 is devoted to the discussion of the results , and their implications for the origin of the emission . finally in 5 , we present our conclusions .

the diffuse x - ray emission from the thin disk surrounding the galactic mid - plane ( the so - called galactic ridge ) was measured with _ rxte _ possible contributions from non - thermal bremsstrahlung of cosmic ray electrons and protons , inverse compton scattering of energetic electrons from ambient microwave , infrared , and optical photons , non - thermal emission from snrs , and emission from discrete x - ray sources are discussed .

the diffuse x - ray emission from the thin disk surrounding the galactic mid - plane ( the so - called galactic ridge ) was measured with _ rxte _ pca in order to determine the spatial extent , spectral nature , and origin of the emission . spatial examination of the diffuse emission in the central of the plane in galactic longitude reveals the presence of two components : a thin disk of full width centered roughly on the galactic mid - plane , and a broad component which can be approximated as a gaussian distribution with fwhm of about . assuming an average distance of 16 kpc to the edge of the galaxy , a scale height of about pc and 500 pc is derived for the thin and broad disk components , respectively . spectral examination of the emission clearly reveals the presence of a hard power law tail above 10 kev and an emission line from he - like iron , indicating both thermal and possibly non - thermal origins for the diffuse emission . the averaged spectrum from the ridge in the kev band can be modelled with a raymond - smith plasma component of temperature kev and a power law component of photon index . based on this finding , we argue that the temperature of the hot phase of the interstellar medium ( ism ) is less than the previously reported values of kev . motivated by the similarities between the characteristics of the thermal component of the galactic ridge emission in our model and the thermal emission from supernova remnants ( snrs ) , we discuss the origin of the thermal emission in terms of a population of snrs residing in the galactic disk . we find that a sn explosion rate of less than 5 per century is adequate to power the thermal emission from the ridge . the origin of the emission in the hard x - ray band modelled by a power law remains uncertain . possible contributions from non - thermal bremsstrahlung of cosmic ray electrons and protons , inverse compton scattering of energetic electrons from ambient microwave , infrared , and optical photons , non - thermal emission from snrs , and emission from discrete x - ray sources are discussed . we speculate that bremsstrahlung of accelerated electrons and protons in snr sites can play a significant role in producing the hard tail of the spectrum . moreover , their collisional losses can play a major role in the ionization of the ism . accepted for publication in the astrophysical journal

astro-ph9804012

c

we first consider the contribution of unresolved discrete sources to the diffuse emission spectrum . the important question is whether there exist classes of unresolved discrete sources with appropriate spatial number densities and similar spectra to that of the diffuse emission that can comprise the bulk of the spectrum . in the hard x - ray band ( above 10 kev ) , the number of known galactic hard x - ray sources with similar spectra to that of the galactic ridge diffuse emission is small ( levine et al . black hole candidates in their soft state have spectra similar to that of the ridge , but this is usually seen at high luminosities when individual sources can be easily detected . neutron star binaries are known to have hard power law spectra with an exponential cut off around 20 kev . however , only a handful of them are known to be active at a time in the galactic disk . also , their luminosities are mostly in the range @xmath136 which can easily be detected from the diffuse emission . unresolved pulsars are also thought to contribute to the galactic ridge diffuse emission particularly in the @xmath13-ray band . a recent study , however , concludes that pulsar contribution to the diffuse galactic emission is significant only above 1 gev ( pohl et al . 1997 ) . in the soft @xmath13-ray band , sigma_/_osse _ observations of the galactic center region has been performed to distinguish the diffuse emission from that of compact sources ( purcell et al . comparison of the source excluded spectrum from the galactic center and that from regions which are known to have fewer sources ( i.e. @xmath137 and @xmath138 ) has revealed that the spectra are similar in both intensity and spectral index . if the emission is due to discrete sources , 10 x - ray sources of flux @xmath139 at 100 kev must be present in the field of view of _ osse _ to make up the spectrum . because of the lack of knowledge of such class of sources with a uniform space density in longitude , it is likely that the emission above 10 kev is of diffuse origin . below 10 kev , because of its better spatial resolution , _ asca _ is far better equipped than _ rxte _ to resolve individual faint sources . a recent fluctuation analysis of the surface brightness of the ridge emission in the scutum arm region ( @xmath140 ) with _ asca _ has concluded that if discrete sources are to make up the entire spectrum , their luminosity must be less than @xmath141 ( yamauchi et al . this conclusion narrows the field of candidate class of sources that can make up the diffuse emission spectrum of the galactic ridge . among possible class of sources , neutron stars ( with x - ray luminosities mostly in the range @xmath142 ) are unlikely due to their large luminosities . a likely class of sources that has been thought to account for the emission is the rs cvn type binaries , since they exhibit the iron k line in their emission spectra however , a study by ottmann & schmitt ( 1992 ) on the contribution of rs cvn systems to the galactic diffuse emission concludes that while they contribute about 6% to the total galactic background , their contribution to the galactic ridge iron line is too small ( @xmath143 ) . therefore , given the strength of the iron line in the spectrum of the diffuse emission , it seems that unresolved rs cvn sources do not contribute to the bulk of the emission . cataclysmic variables ( cvs ) are another candidate that may contribute to the galactic ridge diffuse emission . they have similar spectra to that of the ridge and their luminosities fall in the range @xmath144 . however , from the analysis of the _ asca _ gis pointings of the galactic ridge , kaneda ( 1997 ) has shown that in order for cvs to make up the diffuse emission , their space densities would have to be @xmath145 , a factor of 100 larger than the estimated density of cvs ( patterson 1984 ) . for these reasons , it is more likely that the emission is due to diffuse or extended sources . a more detailed review of the previous works on the contribution of the discrete sources to the ridge spectrum can be found in kaneda ( 1997 ) and yamasaki ( 1996 ) , and references therein . finally , we point out that with the upcoming launch of _ axaf _ , a more sensitive number - flux distribution of galactic sources and their exact contribution to the diffuse galactic background can be determined . based on our measurements presented in this paper , we conclude that the diffuse emission from the ridge in the broad x - ray and soft @xmath13-ray band has both thermal and possibly non - thermal origins . in what follows , we speculate on the origin of the emission , first focusing on the thermal component and then speculating on the origin of the power law tail . the thermal component can be modelled with a raymond - smith plasma of temperature @xmath5 kev ( tables 3 and 4 ) . however , we point out that the spectral resolution of _ asca _ gis or sis is far superior to that of _ rxte _ pca . therefore , in order to interpret the spectrum accurately , we need to carefully examine the spectral features of the diffuse emission below 10 kev using the _ asca _ data . for this reason , we refer to the latest investigation of the diffuse emission from the galactic ridge with _ asca _ ( kaneda 1997 ; kaneda et al . the spectral examination of the _ asca _ data has clearly verified the presence of lower energy emission lines from mg , si , and s. the spectrum has also been carefully examined for the presence of fe k lines . while the emission line from he - like iron was clearly detected , the presence of the emission lines from neutral and h - like iron was not firmly established . this is important since the equivalent width of the h - like iron line sets an upper limit for the plasma temperature . kaneda et al . ( 1997 ) give an upper limit of @xmath146 of that of the he - like iron for the normalization of the h - like iron line . this implies an upper limit of @xmath147 kev for the plasma temperature . this is in agreement with our results since the emission line from h - like fe is expected to be very weak from a @xmath148 kev plasma , supporting our finding that the thermal component of the emission arises from a gas of cooler temperature . therefore , we argue that unlike previous conclusions ( koyama et al . 1986 ; kaneda et al . 1997 ) , the temperature of the x - ray emitting gas need not be so high ( 5 - 15 kev ) in order to produce the observed spectrum . this interpretation lessens the difficulties toward explaining the origin and confinement of the super hot ( @xmath149 kev ) gas . due to the similarities between the characteristics of supernova remnants and the thermal nature of the diffuse emission spectrum presented here , we speculate that a collection of supernova remnants in the galactic disk , below current x - ray and/or radio detection limits , is responsible for the thermal origin of the diffuse emission . the idea was originally introduced by koyama , ikeuchi , & tomisaka ( 1986 , hereafter kit86 ) . however , in their calculation , they assumed that the temperature of the emitting gas is about @xmath20 kev . in addition to the fact that no snr with such high temperature has ever been detected , this assumption also requires a large sn explosion rate ( one per 10 years ) which exceeds the expected galactic rate of 2 - 3 per century ( tammann 1982 ) . below , we revisit their argument in order to derive the sn explosion rate capable of powering the thermal emission from the ridge using the adjusted temperature of @xmath148 kev for the emitting plasma . the first step is to estimate the criteria for which a given snr is below radio detection limit . due to absorption in the galactic disk , the minimum radio surface brightness for detecting a snr is @xmath150 . using the empirical relation between the surface brightness @xmath151 , and the diameter of the snr ( milne 1979 ) , and accounting for the ambient gas density as a function of scale height of the galactic plane ( tomisaka , habe , & ikeuchi 1980 ) , kit86 reduce the criteria to @xmath152 where @xmath153 , and @xmath154 where @xmath155 is the radius of the snr in the adiabatic stage described by the similarity solution ( sedov 1959 ; spitzer 1968 ) , and @xmath156 , @xmath157 and @xmath158 are the age ( years ) , total energy of the snr ( in units of @xmath159 erg ) , and the density of the ambient medium ( @xmath160 ) , respectively . substitution of equation ( 2 ) in equation ( 1 ) yields @xmath161 where @xmath162 . assuming that the thickness of the emitting region at the shock is @xmath163 , the x - ray luminosity of the blast wave shell can be calculated from @xmath164 where @xmath155 is described by equation ( 2 ) and @xmath165 is the total emissivity of the gas and depends on the electron density @xmath166 and the cooling function @xmath167 via the relation @xmath168 . for a strong shock @xmath169 . the cooling function @xmath170 is estimated to be ( raymond , cox , & smith 1976 ) @xmath171 for a gas of @xmath172 ( @xmath173 ) . in figure 9 , we have plotted the condition for the undetectability of a snr in the radio band ( eq . [ 1 ] ) , and the restriction on the temperature of the blast wave ( @xmath174 ) in the @xmath175 phase space where the temperature just behind the shock front can be calculated from @xmath176 and @xmath177 and @xmath178 are the mean mass of the gas particle and the boltzman constant , respectively . we have also plotted relevant constant luminosity lines . from the region of the allowed parameters in this plot , we conclude that the average luminosity and age of the contributing snrs is expected to be @xmath179 and @xmath180 years , respectively . the x - ray luminosity of the entire disk in the @xmath96 kev band from the _ thermal _ component ( which accounts for approximately 50% of the emission ) is estimated to be @xmath181 ( 3.4.2 ) . this implies that a sn explosion rate of @xmath182 per century is required to power the thermal emission from the entire disk . on the other hand , the luminosity of the thermal component of the thin disk is about @xmath183 . then a sn explosion rate of @xmath42 per century is sufficient to power the thermal emission from the thin disk . whether this scenario is viable depends on the number of snrs that are actually detected in the x - ray band in the galactic ridge . if the snrs have an average luminosity of @xmath184 , approximately 200 of them are needed to power the thermal emission from the ridge . so far , 215 snrs have been detected in the radio band ( green 1996 ) . based on the prevalence of snrs among a sample of unidentified galactic radio sources , helfand et al . ( 1989 ) have built a model which predicts the existence of up to @xmath185 snrs in the galactic disk in the radio band . according to their results , these remnants are within detection capability of current instruments but are not yet identified . one of the goals of the _ asca _ galactic plane survey project is to identify snrs in the galactic disk ( in the region @xmath186 and @xmath187 ) that have already been catalogued in other wavebands , and to discover new ones . because of galactic absorption , remnants with low surface brightness will be missed in the survey . however , snrs with fluxes greater than 10 jy at 1ghz will be detected with _ asca _ provided no bright sources are in the field of view . from the most recent _ asca _ survey covering the region @xmath188 and @xmath189 pointed at @xmath30 , 13 snr were detected ( yamauchi et al . 1998 and references therein ) , where 25 snrs in radio and 1 snr in x - ray ( discovered with rosat ) were already known to exist . based on this trend , it can be estimated that approximately half of the radio snrs have significant emission in x - ray . it may then be expected that out of the 215 snrs catalogued in radio , approximately 100 of them should be detected in x - ray . if , we take the prediction of helfand et al . ( 1989 ) at face value , this number increases to @xmath190 . ultimately , whether the galactic snr population can power the thermal emission from the ridge depends on the final number of detected snrs and their average luminosity when the _ asca _ survey is completed . we now turn to the discussion of the origin of the power law tail of the spectrum dominating the hard x - ray / soft @xmath13-ray band . recent analysis of diffuse emission from the galactic ridge with _ asca _ ( kaneda et al . 1997 ) indicates that the spectrum can be fitted with a two temperature non - equilibrium ionization plasma of @xmath191 and 7 , respectively . two factors lead us to believe that the reported high temperature component of 7 kev with _ asca _ is in fact a different interpretation of the power law component reported in this paper . firstly , _ asca _ s sensitivity above 10 kev decreases substantially and goes to zero around 12 kev . thus , distinguishing the power law from the hard thermal component in the _ asca _ data may not be possible . secondly , extension of the two - temperature model above 10 kev does not produce a good fit to the data at higher energies ( as shown in on the other hand , we have unambiguously shown here the presence of the hard power law tail in hard x - ray data . this leads us to conclude that the previously reported super hot ( @xmath192 kev ) component of the ism , is most likely due to non - thermal emission with a power law spectrum that dominates above 10 kev and extends to beyond 100 kev . below , we speculate on the origin of the power law tail . one scenario is to interpret the hard x - ray emission as the result of the superposition of non - thermal tails from snrs . previously non - thermal x - ray emission from sn1006 ( koyama et al . 1995 ) and rx j1713.7 - 3946 ( koyama et al . 1997 ) has been reported . non - thermal @xmath13-ray emission from cas a ( the et al . 1995 ) and a high energy tail in its x - ray spectrum which can be possibly attributed to non - thermal processes ( allen et al . 1997 ) has also been discovered . however , it is not clear if this scenario can account for the bulk of the emission . the x - ray luminosity of the non - thermal emission discovered is about an order of magnitude smaller than the luminosity of the thermal component . in the case of cas a for example ( g. e. allen , private communication ) , the luminosity in the 2 - 10 kev band is @xmath193 , while the luminosity in the 10 - 60 kev is about @xmath194 . from our estimates , the luminosity of the ridge is approximately @xmath195 and @xmath196 in the 2 - 10 kev and 10 - 60 kev bands , respectively . the contribution of the snrs to the thermal component of the spectrum was previously addressed in this section . for the power law tail ( interpreted as non - thermal component ) , this suggests that approximately 750 snrs with non - thermal luminosities of @xmath194 are needed to make up the high energy tail of the spectrum . thus far , substantial number of remnants that exhibit non - thermal emission has not been discovered . therefore , the viability of this scenario awaits further observations . x - rays of 10 - 100 kev can also be produced via inverse compton scattering of energetic electrons on the ambient microwave background , optical , and infrared photons . a power law scattered photon spectrum with photon index @xmath197 is expected if the electron spectrum has energy index @xmath198 . however , the exact contribution from this process is model dependent due to the uncertainty in the interstellar radiation field and the electron spectrum . direct measurement of the electron spectrum is reliable only at gev energies because of the effects of solar modulation at lower energies . irrespective of existing models for the compton scattering contribution and their extrapolation to lower energies , skibo , ramaty , & purcell ( 1996 ) have argued that this mechanism does not produce the bulk of the emission below 100 kev . since compton scattering of microwave background and star light photons require electron energies of 100 mev-10 gev , the electron spectrum must turn up somewhere in that energy range . however , electrons at these energies produce the galactic synchrotron radio emission at 100 mhz frequencies . but since the observed radio spectrum breaks at @xmath199 mhz in the opposite sense to that of the @xmath13-ray emission , they argue that an inverse compton origin is unlikely . a likely possibility for the origin of the power law tail is non - thermal bremsstrahlung . however , bremsstrahlung of sub - mev electrons is highly inefficient due to the fact that ionization and coulomb collision losses exceed bremsstrahlung radiation . for example , for a 100 kev electron , the radiation yield ( i.e. the ratio of energy loss from radiation to that from collision ) is @xmath200 ( berger & seltzer 1964 ) . for a 10 kev electron , the yield drops to @xmath201 . from our estimate , the luminosity of the ridge in the @xmath97 kev band is @xmath202 . an order of magnitude estimate implies that in order to account for the power law tail via electron bremsstrahlung , a power of @xmath203 is required . skibo et al . ( 1996 ) have calculated that a total power input up to @xmath204 is required if the tail extends down to 10 kev . the total injected power into the galaxy via supernova explosion is only @xmath205 assuming @xmath206 is released in a sn explosion every 30 years . several attempts have been made to explain the source of this large power . skibo et al . ( 1996 ) have suggested that the power is derived from the release of the gravitational potential upon the passage of ism through galactic spiral arm compressions . schlickeiser ( 1997 ) explains the implied presence of large population of sub - mev electrons with the existence of interstellar in - situ reacceleration of cosmic ray particles by the ambient interstellar plasma turbulence . based on the empirical results of modelling the data in the wide bandpass of 3 - 500 kev , we suggest that the power law tail should gradually attenuate below some energy in the 10 - 100 kev range ( table 4 ) . this speculation is motivated by comparing the spectral fits of the data above and below 10 kev . above 10 kev , we found that the spectrum can be modelled with a power law of photon index @xmath207 up to 500 kev . on the other hand , when modelling the data in the @xmath4 kev band , the power law slope is @xmath208 . this interpretation lessens the large power requirement for the origin of the power law component via bremsstrahlung and results in the required injection power to be consistent with that expected from sn explosion in the galaxy . unfortunately , the electron spectrum can not be measured due to solar modulation at lower energies . however , our interpretation of the data in this way makes a prediction for the shape of the electron spectrum at lower energies . a detailed calculation of the electron spectrum in this scenario is out of the scope of this paper . in addition to electron bremsstrahlung , we suggest the possibility that _ inverse _ ( or proton ) bremsstrahlung may also contribute to the diffuse emission from the galactic ridge . in the inverse process , the rapidly moving proton radiates instead of the electron and the center of momentum of the proton - electron system is approximately that of the moving proton . boldt & serlemitsos ( 1969 ) have shown that significant radiation is associated with the collisions of suprathermal protons with ambient electrons ( free and bound ) . for the non - relativistic case ( @xmath209 ) , the spectral intensity from the bremsstrahlung of an electron with kinetic energy @xmath210 is the same as that from a suprathermal proton of kinetic energy @xmath211 , where @xmath212 and @xmath213 are the rest mass of the electron and proton , respectively . for example , an electron with kinetic energy of 10 kev produces the same spectral intensity as that of a proton with kinetic energy of @xmath214 mev . the scenario is particularly attractive in the context of particle acceleration and reacceleration in supernova shocks via the diffusive fermi process . for many years , the perception has persisted that supernova remnants are a major source of galactic cosmic rays ( e.g. lagage & cesarsky 1983 ) . recently much work has been done regarding the production of @xmath13-rays in the snrs . modelling of @xmath13-ray production via interaction of the energetic particles with the remnants ambient environment through neutral pion decay , bremsstrahlung , and inverse compton scattering is reviewed by baring ( 1997 ) . one expects that if both electrons and protons are accelerated with equal velocities in the explosion process , both should contribute to the bremsstrahlung emission . the ratio of the bremsstrahlung losses to the collisional losses is roughly the same for both electrons and protons since it is only dependent on the velocity of the radiating particles . however , a simple calculation shows that not only the accelerated protons lifetime is longer than that of electrons , but also they travel farther than electrons from their birthplace . to illustrate this , let us consider bremsstrahlung radiation from an electron of 25 kev . its spectral intensity is similar to that from a proton of 50 mev . however , the range @xmath215 of the 25 kev electron in hydrogen is @xmath216 as opposed to @xmath217 for the 50 mev protons ( berger & seltzer 1964 ; barkas & berger 1964 ) . this translates to distances of approximately 100 pc and @xmath218 mpc for the electrons and protons , respectively . the radial distance @xmath219 from the birthplace of the energetic particles which the particles will travel before they lose all their energy depends on the random walk step length @xmath220 via the relation @xmath221 . while the value of @xmath220 is not well known , it is expected to be much larger than the gyro radii of the particles for the expected galactic magnetic fields but somewhat smaller than the height of the galactic disk . a good estimate is that it is on the order of the coherence length of the magnetic fields . as a quantitative value for this length , we use the study of kim , kronberg , & lancecker ( 1988 ) where they probed the structure of magnetic fields in and around the supernova remnant oa 184 ( g166.2 + 2.5 ) using background radio source rotation measures . based on their study , they find an interstellar magnetic irregularity scale of order 100 pc . using this value , we find the total radial distance @xmath219 from the birthplace of the particles to be approximately 100 pc and @xmath222 kpc for the electrons and protons , respectively . in any case , it is clear that the radial distance travelled by the protons is much larger than that by electrons . likewise , the energy loss lifetime of protons ( @xmath223 ) is much larger than that of the electrons ( by a factor of @xmath224 ) since it is proportional to the mass of the particles . from these estimates , one expects that the proton bremsstrahlung should play a significant role if bremsstrahlung is responsible for the presence of the hard power law tail in the spectrum . this is due to the longer range and energy loss lifetime of the protons compared to electrons . if indeed the birthplace of the energetic electrons and protons are the sites of supernova explosions in the galaxy , electron bremsstrahlung will produce localized hard x - ray emission ( i.e. hot spots ) . on the other hand , proton bremsstrahlung will cause the radiation to be smoothly distributed over the galaxy . this interpretation implies that snrs play a dominant role in the energetics of ism via both thermal and non - thermal emission processes . finally , we calculate the hydrogen ionization rate for the ism in this model . if non - thermal bremsstrahlung dominates above 10 kev , then from our model , the average volume emissivity in the @xmath97 kev for the ridge is @xmath225 . the average radiation yield in the @xmath97 kev band is @xmath226 . this yields a collisional loss rate of @xmath227 . for an average energy loss of 36 ev ( @xmath228 erg ) per hydrogen atom ionized in the ism ( dalgarno & griffing 1958 ) , we find an average ionization rate of @xmath229 for the entire ridge where @xmath230 is the average hydrogen density . previous values derived from observations have been within @xmath231 ( dalgarno & mccray 1972 ; reynolds et al . 1973 from @xmath232 observations ) . our estimate is consistent with these values for an average @xmath233 in the ism . independent of @xmath230 , from the intensity of galactic @xmath234 background at high galactic latitudes , reynolds ( 1984 ) has derived @xmath235 hydrogen ionizations ( with a `` best fit '' value of @xmath236 ) per @xmath237 column perpendicular to the galactic disk for the region within @xmath148 kpc of the sun . our results imply @xmath238 hydrogen ionizations averaged for the ridge . since in our model , the thickness of the broad disk is @xmath42 kpc , our results imply hydrogen ionizations of @xmath239 of the galactic disk which is larger than the @xmath234 estimate by more than a factor of 2 . one reason could be that our estimate is derived by averaging over the central @xmath0 of the plane in longitude where the hard x - ray emission is more intense , while the rate from @xmath234 observation is for regions within @xmath148 kpc of the sun . in any case , this indicates that the collisional losses associated with the bremsstrahlung emission from energetic particles to produce the hard x - ray tail are more than adequate to account for the observed hydrogen ionization rate in the ism .

pca in order to determine the spatial extent , spectral nature , and origin of the emission spectral examination of the emission clearly reveals the presence of a hard power law tail above 10 kev and an emission line from he - like iron , indicating both thermal and possibly non - thermal origins for the diffuse emission . motivated by the similarities between the characteristics of the thermal component of the galactic ridge emission in our model and the thermal emission from supernova remnants ( snrs ) , we discuss the origin of the thermal emission in terms of a population of snrs residing in the galactic disk . we speculate that bremsstrahlung of accelerated electrons and protons in snr sites can play a significant role in producing the hard tail of the spectrum . moreover , their collisional losses can play a major role in the ionization of the ism .

the diffuse x - ray emission from the thin disk surrounding the galactic mid - plane ( the so - called galactic ridge ) was measured with _ rxte _ pca in order to determine the spatial extent , spectral nature , and origin of the emission . spatial examination of the diffuse emission in the central of the plane in galactic longitude reveals the presence of two components : a thin disk of full width centered roughly on the galactic mid - plane , and a broad component which can be approximated as a gaussian distribution with fwhm of about . assuming an average distance of 16 kpc to the edge of the galaxy , a scale height of about pc and 500 pc is derived for the thin and broad disk components , respectively . spectral examination of the emission clearly reveals the presence of a hard power law tail above 10 kev and an emission line from he - like iron , indicating both thermal and possibly non - thermal origins for the diffuse emission . the averaged spectrum from the ridge in the kev band can be modelled with a raymond - smith plasma component of temperature kev and a power law component of photon index . based on this finding , we argue that the temperature of the hot phase of the interstellar medium ( ism ) is less than the previously reported values of kev . motivated by the similarities between the characteristics of the thermal component of the galactic ridge emission in our model and the thermal emission from supernova remnants ( snrs ) , we discuss the origin of the thermal emission in terms of a population of snrs residing in the galactic disk . we find that a sn explosion rate of less than 5 per century is adequate to power the thermal emission from the ridge . the origin of the emission in the hard x - ray band modelled by a power law remains uncertain . possible contributions from non - thermal bremsstrahlung of cosmic ray electrons and protons , inverse compton scattering of energetic electrons from ambient microwave , infrared , and optical photons , non - thermal emission from snrs , and emission from discrete x - ray sources are discussed . we speculate that bremsstrahlung of accelerated electrons and protons in snr sites can play a significant role in producing the hard tail of the spectrum . moreover , their collisional losses can play a major role in the ionization of the ism . accepted for publication in the astrophysical journal

astro-ph9804012

c

our results are summarized as follows : ( 1 ) from the _ rxte _ survey of the galactic plane , we find that the diffuse emission from the galactic ridge has two spatial components : a thin disk of width @xmath240 , and a broad component with a functional form that can be approximated by a gaussian distribution of about @xmath108 fwhm . assuming an average distance of 16 kpc to the edge of galaxy , this translates to a height of 70 pc and 500 pc for the thin and broad disk , respectively . ( 2 ) a hard power law tail is clearly detected in the spectrum and dominates above 10 kev , implying that the emission in hard x - ray possibly has non - thermal origin . on the other hand , the detection of the emission line from he - like iron in the spectrum ( and also lower energy lines from mg , si , s in the spectrum from _ asca _ ) motivates the idea that part of the emission below 10 kev has thermal origin . ( 3 ) the spectrum in the @xmath4 kev band can be well modelled with a raymond - smith plasma component of @xmath148 kev plus a power law component of photon index @xmath6 . the spectrum above 10 kev simultaneously fitted with _ osse _ s spectrum can be fitted with a power law of photon index @xmath123 . the change in the power law slope at lower energies hints at the possibility that the power law either flattens or gradually attenuates below some energy between 10 - 100 kev . ( 5 ) the characteristics of the thermal component of the diffuse emission resembles that of the snrs . from this interpretation , we calculate that a sn explosion rate of less than 5 per century is adequate to power the thermal emission from the ridge . ( 6 ) the origin of the emission in the hard x - ray band modelled by a power law is uncertain . while unresolved discrete sources are expected to contribute , the bulk of the emission is expected to be of diffuse origin . one possibility is the non - thermal bremsstrahlung of electrons and protons which may have been accelerated in the snr sites . based on the empirical modeling of the data in a wide energy band , we speculate that the power law either flattens or gradually attenuates at lower energies . this lessens the large power injection required to explain the hard power law tail via either electron or proton bremsstrahlung . it will also make it consistent with the power injected to the galaxy via supernova explosion . ( 7 ) the hydrogen ionization rate implied from our model is @xmath229 averaged over the central ridge . generally , values of @xmath231 are expected in the ism . this is an indication that the collisional losses associated with the bremsstrahlung radiation of energetic particles that produce the hard power law tail are sufficient to explain the ionization rates observed in the ism . finally , we expect that simultaneous _ rxte_/_osse _ observations of the diffuse emission from the galactic ridge will allow the exclusion of hard discrete sources from the spectrum and will tightly constrain the hard tail slope that dominates in the hard x - ray / soft @xmath13-ray band . this will enhance our understanding of the origin of the power law tail and the energetics of ism . we are grateful to elihu a. boldt for many valuable discussions , in particular for bringing the process of proton bremsstrahlung to our attention and his contribution to the relevant arguments presented in this paper . we also thank him for a careful reading of the manuscript . we acknowledge g. e. allen , e. boldt , k. ebisawa , s. hunter , k. jahoda , g. m. madejski , r. m. mushotzky , and r. petre for useful discussions . we are grateful to j. g. skibo for providing the diffuse emission spectrum measured with _ osse_. the help of pat tyler and seth digel in producing plate 1 is greatly appreciated . we thank the referee , k. koyama , for many insightful comments that led to the improvement of this paper . acknowledges support from the national academy of sciences and the national research council through a research associateship at nasa s goddard space flight center . green , d. a. 1996 , a catalogue of galactic supernova remnants ( 1996 august version) , mullard radio astronomical observatory , cambridge , uk ( available on the www at http://www.mrao.cam.ac.uk/survey/snr/ ) . j1744 - 28 & 0.044 & 0.301 grs1739 - 278 & 0.660 & 1.167 sl1735 - 269 & 0.785 & 2.400 k1731 - 260 & 1.074 & 3.655 4u1744 - 26 & 2.294 & 0.793 gx5 - 1 & 5.079 & -1.018 4u1745 - 203 & 7.725 & 3.795 gx9 + 1 & 9.072 & 1.154 gx13 + 1 & 13.518 & 0.108 gx17 + 2 & 16.432 & 1.276 4u1812 - 12 & 18.033 & 2.362 g21.5 - 0.9 & 21.493 & -0.887 gr11(1 ) & 22.001 & -0.002 exo1846 - 031 & 29.954 & -0.917 g1843 + 009 & 33.108 & 1.746 gps1858 + 015 & 35.416 & -1.648 xte j1856 + 053 & 38.258 & 1.266 exo1902 + 054 & 39.33 & -0.390 ss433 & 39.695 & -2.247 4u1909 + 07 & 42.089 & -0.940 w49b & 43.275 & -0.189 a1907 + 09 & 43.743 & 0.477 grs1915 + 105 & 45.366 & -0.219 msh15 - 52 & 320.321 & -1.161 circinusx-1 & 322.117 & 0.038 4u1553 - 542 & 327.945 & -0.857 2e1614 - 505 & 332.421 & -0.422 1608 - 522 & 330.926 & -0.850 4u1624 - 49 & 334.914 & -0.263 gx340 + 0 & 339.587 & -0.079 2s1702 - 429 & 343.887 & -1.314 oao1653 - 40 & 344.369 & 0.326 nsco94 & 344.982 & 2.456 4u1708 - 408 & 346.327 & -0.928 gps1709 - 396 & 347.300 & -0.333 4u1700 - 37 & 347.755 & 2.173 gps1713 - 388 & 348.394 & -0.543 ctb37a / b & 348.598 & 0.232 gx349 + 2 & 349.105 & 2.750 exo1722 - 363 & 351.474 & -0.548 a1744 - 361 & 354.121 & -4.192 mxb1728 - 34 & 354.305 & -0.151 x1730 - 333 & 354.843 & -0.159 terzan2 & 356.320 & 2.298 sl1746 - 331 & 356.816 & -2.997 h1741 - 322 & 357.125 & -1.607 r1747 - 313 & 358.556 & -2.168 2s1742 - 294 & 359.559 & -0.390 a1742 - 289 & 359.930 & -0.043 absorption & @xmath79 ( @xmath247 ) & @xmath248 raymond - smith & @xmath95 ( kev ) & @xmath249 & abundance ( solar ) & @xmath250 & normalization & @xmath251 power law & photon index & @xmath208 & normalization & @xmath252 & @xmath253 & absorption & @xmath79 ( @xmath247 ) & @xmath254 raymond - smith & @xmath95 ( kev ) & @xmath255 & abundance ( solar ) & @xmath250 & normalization & @xmath256 power law & photon index & @xmath257 & @xmath258 & @xmath259 & normalization & @xmath260 & @xmath261 & absorption & @xmath79 ( @xmath247 ) & @xmath262 raymond - smith & @xmath95 ( kev ) & @xmath263 & abundance ( solar ) & @xmath250 & normalization & @xmath264 power law & photon index & @xmath265 & normalization & @xmath266 & @xmath267 & absorption & @xmath79 ( @xmath247 ) & @xmath268 raymond - smith & @xmath95 ( kev ) & @xmath269 & abundance ( solar ) & @xmath250 & normalization & @xmath270 power law & photon index & @xmath271 & normalization & @xmath272 & @xmath273 &

. spatial examination of the diffuse emission in the central of the plane in galactic longitude reveals the presence of two components : a thin disk of full width centered roughly on the galactic mid - plane , and a broad component which can be approximated as a gaussian distribution with fwhm of about . assuming an average distance of 16 kpc to the edge of the galaxy , a scale height of about pc and 500 pc is derived for the thin and broad disk components , respectively . the averaged spectrum from the ridge in the kev band can be modelled with a raymond - smith plasma component of temperature kev and a power law component of photon index . based on this finding , we argue that the temperature of the hot phase of the interstellar medium ( ism ) is less than the previously reported values of kev . we find that a sn explosion rate of less than 5 per century is adequate to power the thermal emission from the ridge . the origin of the emission in the hard x - ray band modelled by a power law remains uncertain .

the diffuse x - ray emission from the thin disk surrounding the galactic mid - plane ( the so - called galactic ridge ) was measured with _ rxte _ pca in order to determine the spatial extent , spectral nature , and origin of the emission . spatial examination of the diffuse emission in the central of the plane in galactic longitude reveals the presence of two components : a thin disk of full width centered roughly on the galactic mid - plane , and a broad component which can be approximated as a gaussian distribution with fwhm of about . assuming an average distance of 16 kpc to the edge of the galaxy , a scale height of about pc and 500 pc is derived for the thin and broad disk components , respectively . spectral examination of the emission clearly reveals the presence of a hard power law tail above 10 kev and an emission line from he - like iron , indicating both thermal and possibly non - thermal origins for the diffuse emission . the averaged spectrum from the ridge in the kev band can be modelled with a raymond - smith plasma component of temperature kev and a power law component of photon index . based on this finding , we argue that the temperature of the hot phase of the interstellar medium ( ism ) is less than the previously reported values of kev . motivated by the similarities between the characteristics of the thermal component of the galactic ridge emission in our model and the thermal emission from supernova remnants ( snrs ) , we discuss the origin of the thermal emission in terms of a population of snrs residing in the galactic disk . we find that a sn explosion rate of less than 5 per century is adequate to power the thermal emission from the ridge . the origin of the emission in the hard x - ray band modelled by a power law remains uncertain . possible contributions from non - thermal bremsstrahlung of cosmic ray electrons and protons , inverse compton scattering of energetic electrons from ambient microwave , infrared , and optical photons , non - thermal emission from snrs , and emission from discrete x - ray sources are discussed . we speculate that bremsstrahlung of accelerated electrons and protons in snr sites can play a significant role in producing the hard tail of the spectrum . moreover , their collisional losses can play a major role in the ionization of the ism . accepted for publication in the astrophysical journal

0901.0208

i

let @xmath0 be a properly embedded , separating surface with no torus components in a compact , orientable 3-manifold @xmath5 . then the _ disk complex _ , @xmath6 , is defined as follows : 1 . vertices of @xmath6 are isotopy classes of compressions for @xmath0 . 2 . a set of @xmath7 vertices forms an @xmath8-simplex if there are representatives for each that are pairwise disjoint . here we explore what information is contained in the topology of @xmath6 . to this end , we define : [ d : indexn ] the _ homotopy index _ of a complex @xmath9 is defined to be 0 if @xmath10 , and the smallest @xmath1 such that @xmath11 is non - trivial , otherwise . we say a surface @xmath0 is _ topologically minimal _ if its disk complex @xmath6 is either empty or non - contractible . when @xmath0 is topologically minimal , we say its _ topological index _ is the homotopy index of @xmath6 . for example , a surface @xmath0 has topological index 1 if and only if @xmath12 is non - trivial , i.e. its disk complex is disconnected . when @xmath0 is the boundary of a handlebody then the disk complex was first defined by mccullough in @xcite , who showed that in this case @xmath6 is contractible . it follows that such surfaces are not topologically minimal . the goal of the present paper is to show that topologically minimal surfaces are a natural generalization of several well - known classes of surfaces in 3-manifolds , and that the results that hold for each of these classes also hold true for all topologically minimal surfaces . as an added benefit , proofs involving the set of all topologically minimal surfaces are often much shorter than existing proofs involving just , say , index 2 surfaces . this is largely owing to the inductive nature of the arguments . by definition , incompressible surfaces have topological index 0 . in the next section we show that the _ strongly irreducible _ surfaces of casson and gordon @xcite are precisely those that have topological index 1 . we also show that _ critical surfaces _ , previously defined by the author in @xcite and @xcite , have topological index 2 . one important property shared by these types of surfaces is that they may always be isotoped to meet an incompressible surface in a collection of loops that are essential on both . we show here that this is in fact a corollary of a powerful result about all topologically minimal surfaces . this is given by theorem [ c : maincorollary ] , which asserts that a topologically minimal surface @xmath0 and an incompressible surface @xmath2 can be isotoped so that @xmath3 is topologically minimal in @xmath13 . section [ s : heegaard ] contains corollaries to theorem [ c : maincorollary ] . we show there that if @xmath5 contains a topologically minimal heegaard surface then @xmath14 is incompressible . it then follows that if a closed 3-manifold @xmath5 contains any topologically minimal surface @xmath0 then either it is a heegaard surface , @xmath5 is haken , or @xmath0 is contained in a ball . ( in the final section we conjecture that this last possibility can not happen . ) finally , we show that if the disjoint union of surfaces is topologically minimal then so are its components , and its topological index is the sum of the indices of its components . combining this with theorem [ c : maincorollary ] , we find that a surface @xmath0 with topological index @xmath1 can be isotoped to meet an incompressible surface @xmath2 in such a way so that the sum of the indices of the components of @xmath3 is at most @xmath1 . this is a generalization of known results about topological index 0 and 1 surfaces . in any new theory , the questions raised are as important as the new results . in the final section of this paper we list a few tantalizing questions and conjectures about topologically minimal surfaces . these include conjectures about the possible indices of topologically minimal surfaces in various kinds of 3-manifolds , a natural generalization of hempel s _ distance _ invariant @xcite to surfaces of arbitrary topological index , and conjectures which relate geometric minimal surfaces to topologically minimal surfaces . much of the motivation for this work comes from ideas of hyam rubinstein . in the late 1990 s rubinstein pioneered the viewpoint that strongly irreducible heegaard splittings were the right class of surfaces within which to search for unstable ( geometrically ) minimal surfaces of index 1 , as well as their pl analogues , the so - called almost normal " surfaces . one often finds such surfaces by minimax arguments involving 1-parameter sweepouts . many of the topological arguments involving strongly irreducible surfaces also use 1-parameter sweepouts , so it became natural to think about such surfaces as being topologically minimal , " in a very imprecise sense . in later work the author defined critical surfaces as an attempt to find some topological analogue to geometrically minimal surfaces that have index 2 . as one would expect from such an analogue , arguments involving critical surfaces often involve 2-parameter sweepouts . in this paper we make precise the idea of topological index , demonstrate its usefulness , and conjecture its relation to geometric minimal surfaces . the present work is the first in a sequence of papers on this topic . in @xcite we define a relative version of topological index for surfaces with non - empty boundary . the main result of that paper is that complicated amalgamating surfaces act as barriers to low index , low genus , topologically minimal surfaces . this is the key technical tool necessary for the author s construction of a counter - example to the _ stabilization conjecture _ for heegaard splittings @xcite . further applications are given in @xcite , where we prove several results about amalgamation and isotopy of heegaard splittings . finally , in joint work with jesse johnson , we produce examples of 3-manifolds containing surfaces with high topological index @xcite . the author thanks several people for helpful comments during the preparation of this paper . jesse johnson had helpful suggestions regarding the construction of the family @xmath15 defined in the proof of theorem [ t : maintheorem ] . cameron gordon , daryl cooper , and andrew casson provided advice necessary for the proof of corollary [ c : indexsum ] . general helpful comments were made by martin scharlemann and yoav moriah . finally , it was saul schleimer and eric sedgiwck who first brought the index 1 case of theorem [ c : componentsintersection ] to the attention of the author , which was the beginings of the paper @xcite . in some sense this work is an extension of the main result of that paper .

the disk complex of a surface in a 3-manifold is used to define its _ topological index_. surfaces with well - defined topological index are shown to generalize well known classes , such as incompressible , strongly irreducible , and critical surfaces . the main result is that one may always isotope a surface with topological index to meet an incompressible surface so that the sum of the indices of the components of is at most . this theorem and its corollaries generalize many known results about surfaces in 3-manifolds , and often provides more efficient proofs . the paper concludes with a list of questions and conjectures , including a natural generalization of hempel s _ distance _ to surfaces with topological index .

the disk complex of a surface in a 3-manifold is used to define its _ topological index_. surfaces with well - defined topological index are shown to generalize well known classes , such as incompressible , strongly irreducible , and critical surfaces . the main result is that one may always isotope a surface with topological index to meet an incompressible surface so that the sum of the indices of the components of is at most . this theorem and its corollaries generalize many known results about surfaces in 3-manifolds , and often provides more efficient proofs . the paper concludes with a list of questions and conjectures , including a natural generalization of hempel s _ distance _ to surfaces with topological index .

1004.5444

i

for a heavy hadron which contains a single heavy quark ( bottom or charm ) , the heavy quark mass @xmath4 is much larger than the qcd energy scale @xmath5 which characterizes the light degrees of freedom in the heavy hadron . the four momentum of the heavy quark can be expressed as @xmath6 , where @xmath7 is taken to be the velocity of hadron at the rest frame , and @xmath8 is the residual momentum of the order of binding energy , which is much smaller than @xmath4 . the heavy quark symmetry @xcite and its breaking effects are of particular importance in studying such hadrons . consequently , the heavy quark effective theory ( hqet ) has been developed , where the effective lagrangian is expanded in @xmath9 . in deriving the lagrangian of hqet , the quark and antiquark are assumed to be conserved separately . namely the heavy antiquarks are regarded as completely decoupled from the heavy quarks at the beginning . the transition matrix elements can also be represented in series of @xmath9 through the heavy quark expansion ( hqe ) and evaluated order by order . hqet and hqe have been discussed by many authors @xcite . in the past two decades they are widely used in studying heavy hadrons . when the momentum of the heavy quark is much lower than the quark - antiquark pair creation threshold , an alternative framework of effective field theory for heavy quarks can directly be derived from the full qcd @xcite . just like for other effective theories , the basic idea is that some degrees of freedom characterizing higher scale physics can be decomposed and integrated out when we consider physics at low energy scales . concretely speaking , for heavy quarks with @xmath10 , one may perform a complete decomposition of the qcd full field into quark field and antiquark field via positive and negative energy components ( see below ) of a full field , and integrate out the small components of quark field and antiquark field , which leads to the so - called @xmath9 corrections . when considering heavy quark ( or antiquark ) systems , one should further integrate in the contributions of heavy antiquark ( or quark ) components . as a consequence , additional @xmath9 corrections arise from the quark - antiquark coupling terms in the full qcd . it should be noted that such a framework is distinguishable from the usual hqet in which the particle and antiparticle were assumed to be conserved separately and treated in a different way . for convenience , we refer to such a framework as a heavy quark effective field theory ( hqeft ) . though the heavy quark - antiquark coupling effects vanish in the heavy quark limit , they are actually nonzero when one considers the finite mass contributions . it is then not surprising that the @xmath9 corrections evaluated in hqeft and hqet could be different though they are the same in the infinity mass limit . for instance , the transition matrix elements of @xmath9 corrections concern less independent wave functions in hqeft than in the usual hqet and the @xmath9 order corrections at zero recoil automatically vanish in hqeft , and there exist some relations between wave functions and heavy hadron masses in hqeft . hqeft has been applied to explore various processes of heavy hadrons . in particular , the cabibbo - kobayashi - maskawa ( ckm ) matrix elements @xmath3 and @xmath11 are extracted from both inclusive @xcite and exclusive @xcite b decays . in the treatment of inclusive b decays , the dressed heavy quark mass @xmath0 as a whole enters the formulation , which implies that a dressed heavy quark "- hadron duality is more reasonable than the naive heavy quark - hadron duality . as a consequence , when the inclusive decay rates of heavy hadrons are expressed in terms of the physical hadron masses , they receive no @xmath2 order corrections . this treatment not only suppresses the next - to - leading order contributions and makes the operator product expansion ( ope ) reliable , but also diminishes the large uncertainties arising from the heavy quark mass . for exclusive decays , hqeft has also been demonstrated to be reliable . whereas in our previous works the heavy quark expansion for the effective lagrangian and transition matrix elements is carried out in powers of @xmath9 . in this paper , we briefly review the description of hqeft and show that a @xmath2 expansion is also consistently applicable to the heavy quark effective lagrangian and transition matrix elements . in sec . [ sectionlagrangian ] , we first outline the derivation of a complete hqeft and then extend it to the formulation in terms of @xmath2 expansion . in sec . [ sectionmatixelement ] , we present new formulae for hqe of heavy - to - heavy transition matrix elements by applying the @xmath2 expansion . in sec . [ sectionvcb ] , we extract the ckm matrix element @xmath3 based on the new formulation and the most recent experimental data . our conclusions are given in sec . [ sectionsummary ] .

a heavy quark expansion in terms of the inverse of the dressed heavy quark mass is presented with a complete decomposition of the full field and integrating out the small components . the heavy quark - antiquark coupling effects are included in the finite mass corrections . the extraction of from exclusive b decays is studied by using such a new expansion approach .

the dressed heavy quark mass with being the binding energy is introduced to characterize the heavy hadrons containing a single heavy quark . a heavy quark expansion in terms of the inverse of the dressed heavy quark mass is presented with a complete decomposition of the full field and integrating out the small components . the heavy quark - antiquark coupling effects are included in the finite mass corrections . it is shown that the expansion is more favorable in application . the extraction of from exclusive b decays is studied by using such a new expansion approach .

1703.02911

i

engines are machines that convert some form of energy ( e.g. , thermal or electrical energy ) into work . their efficiency , defined as the ratio of the extracted work to the invested energy , is restricted to @xmath0 at most by the energy - conservation law . while mechanical engines may reach this bound , carnot showed @xcite that the efficiency of any heat engine that cyclically operates between two thermal baths is universally limited by the ratio of the bath temperatures , regardless of the concrete design @xcite . the universality of this bound led to the formalisation of the second law of thermodynamics and the introduction of the notion of entropy by clausius @xcite . in terms of entropy , the carnot bound is attained by ( idealised ) heat engines that operate reversibly , so that the total entropy of the engine and the baths is unaltered over a cycle @xcite . this corresponds to the minimum amount of heat being dumped into the cold bath , so as to close the cycle , and hence to the maximum input heat being transformed into work . by contrast , in an irreversible cycle , a larger amount of heat must be dumped into the cold bath , so that less input heat is available for conversion into work , causing the engine efficiency to decrease @xcite . as part of the effort to understand the rapport between quantum mechanics and thermodynamics @xcite ( see @xcite for recent reviews ) , the carnot bound has been challenged for quantum engines that exploit non - thermal quantum baths @xcite . in this respect , a distinction is to be drawn between two types of non - thermal engines @xcite , ( i ) engines wherein the working medium equilibrates to a thermal state whose temperature is adjustable ( e.g. , by the phase of the coherence in a `` phaseonium '' bath @xcite ) , which qualify as genuine heat engines with a controllable carnot bound , and ( ii ) engines wherein the non - thermal ( e.g. , squeezed @xcite ) bath may render the working - medium state non - thermal , making the carnot bound irrelevant . the efficiency bound of the latter type of engines has been addressed @xcite but still needs elucidation : what is particularly puzzling is that , contrary to heat engines , their efficiency bound can not be deduced from the requirement of reversible operation : reversibility may entail an efficiency bound that not only surpasses the carnot bound but also unity @xcite , making it unachievable . hence , the question naturally arises whether such engines are limited by constraints other than the second law . the second law for quantum relaxation processes is widely accepted @xcite to be faithfully rendered by spohn s inequality @xcite . here we show that the inadequacy of assessing the maximum efficiency via this standard reversibility criterion arises whenever the engine s working medium is in a non - passive quantum state @xcite . the definition @xcite of a non - passive state is that its energy can be _ unitarily _ reduced until the state becomes passive , thereby extracting work . non - passive states may thus be thought of as being `` quantum batteries '' @xcite or `` quantum flywheels '' @xcite ( fig . [ fig_ergotropy ] ) . the maximum amount of work extractable from such states ( their `` work capacity '' ) has been dubbed `` ergotropy '' in ref . for example , every population - inverted state is non - passive and so are , e.g. , coherent or squeezed field states , whereas thermal states are passive . as we show , the standard reversibility criterion provides an inequality for the change in the engine entropy which may be much too loose ( non - tight ) to be useful if non - passive states are involved . the distinction between non - passive and passive states is at the heart of our analysis and underlies our division of the energy exchanged between a quantum system and a bath into a part that _ necessarily _ causes an entropy change , and ergotropy . our proposed division is in fact a new unraveling of the first law of thermodynamics for quantum systems . in scenarios where non - thermal baths may create non - passive states of the working medium , we derive a new inequality for the entropy change which yields a physical efficiency limit of the engine that never surpasses unity . this efficiency limit is universal and in general can not be assessed by the standard reversibility criterion . concrete examples of such engines are given .

quantum engines fuelled by non - thermal ( e.g. , squeezed - thermal ) baths have been shown to surpass this bound . yet , their maximum efficiency can not be determined by the reversibility condition , which may yield an unachievable efficiency bound above . this prompts the question : what does really limit the efficiency ? we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive a new inequality for the latter . this bound thus can not be solely deduced from the laws of thermodynamics .

the efficiency of heat engines is limited by the carnot bound , attained when the engine cycle is reversible . quantum engines fuelled by non - thermal ( e.g. , squeezed - thermal ) baths have been shown to surpass this bound . yet , their maximum efficiency can not be determined by the reversibility condition , which may yield an unachievable efficiency bound above . this prompts the question : what does really limit the efficiency ? we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive a new inequality for the latter . this formulation reveals a universal efficiency bound for quantum engines which is invariably attained for the least dissipation over the engine cycle but does not imply reversibility , unless the baths are thermal . this bound thus can not be solely deduced from the laws of thermodynamics . we illustrate these results for the practically - relevant carnot- and otto cycles energised by non - thermal baths , which are both shown to be restricted by our new efficiency bound .