article
stringlengths 0
10k
| abstract
stringlengths 21
108k
|
|---|---|
planetary and proto - planetary nebulae ( pne , ppne ) present conspicuous departures from spherical symmetry , including e.g. multiple lobes and jets . to explain their evolution from spherical agb envelopes ,
several models have postulated the presence of dense rings or disks close to the central post - agb stars as the agents of the mechanical collimation of the stellar wind .
existing observations reveal the presence of central disks in several ppne , but their limited spatial resolution can not unveil the very inner regions of the disks that are relevant for the processes mentioned above .
our first vlba observations of sio masers in oh231.8 + 4.2 , carried out at 7 mm ( @xmath0=2 , @xmath1=10 ) in april 2000 , revealed for the first time the structure and kinematics of the close stellar environment in a ppn ( sanchez contreras et al . , 2002 ) .
the sio maser emission arises in several compact , bright spots forming a structure elongated in the direction perpendicular to the symmetry axis of the nebula .
such a distribution is consistent with an equatorial torus with a radius of @xmath26 au around the central star .
a complex velocity gradient was found along the torus , which suggests rotation and infall of material towards the star .
the rotation and infalling velocities deduced are of the same order and range between @xmath27 and @xmath210kms@xmath3 .
such a distribution is remarkably different from that found in other late - type stars , where the masers form a roughly spherical ring - like chain of spots resulting from tangential maser amplification in a thin , spherical shell ( diamond et al . , 1994 , desmurs et al . , 2000 ) .
the new vlba observations at 3 mm were observed on april 2002 .
the data were recorded in dual circular polarization over a bandwidth of 16 mhz , assuming a rest frequency of 86243.442 mhz for the @xmath0=1 @xmath1=21 sio maser emission , for a final spectral resolution of about 0.1 km s@xmath3 .
we frequently observed several calibrators for band - pass and phase calibration ; pointing was checked and corrected every less than half an hour .
the data reduction followed the standard scheme for spectral line calibration data in aips . to improve the phase calibration solutions , we extensively map all the calibrators , and their brightness distribution
were introduced and taken into account in the calibration process .
our vlba maps at 3 mm ( fig .
1 ) show two sio maser spots that are globally aligned with those at 7 mm , i.e. , they are roughly distributed orthogonally to the nebular symmetry axis .
the velocities of the two maser spots observed at 3 mm are in good agreement with velocities observed at 7 mm .
the spatial distribution and velocity structure of the sio maser spots at 3 mm and 7 mm are consistent with a torus with radius @xmath46a.u@xmath5 , perpendicular to the nebular symmetry axis ( inclined @xmath6 with respect to the plane of the sky ) .
this torus - like structure is not totally traced by the maser spots .
such a spot distribution is expected , even for a homogeneous torus , if the maser is tangentially amplified .
this amplification mechanism leads to the most intense maser features at the edges of the torus - like structure .
moreover , given the comparable size of the star and the maser emitting region , occultation by the star of the far side of the torus is very likely , which would partially explain the small number of detected spots . in our opinion ,
the structure traced by the sio maser emission in oh231.8 + 4.2 , compatible with a rotating+infalling torus very close to the central star , is unlikely an accretion disk .
the dynamic is well reproduced by a simple model considering the presence of an inner torus in rotation and infall with a radius of @xmath2 5au ( r@xmath74.5 au ) , which means very close to the surface of the star ( sanchez contreras et al . , 2002 ) .
in fact , the dramatic changes with time of the sio @xmath0=2 , @xmath1=10 profile suggest that the masers lie in a region with an unstable structure and/or kinematics , rather than in a stable accretion disk .
moreover , accretion disks are expected around the compact companion in a binary system and less likely around the mass - losing star .
finally , it is worth mentioning that : ( a ) 3 mm maser spots are located further away from the central star than those at 7 mm , similarly to what has been recently found in agb stars ( see soria - ruiz et al . , these proceedings ) ; and ( b ) the rotation velocity measured in the torus of oh231.8 + 4.2 is consistent with the values of the rotation velocity found in inner envelopes of several agbs ( nml cyg : boboltz & marvel , 2000 ; tx cam and irc+10011 : desmurs et al .
, 20001 , r aqr : hollis et al . , 2001 ) .
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ boboltz , d. a. & marvel , k. b. , 2000 , , 545 , 149 .
+ desmurs , j. f. , bujarrabal , v. , colomer , f. , & alcolea , j.2000 , , 360 , 189 .
+ desmursj.f . , v. bujarrabal , f. colomer & j. alcolea , 2001 , iau symposium 206 , eds .
v. migenes et al . ,
+ hollis , j. m. , boboltz , d. a. , pedelty , j. a. , white , s. m. & forster , j. r. 2001 , , 559 , l37-l40 .
+ sanchez contreras , c. , desmurs , j. f. , bujarrabal , v. , colomer , f. , alcolea , j. , 2002 , a&a 385 , l1-l4 .
+ soria - ruiz r. , colomer f. , alcolea j. , desmurs j.- f. , bujarrabal v. , marvel k.b . ,
diamond p.j . , & boboltz d. , 2003 , these proceedings .
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ | we present milliarsecond - resolution maps of the sio maser emission @xmath0=1 j=21 ( 3 mm ) in the bipolar post - agb nebula oh231.8 + 4.2 , and compare them with our previous observations of the @xmath0=2 j=10 line ( 7 mm ) .
our observations show that the sio masers arise in several bright spots forming a structure elongated in a direction perpendicular to the symmetry axis of the nebula .
this , and the complex velocity gradient observed , is consistent with the presence of an equatorial torus in rotation and with an infall of material towards the star .
# 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
over the past decade , the analysis of particle multiplicities in heavy ion collions has shown overwhelming evidence for chemical equilibrium in the final state except for particles carrying strangeness which are mildly suppressed ; however , their relative yields fulfill statistical equilibrium . a summary as of 2006 , combining the results from many different groups @xcite , is shown in fig . [ eovern ] . us determined from heavy ion collisions at different beam energies .
the lower ags points are based on a preliminary analysis of @xmath2 data.,width=226 ] except for particle multiplicities at rhic energies , all data in fig .
[ eovern ] use integrated particle yields , the very systematic change of thermal parameters over the full range of beam energies is one of the most impressive features of relativistic ion collisions to date .
it is now possible to use the thermal model to make solid predictions for particle multiplicities at lhc energies @xcite and to determine which beam energy will lead to the highest baryon density at freeze - out @xcite . with chemical equilibrium for integrated yields
thus firmly established , we focus on other properties , in particular , since the rapidity distributions of identified particles is now becoming available also at rhic energies @xcite , it is now possible to determine the rapidity dependence of thermal parameters .
a first analysis was done by stiles and murray @xcite for the data obtained by the brahms collaboration at 200 gev @xcite .
this shows a clear dependence of the baryon chemical potential on rapidity in particular due to the changing @xmath3 ratio .
subsequently it was shown by rhrich @xcite that the particle ratios at large rapidities are consistent with those measured at the sps energies .
this opens the possibility to compare measurements for e.g. the @xmath4 ratio at high rapidities and check them with the corresponding values measured in the energy scan at the sps , thus complementing the rapid variation of this ratio as a function of beam energy .
a further analysis of the rapidity dependence was recently done in ref .
a detailed report of our results will be presented elsewhere @xcite .
the general procedure is as follows : the rapidity axis is populated with fireballs following a gaussian distribution function given by @xmath5 where @xmath6 is the rapidity of the fireball .
particles will appear when the fireball freezes out and will follow a thermal distribution centered around the position of the fireball @xmath7 the momentum distribution of hadron @xmath8 is then calculated from the distribution of fireballs as given by eq .
[ [ eqrho ] ] along the rapidity axis as follows @xmath9 where @xmath10 is the the distribution of hadrons from a single fireball .
the temperature @xmath0 and the baryon chemical potential @xmath1 will depend on the rapidity of the fireball and are not assumed to be constant .
an important parameter is the width of the distribution . for the rhic data at 200 gev
this was determined from the @xmath11 s as these are very sensitive to the value of @xmath12 and less to variations in the baryon chemical potential .
the width of the distribution @xmath13 is compatible with the values quoted by the brahms collaborationi @xcite , e.g. @xmath14 and @xmath15 .
the hadrons described by eq . [ [ eqdist ] ] are mainly resonances
. only a fraction of these are stable under strong interactions .
the majority of them will decay into stable hadrons at chemical freeze - out , hence the need to implement multi - particle decays .
we assume that the temperature @xmath0 and the chemical potential @xmath1 are always related via the freeze - out curve as given in fig . [ [ eovern ] ] ; if the temperature varies along the rapidity axis , then also the chemical potential will vary .
thus a decrease in the temperature of the fireball will be accompanied by an increase in the baryon chemical potential . in other words , we assue a universality of the chemical freeze - out condition .
this relationship between temperature and baryon chemical potential is very reasonable since all particle abundancies measured so far follow it .
once the width of the distribution of fireballs has been fixed , we can go on with the dependence of the baryon chemical potential on the rapidity of the fireball ( units are in gev ) . @xmath16
the dependence of the @xmath3 ratio on the parameter @xmath17 is shown in figure [ [ fig : mub_y ] ] .
the best value is @xmath18 gev .
ratio as a function of rapidity .
the curves show the dependence on the baryon chemical potential on the rapidity as discussed in the text.,width=226 ] the variation of the temperature along the rapidity axis is shown in fig .
[ fig : tmuy ]
. the temperature is maximal at mid - rapidity and gradually decreases towards higher ( absolute ) values of the rapidity .
the baryon chemical potential follows a different pattern : it has a minimum at mid - rapidity and increases quite substantially towards higher values of the rapidity .
of particular interest are the largest values of the rapidity ( say @xmath19 ) .
it can be seen that there is a region of overlap with the data obtained at the na49 experiment at cern - sps .
particle yields measured in heavy ion collisions show an overwhelming evidence for chemical equilibrium at all beam energies . the rapidity dependence of the thermal parameters @xmath0 and @xmath1 can now be determined over a wide range of rapidities and
show a systematic behavior towards an increase in @xmath1 as the rapidity is increased .
this work was supported in part by the scientific and technological co - operation programme between italy and south africa , project number 16 .
the help of d. cebra with the preliminary 4@xmath20 data at the lower ags beam energies is gratefully acknowledged , r. adams has helped in the analysis of these data in fig .
[ 1 ] is acknowledged .
99 for references see e.g. j. cleymans , h. oeschler , k. redlich , s. wheaton , phys .
c73 ( 2006 ) 034905 .
j. cleymans , i. kraus , h. oeschler , k. redlich , s. wheaton , phys .
c74 ( 2006 ) 034903 .
j. randrup and j. cleymans , phys .
c74 ( 2006 ) 047901 .
stiles and m. murray , nucl - ex/0601039 , unpublished .
d. rhrich , proceedings of the talk given at the workshop on `` critical point and the onset of deconfinement '' , florence , italy , july 2006 .
i. arsene at al . ,
brahms collaboration , phys .
94 ( 2005 ) 162301 .
bearden , brahms collaboration , contribution to the qm2006 conference , shanghai , china , november 2006 .
b. biedron , w. broniowski , nucl - th/0610083 . f. becattini and j. cleymans ( in preparation ) .
w. broniowski and f. florkowski , phys .
c65 ( 2002 ) 064905 ; j. phys .
g31 ( 2005 ) s1087 . | particle yields in heavy ion collisions show an overwhelming evidence for chemical or relative chemical equilibrium at all beam energies . the rapidity dependence of the thermal parameters @xmath0 and @xmath1 can now be determined over a wide range of rapidities and
show a systematic behavior towards an increase in @xmath1 away from mid - rapidity . |
the lhcb detector @xcite at the large hadron collider is dedicated to study the physics in the decay of b - flavoured and other heavy hadrons . at the nominal luminosity of @xmath0 at the location of lhcb and a production cross section of @xmath1 at 14tev proton - proton collisions , @xmath2 pairs
are expected to be produced annually .
the modest luminosity requirement for lhcb can be met very early during lhc operation , long before the high luminosity runs and later maintained adjusting the lhc optics when larger luminosities are delivered to the other multi - purpose experiments at the lhc .
lhcb is designed as a single arm forward spectrometer adapted to the angular distribution of the pairs which are produced predominantly at low polar angles as shown in figure [ fig : lhcb ] .
the detector covers an angular region from about 10mrad to 300(250)mrad in the bending ( non - bending ) plane of the magnet .
lhcb uses a warm dipole magnet that delivers an integrated magnetic field of 4tm .
there are two ring imaging cherenkov detectors , rich1 and rich2 located before and behind the magnet , respectively .
these two detectors that use three different radiator materials , aerogel , @xmath3 and @xmath4 , give excellent @xmath5-k separation in a large momentum range of 2 - 100 gev / c . the vertex detector ( velo ) and the full silicon tracking station ( tt - station ) before the magnet and the three tracking stations behind the magnet
provide the tracking system of lhcb .
the stations behind the magnet are divided into the silicon strip inner tracker and the straw tube outer tracker .
the calorimeter system consists of a scintillator pad detector and preshower ( spd / ps ) , a `` shashlik type '' electromagnetic calorimeter , and the fe plus scintillating tile hadronic calorimeter .
the detector is completed with a muon system that uses multi - wire proportional chambers and triple - gem s in the very first muon station .
lhcb is using a level-0 hardware trigger that reduces the initial interaction rate of 16mhz down to 1mhz using transverse energy measured in the calorimeters and the two highest @xmath6 muons seen in the muon chambers .
after a level-0 trigger , the whole detector is read out and the information used in the high level trigger ( hlt ) where in several stages of reconstructing the events , the rate is reduced to 2khz at which the events are stored .
commissioning activities have started in 2007 with the first individual sub systems and safety devices being tested in parallel with the final installation of subdetectors which finished in spring 2008 .
first commissioning activity made use of internal test pulses to test the functionality of the readout and of detector elements .
sending test pulses and receiving the detector responses allows testing the full control and readout chain of the sub - detectors .
dead or noisy channels are located ( and eventually fixed / replaced where possible ) and consistency checks also allow in certain cases to track down possible cabling swapping and alike . from known cable lengths and delays measured using test pulses the initial settings for the time alignment were set for the different sub - detectors . despite the horizontal geometry of the lhcb detector and a very low rate under 1hz of reasonably horizontal cosmic particles within the 250mrad of the horizontal acceptance , over a million cosmic events were recorded in lhcb .
first these rare cosmic events were used to commission the level-0 trigger , aligning calorimeters and later the muon chambers in time to one another as done end of 2007 .
special low thresholds were used in the calorimeter to be able to trigger on mips together with a loose coincidence between ecal and hcal which in the end results in a trigger rate of about 10hz .
a cosmic particle showing a nice `` track '' in the calorimeters is shown in figure [ fig : cosmic ] .
internal time alignment of the various calorimeter cells using the known pulse - shape from test - beam measurements is reaching a precision of about 3ns .
the muon trigger also was used for cosmic events using a coincidence between two stations omitting the vertex constrained used in the real experiment s trigger .
the muon stations were also time aligned using these cosmic events as shown in the left part of figure [ fig : cosmic ] .
time alignment with cosmic muons in lhcb needs to disentangle the forward from the backward going particles . which is nicely displayed in figure [ fig : cosmic ] , showing the timeing for forward and backward particles .
the outer tracker and inner tracker stations located in front of the calorimeter stations ( separated only by the rich2 detector ) were commissioned using the cosmic particles triggered by either the calorimeters or the muon detector . despite the small surface of the inner tracker
, some clear cosmic events could be seen as `` coincidences '' of hits in neighbouring silicon layers within a detector box .
this allowed for a very first rough time alignment of the inner tracker with the calorimeters , using known cable lengths for the internal time alignment . very helpful for this exercise was the possibility in lhcb to trigger on and read out up to 15 consecutive events .
this allowed to read out a window of @xmath77 events around an event triggered by the calorimeters and find the corresponding coincidences in the inner tracker .
two tracks with hits in all three inner tracker stations were found in over a million cosmic triggers .
while commissioning with cosmic events is not feasible for the vertex detector and the tt - station `` far away '' from the calorimeters , we profited here from synchronisation tests in the injection lines done by the lhc machine group . during these tests ,
the injection beam of the sps accelerator was dumped on a beam stopper ( ted ) located about 300 m downstream of lhcb .
this resulted in a large number of about 10gev muons in lhcb and the first tracks seen in the velo .
careful analysis of these data allowed also for first spatial alignment studies of the velo , and some of those results are shown in figure [ fig : velott ] .
it shows the hit residuals as a function of the strip pitch which increases with radius of the radial strips .
the plot shows the performance achieved during the test - beam measurements and the expected performance for binary resolution without any charge sharing between the strips . the current measured resolution after this first alignment step was already well inbetween these two lines . of the velo as a function of the strip pitch which changes with sensor position .
the left plot shows the residual of tracks reconstructed in the velo and extrapolated to one of the tt - station layers.,title="fig:",scaledwidth=28.0% ] of the velo as a function of the strip pitch which changes with sensor position .
the left plot shows the residual of tracks reconstructed in the velo and extrapolated to one of the tt - station layers.,title="fig:",scaledwidth=38.0% ] the tt - station consists of only four individual layers , too little to make stand alone tracking .
however , once can extrapolate the velo tracks and look at the hit residuals in the different layers of the tt - station .
this results in very nice peaks with a widths of about 500@xmath8 and small overall shifts of the order of some hundred @xmath8depending on the layer . for one layer
this is shown in figure [ fig : velott ] .
the spread expected from simple extrapolation of the tracks would be of the order of 300@xmath8due to the resolution in the velo .
this shows a very good initial alignment of the two sub - detectors w.r.t each other as well as a first hint of the internal positioning accuracy of the tt - station modules .
the large number of hits recorded in the silicon trackers during these `` ted - events '' also allowed for a very accurate time alignment of the detectors within a few ns , not achievable with the very limited number of cosmic events .
a reconstructed charge distribution in the inner tracker and a pulseshape derived from varying the relative timing between the beam and the readout clock is shown in figure [ fig : pulseshape ] .
commissioning in lhcb had started as early as 2007 . making extensive use of internal generated test pulses but also cosmic ray events despite the horizontal geometry of lhcb .
very useful proved the beam induced events when the injection beam was dumped in the injection line some 300 m behind the detector which in the end allowed us to get first time alignment and spatial alignment of basically all sub - detectors .
the long shutdown that followed after the lhc incident on september 19 is being used for maintenance and further improvement on the overall efficiency of the detector .
the time is also being used for more tests of the detector readout at the full trigger rate of 1mhz , data processing and writing .
the latter has been successfully tested to speeds up to 1.9khz , close to the design of 2khz . for the year
2009 run , the full hlt computer farm will be available which will allow to take data at full lhcb rate . | lhcb has been installed by spring 2008 , followed by intensive testing and commissioning of the system in order to be ready for first data taking . despite the horizontal geometry of the lhcb detector it was possible to collect over one million useful cosmic events that allowed a first time alignment of the sub - detectors .
moreover events from beam dumps during the lhc synchronisation tests provided very useful data for further time and spacial alignment of the detector . here
we present an overview of our commissioning activities , the current status and an outlook on the startup in 2009 . |
a lot of research in the field of information retrieval aims at improving the _ quality _ of search results .
search quality might for instance be improved by new scoring functions , new indexing approaches , new query ( re-)formulation approaches , etc . to make a scientific judgment of the quality of a new search approach , it is good practice to use so - called benchmark test collections , such as those provided by trec @xcite .
the following steps typically need to be taken : 1 .
the researcher codes the new approach by adapting an experimental search system , such as lemur @xcite , pf / tijah @xcite , or terrier @xcite ; 2 .
the researcher uses the system to create an inverted index on the documents from the test collection ; 3 .
the researcher puts the queries to the experimental search engine and gathers the top @xmath0 search results ( a common value for trec experiments is @xmath1 ) ; 4 .
the researcher compares the top @xmath0 to a golden standard by computing standard evaluation measures such as mean average precision .
in our experience , step 1 , actually coding the new approach , takes by far the most effort and time when conducting an information retrieval experiment .
coding new retrieval approaches into existing search engines like lemur , pf / tijah and terrier is a tedious job , even if the code is maintained by members of the same research team .
it requires detailed knowledge of the existing code of the search engine , or at least , knowledge of the part of the code that needs to be adapted .
radical new approaches to information retrieval , i.e. , approaches that need information that is not available from the search engines inverted index , require reimplementing part of the indexing functionality .
such radical new approaches are therefore not often evaluated , and most research is done by small changes to the system . in his wsdm keynote lecture , dean
@xcite describes how mapreduce @xcite is used at google for experimental evaluations .
new ranking ideas are tested off - line on human rated query sets similar to the queries from trec . running such off - line tests
has to be easy for the researchers at google , possibly at the expense of the efficiency of the prototype .
so , it is okay if it takes hours to run for instance 10,000 queries , as long as the experimental infrastructure allows for fast and easy coding of new approaches .
a similar experimental setup was followed by microsoft at trec 2009 : craswell et al .
@xcite use dryadlinq @xcite on a cluster of 240 machines to run web search experiments .
their setup also sequentially scans all document representations , providing a flexible environment for a wide range of experiments .
the researchers plan to do many more to discover its benefits and limitations .
the work at google and microsoft shows that sequential scanning over large document collections is a viable approach to experimental information retrieval .
some of the advantages are : 1 .
researchers spend less time on coding and debugging new experimental retrieval approaches ; 2 .
it is easy to include new information in the ranking algorithm , even if that information would not normally be included in the search engine s inverted index ; 3 .
researchers are able to oversee all or most of the code used in the experiment ; 4 .
large - scale experiments can be done in reasonable time .
we show that indeed sequential scanning is a viable experimental tool , even if only a few machines are available . in section [ sec : approach ] we describe the mapreduce search system .
sections [ sec : results ] and [ sec : conclusion ] contain experimental results and concluding remarks .
mapreduce is a framework for batch processing of large data sets on clusters of commodity machines @xcite .
users of the framework specify a _
mapper _ function that processes a key / value pair to generate a set of intermediate key / value pairs , and a _ reducer _ function that processes intermediate values associated with the same intermediate key .
the pseudo code in figure [ tab : pseudocode ] outlines our sequential search implementation .
the implementation does a single scan of the documents , processing all queries in parallel .
[ cols= " < " , ] anchor text extraction on all english documents of clueweb09 takes about 11 hours on our cluster .
the anchor text representation contains text for about 87 % of the documents , about 400 gb in total .
a subsequent trec run using 50 queries on the anchor text representation takes less than 30 minutes .
our linear search system implements a fairly simple language model with a length prior without stemming or stop words .
it achieves expected precision at 5 , 10 and 20 documents retrieved of respectively 0.42 , 0.39 , and 0.35 ( mtc method ) , similar to the best runs at trec 2009 @xcite .
figure [ fig : time ] shows how the system scales when processing up to 5,000 queries , using random sets of queries from the trec 2009 million query track .
reported times are full hadoop job times including job setup and job cleanup averaged over three trials .
processing time increases only slightly if more queries are processed .
whereas the average processing time per query is about 35 seconds per query for 50 queries , it goes down to only 1.6 second per query for 5,000 queries . for comparison ,
the graph shows the performance of `` lemur - one - node '' , i.e. , lemur version 4.11 running on _
one fourteenth _ of the anchor text representation on a single machine . a distributed version of lemur searching the full full anchor text representation would not do faster
: it would be as fast as the slowest node , it would need to send results from each node to the master , and to merge the results .
lemur - one - node takes 3.3 seconds per query on average for 50 queries , and 0.44 seconds on average for 5,000 queries .
the processing times for lemur were measured after flushing the file system cache .
although lemur can not process queries in parallel , the system s performance benefits a lot from receiving a lot of queries .
lemur s performance scales sublinearly because it caches intermediate results .
still , at 5,000 queries lemur - one - node is only 3.6 times faster than the mapreduce system . for experiments at this scale , the benefits of the full , distributed lemur are probably negligible .
the idea to use sequential scanning of documents to research new retrieval approaches is certainly not new : we know of at least one researcher who used sequential scanning over ten years ago for his thesis @xcite . without high - level programming paradigms like mapreduce , however , efficiently implementing sequential
scanning is not a trivial task , and without a cluster of machines the approach does not scale to large collections .
lin @xcite used hadoop mapreduce for computing pairwise document similarities .
our implementation resembles lin s brute force algorithm that also scans document representations linearly .
our approach is simpeler because our preprocessing step does not divide the collection into blocks , nor does it compute document vectors .
a faster turnaround of the experimental cycle can be achieved by making coding of experimental systems easier .
faster coding means one is able to do more experiments , and more experiments means more improvement of retrieval performance .
we implemented a full experimental retrieval system with little effort using hadoop mapreduce . using 15 machines to search a web crawl of 0.5 billion pages ,
the proposed mapreduce approach is less than 10 times slower than a single node of a distributed inverted index search system on a set of 50 queries .
if more queries are processed per experiment , the processing times of the two systems get even more close .
the code used in our experiment is open source and available to other researchers at : http://mirex.sourceforge.net
many thanks to sietse ten hoeve , guido van der zanden , and michael meijer for early implementations of the system .
the research was partly funded by the netherlands organization for scientific research , nwo , grant 639.022.809 .
we are grateful to yahoo research , barcelona , for sponsoring our cluster .
n. craswell , d. fetterly , m. najork , s. robertson , and e. yilmaz . at trec 2009 : web and relevance feedback tracks . in _ proceedings of the 18th text retrieval conference ( trec)_. nist special publication 500 - 278 , 2009 .
brute force and indexed approaches to pairwise document similarity comparisons with mapreduce . in _ proceedings of the 32nd international acm sigir conference on research and development in information retrieval _ , 2009 .
y. yu , m. isard , d. fetterly , m. budiu , u. erlingsson , p. kumar , and j. currey . : a system for general - purpose distributed data - parallel computing using a high - level language . in _ proceedings of the 8th symposium on operating system design and implemention ( osdi ) _ , 2008 . | we propose to use mapreduce to quickly test new retrieval approaches on a cluster of machines by sequentially scanning all documents .
we present a small case study in which we use a cluster of 15 low cost machines to search a web crawl of 0.5 billion pages showing that sequential scanning is a viable approach to running large - scale information retrieval experiments with little effort .
the code is available to other researchers at : http://mirex.sourceforge.net |
sensitivity of diffractive lepto and photoproduction to the gluon density in the proton gives an excellent tool to test these structure functions .
intensive experimental study of diffractive processes were performed in desy @xcite .
theoretical analysis shows that the cross sections of diffractive hadron production are expressed in terms of skewed parton distributions ( spd ) @xcite .
the diffractive charm @xmath0 production and @xmath2 production are determined by the gluon spd @xmath3 because the charm component in the proton is small . for
light hadron production effects of the quark spd should be important for not small @xmath4 . in the polarized case
, the spin - dependent gluon distributions can be investigated . in future , there will be an excellent possibility of studying spin effects with transversely polarized target at hermes and compass . in this report
, we consider double spin asymmetries for longitudinally polarized leptons and transversely polarized protons in diffractive vector @xmath0 production at high energies ( see @xcite ) which is expressed in terms of the polarized cross sections @xmath5 at small @xmath4 the diffractive contribution to the asymmetry @xmath1 determined by the pomeron exchange should be important . in the qcd-
based models the pomeron is usually regarded as a two - gluon state . within the two - gluon exchange model the two - gluon coupling with the proton can be written as follows : @xmath6 here the structure proportional to @xmath7 determines the spin - non - flip contribution .
the term @xmath8 leads to the transverse spin - flip at the vertex .
it has been found within the model approaches @xcite that the ratio @xmath9 and has a weak energy dependence ( weak @xmath4 dependence ) .
the weak energy dependence of spin asymmetries in exclusive reactions is not in contradiction with the experiment @xcite .
the diffractive @xmath0 production in the lepton - proton reaction is determined by the photon - two - gluon fusion .
the spin - average and spin - dependent cross section can be written in the form @xmath10 here @xmath11 is a normalization coefficient , the functions @xmath12 are determined by a sum of all graphs integrated over the gluon momenta @xmath13 and @xmath14 .
we calculate here the imaginary parts of the photon - two - gluon fusion amplitudes which are expressed directly in terms of the functions @xmath15 and @xmath16 from ( [ ver ] ) .
the function @xmath17 has the form @xmath18 here @xmath19 and @xmath20 with @xmath21 .
the gluon structures @xmath22(@xmath23 ) are connected with the @xmath24(@xmath25 ) spd ( see ( [ bqq],[kqq ] ) ) .
thus , the functions @xmath15 and @xmath16 are the nonintegrated gluon distributions . the hard part @xmath26 in ( [ np ] ) can be calculated perturbatively when @xmath27 is not small , about @xmath28 or larger .
the spin - dependent contribution @xmath29 has two terms proportional to the scalar products ( @xmath30 ) and ( @xmath31 ) @xcite .
we consider here only the term proportional to @xmath32 which can be written as follows : @xmath33.\ ] ] the other term @xmath34 has been discussed in @xcite .
the asymmetry is determined by the ratio @xmath35 . at small @xmath4 the gluon structure functions
have large imaginary part . in this case
the asymmetry can be approximated as @xmath36 in numerical calculations we use a simple parameterization of the spd as a product of the form factor and the ordinary gluon distribution @xcite . in our estimations
we use the value @xmath37 .
we analyze the case when the @xmath38 asymmetry has a maximal value ( the momentum @xmath39 is parallel to the target polarization @xmath40 ) . the predicted @xmath1 asymmetry in diffractive light @xmath0 production at @xmath41
is shown in fig .
this asymmetry is not small for @xmath42 .
the @xmath38 asymmetry has a strong mass dependence . for heavy quark production
this asymmetry becomes negative , fig .
it is interesting to have predictions for a light quark production at the slac and hermes low energy range @xmath43 . here
the `` window '' for perturbative calculation is quite small .
really , it can be found in this case that the maximum value of the transverse momentum is limited by @xmath44 because we have the restriction @xmath45 from ( [ sigma ] ) . in
target experiments , it is usually difficult to detect the final hadron and determine the momentum transfer . in this case , we estimate the asymmetry integrated over momentum transfer @xmath46 @xmath47 ; @xmath48 .
the predicted integrated asymmetry is about 3% .
note that we have calculated here only the gluon contribution to the asymmetry . at hermes energies
the contribution of the quark spd to the @xmath1 asymmetry should be important .
to conclude , we would like to emphasize that the diffraction contribution to the @xmath1 asymmetry is found to be proportional to the ratio of @xmath49 structure functions .
the predicted coefficient @xmath50 in ( [ cltqq ] ) is not small , about 0.3 - 0.5 .
this shows the possibility of studying the transverse distribution @xmath51 in future experiments with a transversely polarized target ( hermes , compass and future erhic facilities )
. these results could be applicable to reactions with heavy quarks . for processes with light hadron production
, our predictions can be used in the small @xmath4 region ( @xmath52 e.g. ) where the contribution of the quark spd is expected to be small .
the recoil particle detector is needed to distinguish the diffractive events .
really , in the case when the recoil detector is absent , the diffractive events are detected together with nondiffractive ones .
the measured asymmetry in this case looks like @xmath53 here @xmath54 and @xmath55 .
the ratio @xmath56 integrated over @xmath4 has been found at hera to be about 0.200.30 @xcite . in this case , the diffractive contribution to asymmetry will be smaller by the factor 3 - 5 .
99 h1 collaboration , s. aid et al .
b472 * , 3 ( 1996 ) ; + zeus collab . , j. breitweg et al . , z. phys , * c75 * , 215 ( 1997 ) .
zeus collab . , j. breitweg et al . , eur .
j. * c5 * , 41 ( 1998 ) ; + h1 collab .
, c. adloff et al . , eur .
j. * c6 * 421 ( 1999 ) .
radyushkin , phys.rev , d * 56 * , 5524 ( 1997 ) .
x. ji , phys.rev .
d * 55 * 7114 ( 1997 ) .
goloskokov , hep - ph/0112268 to appear in euro .
goloskokov , s.p .
kuleshov , o.v .
selyugin , z. phys . *
c50 * , 455 ( 1991 ) .
goloskokov , p. kroll , phys .
d * 60 * , 014019 ( 1999 ) .
h1 collaboration , aid s. et al , _ z. phys . _ * c69 * , 27 ( 1995 ) . | we consider double spin asymmetries for longitudinally polarized leptons and transversely polarized protons in diffractive @xmath0 production which is connected with @xmath1 asymmetry .
the predicted asymmetry is large and can be used to obtain the information on the polarized skewed gluon distributions in the proton . |
are the dark matter halos of lsb galaxies `` cuspy '' nfw halos , or are they `` cored '' isothermal halos ?
nfw halos can be fit to the observations , but the cosmological parameters implied by the fits are inconsistent with the standard lcdm picture .
isothermal halos provide much better fits , but they have no cosmological dependence or theoretical basis .
we address this question with new data that is both high resolution and two - dimensional .
we observed 12 lsb galaxies using the densepak integrated field unit on the wiyn telescope at kitt peak .
densepak is comprised of 3 diameter fibers arranged in a 43 @xmath1 28 rectangle .
velocities of the h@xmath2 , [ ] @xmath36584 , [ ] @xmath36717 , and [ ] @xmath36731 emission lines were measured in each fiber .
rotation curves were derived from the two - dimensional velocity fields using the nemo program rotcur .
we combined the densepak rotation curves with previous longslit and hi curves .
we fit the combined data with isothermal and nfw@xmath4 halos .
we also fit an nfw@xmath5 halo which was required to match the velocities at the outer radii of each galaxy , in effect , constraining the concentrations to agree with cosmology .
image of ugc 5750 ; observed velocity field ( km s@xmath6 ) ; minimum disk halo fits to combined data ; combined rotation curves.,title="fig : " ] image of ugc 5750 ; observed velocity field ( km s@xmath6 ) ; minimum disk halo fits to combined data ; combined rotation curves.,title="fig : " ] + image of ugc 5750 ; observed velocity field ( km s@xmath6 ) ; minimum disk halo fits to combined data ; combined rotation curves.,title="fig:",width=181 ] image of ugc 5750 ; observed velocity field ( km s@xmath6 ) ; minimum disk halo fits to combined data ; combined rotation curves.,title="fig:",width=181 ]
we found only one galaxy to be well fit by the nfw halo .
this shows that we would have detected cusps in the other cases had they been present .
future work will include mass modeling and an assessment of systematic effects .
* acknowledgments .
* this research was supported by nsf grant ast 0206078 . | we present high resolution two dimensional velocity fields from integral field spectroscopy along with derived rotation curves for nine low surface brightness galaxies .
this is a positive step forward in terms of both data quality and number of objects studied .
we fit nfw and pseudo - isothermal halo models to the observations .
we find that the pseudo - isothermal halo better represents the data in most cases than the nfw halo , as the resulting concentrations are lower than would be expected for @xmath0cdm . |
since their first detection by cobe , the cmb temperature fluctuations have become an essential tool for constraining cosmological parameters . from the beginning of 2000 , new experiments have released data set of good quality up to the third acoustic peak .
better constraints have been obtained on several cosmological parameters .
nevertheless , it has been shown that even with precise measurements of the power spectrum , it is nearly impossible to distinguish models with the same physical parameters on the last scattering surface . basically , some degeneracies are inherent to the cmb . we consider in this work x
ray clusters as an independent way for constraining cosmological parameters .
in the present analysis we consider the data from cobe , boomerang , maxima and dasi .
we analysed the likelihood of inflationary models with @xmath0 , @xmath1 as free cosmological parameters .
this corresponds to @xmath2 models tested.to derive the likelihood values for the models we considered , we used the method developed in bartlett et al .
( 2000 ) , and already used in le dour et al .
( 2000 ) .
the results are presented as two - dimensional contours plots of the likelihood projected onto various parameters planes .
this 2-d presentation has the advantage of showing clearly all the degeneracies between parameters .
the left contour plots of figure 1 show some degeneracies between our parameters .
basically , @xmath3 , @xmath4 and @xmath5 are strongly degenerated if only cmb data are used in parameter estimation .
this means that one should consider another source of constraints , independent from cmb observations , for a better cosmological parameter estimation .
we choose x - ray clusters as additional constraints .
clusters are interesting object for which both the luminous baryonic mass ( x - ray emitting intracluster gas ) and the total gravitating mass can be determined .
therefore , an upper limit on the fraction baryon , @xmath6 , can be estimated .
results are not necessary in agreement allowing values between @xmath7 and @xmath8 . in this work ,
we consider the constraints given in sadat and blanchard 2001 @xcite for the baryon fraction : @xmath9 .
the aim of this contribution being to show that clusters may help for breaking degeneracies shown by cmb parameters estimations , we did not consider constraints given by other groups .
a better consideration of these different results on x - ray clusters will be found in douspis et al .
( 2001b ) .
given the constraints of cmb and x - ray clusters , one could combined the two by multiplying the corresponding likelihood . the right figure of fig .
1 shows the constraints from the combined analysis in the same plane as the left figure .
we can see that the degeneracies are broken .
confidence intervals are now determined for @xmath3 and @xmath4 . for both parameters ,
low values are preferred : @xmath10 and @xmath11 at 99% cl . due to inherent degeneracies in the cmb
it is nearly impossible to specify some of the cosmological parameter ; `` cross constraints '' are then necessary .
this work is thus a preliminary view of the kind of constraints one would obtain in a near future , using last x ray satellite data , and in a less near future the cmb satellite data ( map and planck ) . | we present the results of a combined analysis of cosmic microwave background ( cmb ) and x - ray galaxy clusters baryon fraction to deduce constraints over 6 inflationnary cosmological parameters .
such a combination is necessary for breaking degeneracies inherent to the cmb .
# 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
enormous effort has gone into understanding the nature of sub - mm selected galaxies since they were first discovered with the submillimetre common user bolometer array ( scuba , holland et al .
1999 ) just under a decade ago ( e.g. smail et al . 1997 ; barger et al . 1998 ; hughes et al .
1998 ) . a general understanding of the sub - mm population and its role in galaxy evolution
is severely limited by the poor spatial resolution of current sub - mm telescopes and the faintness of these sources at other wavelengths ( e.g. pope et al .
the sub - mm population appears to consist of massive objects ( borys et al .
2005 ; greve et al . 2005 ) at @xmath1 ( chapman et al . 2005 ;
pope et al . 2005 ) .
these galaxies are rare and have very high star formation rates ( sfrs , lilly et al . 1999 ;
scott et al . 2002 ) , and hence may represent an early phase in the evolution of massive elliptical galaxies .
an outstanding question remains : are the incredible infrared luminosities of sub - mm galaxies powered by huge bursts of star formation or agn activity ? to assess in detail what powers the intense ir luminosity of sub - mm galaxies it is important to obtain a complete multi - wavelength picture .
the sample of sub - mm galaxies discussed in this paper is taken from the goods - n scuba super - map ( borys et al . 2003 ; pope et al . 2005 ) .
this is a purely sub - mm selected sample and it is almost completely identified at other wavelengths thanks to the deep multi - wavelength data available in the goods - n field ( see pope et al .
2006 for more details ) .
the addition of the mips photometry to the multi - wavelength dataset for sub - mm galaxies provides powerful constraints on the shape of the sed , the nature of the power source , and the source redshift . in the left panel of fig . 1
, we plot the @xmath2 flux ratio as a function of redshift as compared to several models . in general , this flux ratio as a function of redshift is lower than that of other ultra luminous infrared galaxies ( ulirgs ) of the same luminosity at low and high redshift .
this suggests that sub - mm galaxies either have higher levels of extinction or cooler dust temperatures .
this can be tested further by looking in detail at the mid - ir spectrum .
using deep multi - wavelength follow - up observations of sub - mm galaxies , it is possible to study their seds to derive fundamental properties such as dust properties and sfrs . in the right panel of fig . 1 , we plot a composite rest - frame sed for the sub - mm sources with spectroscopic redshift as compared to several models . we find that sub - mm galaxies have cooler average dust temperatures than those of local ulirgs of the same luminosity ( see pope et al .
2006 for more details ) .
this result is confirmed with the addition of deep @xmath3 m imaging of these sub - mm galaxies ( huynh et al .
this may indicate that their far - ir emission is more extended than that of local ulirgs , in which the majority of the ir emission comes from within the central kpc ( charmandaris et al .
the seds of sub - mm galaxies are also different from those of their high redshift neighbours selected at near - ir wavelengths ( e.g. bzk galaxies , daddi et al .
2005 ) , whose mid - ir to radio seds are more like those of local ulirgs .
we may understand this difference in terms of the evolutionary scenario advocated by vega et al .
( 2005 ) , in which enshrouded star forming galaxies undergo four distinct phases characterized by different mid- and far - ir colours . under their scheme , the sub - mm galaxies , with cooler temperatures , may be an earlier phase in the star formation than bzk galaxies .
many sub - mm galaxies show evidence of an agn , as determined either through x - ray observations ( alexander et al .
2005 ) , or with optical spectra ( swinbank et al
. 2004 ; chapman et al . 2005 ) , however it is unclear if the agn is a significant contributor to the bolometric luminosity of the galaxy .
mid - ir spectroscopy can help determine what powers sub - mm galaxies since these wavelengths contain a number of features which are sensitive to the nature of the energy source ( clavel et al .
2000 ; hudgins & allamandola 2004 ) .
we obtained _ spitzer _ irs observations of a sample of the sub - mm galaxies and agn in goods - n ( go2 pi : r. chary ) .
2 shows the rest - frame raw irs spectra for 10 sub - mm sources from this sample , offset for clarity .
all of these spectra show at least weak polycyclic aromatic hydrocarbon ( pah ) emission .
we have obtained several new redshifts from these irs spectra ( pope et al . in preparation ) .
3 shows the mean irs spectrum for these sub - mm galaxies compared to those of several local galaxies .
this composite spectrum was calculated by taking the mean of the individual spectra .
note that using the median instead of the mean does not make a significant difference to the shape of the composite spectrum .
we have excluded the top source in fig . 2 since its steeply rising mid - ir continuum is not seen in the other 9 spectra in our sample .
this source is not typical of our sample and is likely to have a stronger agn component . in the composite spectrum
, we see the 6.2 , 7.7 , 8.6 and 11.3@xmath4 m pah features much more clearly . while arp220 is often considered the typical local analog to high redshift sub - mm galaxies , it appears to have more silicate absorption and less 6.2@xmath4 m pah emission than the average sub - mm galaxy .
interestingly , the mid - ir spectra of the sub - mm galaxies seems to resemble that of m82 with the addition of a shallow power - law component ( @xmath5@xmath6 ) .
the total contribution of the power - law component to the total luminosity in this wavelength range is @xmath7 .
m82 is a typical local starburst galaxy but it is at least 2 orders of magnitude less luminous in the ir than the average sub - mm galaxy .
this composite suggests that the mid - ir emission in sub - mm galaxies is dominated by star formation activity and there is little contribution from an agn .
the average 7.7@xmath4 m line to continuum ratio for this sample is @xmath83.5 . comparing this with figure 4 from genzel et al .
( 1998 ) , we find that this ratio for sub - mm galaxies is consistent with the ratios for sbs and ulirgs and not as low as those found for agn .
our preliminary analysis suggests that sub - mm galaxies are powered primarily by sbs and not agn activity .
we are currently working on fitting templates to quantify the level of agn contributing to the ir luminosity and investigating various emission and absorption line strengths as diagnostics for the star formation activity .
combined with the other multi - wavelength data that are already tabulated on these sub - mm sources , we will create a complete picture of the energetics of sub - mm galaxies ( pope et al . in preparation ) .
these data will help determine if sub - mm galaxies and agn populations are connected via an evolutionary sequence .
thanks to the organizers of this conference for a very fruitful meeting .
we also thank our collaborators involved in the goods - n irs project .
this work was supported by the natural sciences and engineering research council of canada and the canadian space agency .
this work is based in part on observations made with the _
spitzer space telescope _ , which is operated by the jet propulsion laboratory , california institute of technology under a contract with nasa .
support for goods , part of the _ spitzer space telescope _
legacy science program , was provided by nasa through contract number 1224666 issued by jpl , caltech , under nasa contract 1407 .
alexander d.m . ,
et al . , 2005 , apj , 632 , 736 barger a.j . , et al . , 1998 , nat , 394 , 248 borys c. , et al . , 2003 , mnras , 344 , 385 borys c. , et al . , 2005 ,
apj , 635 , 853 chapman s.c . , et al . , 2005 , apj , 622 , 772 charmandaris , v. , et al . , 1999 , , 266 , 99 charmandaris v. , stacey g.j . , gull g. , 2002 , apj , 571 , 282 chary r. , elbaz d. , 2001 , apj , 556 , 562 clavel j. , et al . , 2000 , a&a , 357 , 839 daddi e. , et al .
, 2005 , apj , 631 , l13 draine b.t . , 2003 , ara&a , 41 , 241 fischer , j. , et al . 1999 , , 266 , 91 frster schreiber , n. m. , et al .
, 2003 , , 399 , 833 genzel , r. , et al .
1998 , , 498 , 579 greve t.r . , et al . , 2005 ,
mnras , 359 , 1165 holland w.s . , et al . , 1999 , mnras , 303 , 659 hudgins d. m. , allamandola l. j. , 2004 , aspc , 309 , 665 hughes d.h .
, 1998 , nature , 394 , 241 huynh m. et al .
, 2006 , apj submitted lilly s.j .
, et al . , 1999 , apj , 518 , 641 pope a. , et al . , 2005 , mnras , 358 , 149 pope a. , et al . , 2006 , mnras , 370 , 1185 scott s.e . , et al . , 2002 , mnras , 331 , 817 smail i. , ivison r.j . ,
blain a.w . , 1997 ,
apj , 490 , l5 swinbank a.m. , et al . , 2004 , apj , 617 , 64 vega o. , et al .
, 2005 , mnras , 364 , 1286 | submillimetre ( sub - mm ) galaxies have very high infrared ( ir ) luminosities and are thousands of times more numerous at @xmath0 than local ultra - luminous ir galaxies .
they therefore represent a key phase in galaxy evolution which can be missed in optical surveys .
determining their contribution to the global star formation rate requires dissecting their ir emission into contributions from starbursts ( sb ) and active galactic nuclei ( agn ) .
there are several examples of agn systems which masquerade as sbs in either the ir or x - ray , and sbs can often look like agn in some wavebands .
a combination of sb and agn emission is not unreasonable , given models of merger - driven evolution .
to assess in detail what powers the intense ir luminosity of sub - mm galaxies it is important to obtain a complete multi - wavelength picture .
mid - ir spectroscopy is a particularly good probe of where the intense ir luminosity is coming from .
we present the first results from a program to obtain _ spitzer _ irs spectroscopy of a sample of high redshift galaxies in the goods - n field , a large fraction of which are sub - mm galaxies .
this field is already home to the deepest x - ray , optical , ir and radio data .
we piece together the sub - mm data with the _ spitzer _ photometry and irs spectra to provide a well sampled ir spectral energy distribution ( sed ) of sub - mm galaxies and determine the contribution to the bolometric luminosity from the agn and sb components . |
parametric decomposition of galaxy images has become a popular tool to estimate the structural parameters of different galactic components , particularly bulges and discs . through this sort of analysis , one is also able to determine the relative importance of the bulge component , with parameters such as the bulge - to - total luminosity ratio b / t , one of the major features that define the @xcite sequence .
it thus provides indispensable means to investigate the formation and evolution of galaxies , and the origin of the hubble sequence , some of the key subjects in current astrophysical research .
recently , the focus of studies using image decomposition shifted from relatively small samples of very nearby galaxies , where the fits can be done on a more careful , individual basis ( e.g. , ( * ? ? ?
* de jong 1995 ) ) , to include large samples of more distant galaxies , using automated procedures , that allow solid statistical analyses ( e.g. , ( * ? ? ?
* allen 2006 ) ) .
so far , most studies have ignored other components , such as bars ( but see ( * ? ? ?
* ; * ? ? ?
* laurikainen 2004 , 2005 ) ) , although the majority of disc galaxies host bars that usually contain a significant fraction of the galaxy total stellar mass .
it is unclear how the parameters of bulge and disc are affected when bars are ignored .
a similar issue concerns galaxies that host bright , type 1 agn : if the light contribution from the agn is not modelled , the structural parameters obtained might be incorrect .
it is also not clear if the low physical spatial resolution usually found in images of more distant galaxies introduces any bias in the parameters recovered . to shed light on these issues , i performed multi - component image decomposition of a sample of very nearby galaxies and their artificially redshifted images , and verified the effects of removing the bar and agn components from the models .
the results of these tests are shown in the next section [ the reader is referred to @xcite for full details on this work ] .
the images used here are from @xcite . these are v and r images of 17 galaxies at @xmath1 , most of them hosting bars and agn .
image decomposition is done using budda v2.1 ( see ( * ? ? ? * de souza , gadotti & dos anjos 2004 ) ) .
all components are modelled as sets of concentric ellipses , with constant ellipticity and position angle .
bulges are described with a srsic luminosity profile and discs are exponential .
bars are described with boxy ellipses , also with a srsic profile , and the agn contribution is modelled using a circular moffat profile .
when one takes advantage of the full capabilities of the code ( i.e. , all necessary components ) on these images , the results show a fairly good agreement with other studies .
in addition , several known scaling relations are reproduced .
0.3 cm when one does not include the bar component in the models , the major effect is seen in the bulge models recovered : bulges get bigger , in a way to accommodate light from the bar . as a result
, b / t is overestimated , on average , by 50% , but this overestimation can reach a factor of 2 .
disc models are also systematically affected , but to a lesser extent : d / t is overestimated , on average , by 10% , with a maximum overestimation of 30% ( see fig . [ nobar ] ) .
similar effects ( albeit restricted to the bulge component ) result when bright , type 1 agn are not considered in the models : b / t and the srsic index of the bulge @xmath2 can be overestimated by factors of 2 and 4 , respectively . to verify if these results hold when the physical spatial resolution of the images is relatively low , i degraded the original images , thus artificially redshifting them to @xmath3 .
the resolution in these images is 1.5 kpc , which is the typical resolution of sdss at this redshift .
such a resolution is also typical in other works as well , and is what can be achieved at @xmath4 with hst . as with the original images ,
the redshifted images were first used to perform a complete decomposition , and then to test the effects of removing the bar and agn components from the models .
figure [ hz ] shows that , in general , structural parameters can be reliably retrieved through image fitting even in a low resolution regime .
this is particularly true for the disc parameters .
however , bulge parameters are prone to errors if its effective radius @xmath5 is small compared to the seeing radius , and b / t might suffer from systematic effects .
b / t seems to be systematically overestimated , on average , by 0.05 , i.e. , 5% of the total galaxy luminosity , even when @xmath5 is similar to the seeing radius .
when bars are excluded from the models to fit the redshifted images , one still sees similar effects as with the original images , namely , a significant overestimation of b / t and @xmath5 , if bars are prominent .
the change in @xmath5 is even more pronounced in the redshifted images , likely because the geometrical properties of the bulge are substantially smoothed by the seeing , making it more difficult to constrain its properties . for less prominent bars
these effects are reduced in strength .
the effects caused by not taking into account bright agn , i.e. , the overestimation of b / t and @xmath2 , do _ not _ occur with the redshifted images , as the agn contribution is smeared out by the seeing .
when bars are not taken into account , the amount of mass in stars in bulges and discs is overestimated , and the excess is an indication of the amount of mass in stars that reside in bars .
@xcite estimated the @xmath6 stellar mass content in classical bulges and discs through image decomposition of @xmath7 galaxies , with a spatial resolution similar to that of the redshifted images above .
bars are not taken into account in the fitted models , but these authors made a thorough quality control , removing poor fits .
however , it is usually the case that , even when there is no bar in the model , when fitting a barred galaxy , one gets an acceptable ( though wrong ) fit , essentially because the bulge model is distorted . hence , with reasonable assumptions , one can use their results to obtain a _ rough _ estimate of what can be the stellar content in bars , assuming that the biases produced in a low resolution regime and by ignoring bars , as found above , can be used in this case to obtain the true bulge and disc luminosity fractions
thus , the stellar content in classical bulges and discs is found to be @xmath8 and @xmath9 , respectively . and
the stellar content in bars is @xmath10 .
although these are rough estimates , that need to be confirmed by further studies , they open up the possibility of bars being as important as bulges in what concerns their stellar mass content in the local universe .
are disc galaxies ) from the sdss .
bulges show a remarkably different distribution as compared to ellipticals , with the family of pseudo - bulges ( i.e. , those with srsic index less than about 2 ) standing out clearly.,width=340 ] figure [ ndistr ] shows the distribution of the srsic index of bulges and ellipticals in a sample of about 200 disc galaxies and 100 ellipticals from the sdss , obtained using budda v2.1 ( see ( * ? ? ?
* gadotti & kauffmann 2007 ) ) .
one clearly sees the dichotomy between classical bulges , with @xmath11 , and pseudo - bulges , with @xmath12 .
this figure indicates that the fraction of pseudo - bulges at @xmath6 is @xmath13 .
i would like to thank martin bureau and the organisers for this very fruitful meeting .
it is a pleasure to thank guinevere kauffmann for her active role in this work , with insightful comments and suggestions , and ronaldo de souza , for his help in the making of the new budda version .
dag is supported by the deutsche forschungsgemeinschaft priority program 1177 ( `` witnesses of cosmic history : formation and evolution of galaxies , black holes and their environment '' ) , and the max planck society .
2006 , _ mnras _ 371 , 2 1995 , phd thesis , university of groningen , the netherlands 2004 , _ apjs _ 153 , 411 2007 , _ apjl _ , in press ( astro - ph/0701728 ) 2007 , _ mnras _ , submitted 2006 , _ apjs _ 163 , 270 2007 , in : stellar populations as building blocks of galaxies , iau symp .
241 , a. vazdekis , r. peletier ( eds . ) , in press ( astro - ph/0702054 ) 1926 , _ apj _ 64 , 321 2004 , _ mnras _ 355 , 1251 2005 , _ mnras _ 362 , 1319 | image decomposition of galaxies is now routinely used to estimate the structural parameters of galactic components . in this work ,
i address questions on the reliability of this technique .
in particular , do bars and agn need to be taken into account to obtain the structural parameters of bulges and discs ? and to what extent can we trust image decomposition when the physical spatial resolution is relatively poor ? with this aim , i performed multi - component ( bar / bulge / disc / agn ) image decomposition of a sample of very nearby galaxies and their artificially redshifted images , and verified the effects of removing the bar and agn components from the models .
neglecting bars can result in a overestimation of the bulge - to - total luminosity ratio of a factor of two , even if the resolution is low .
similar effects result when bright agn are not considered in the models , but only when the resolution is high .
i also show that the structural parameters of more distant galaxies can in general be reliably retrieved , at least up to the point where the physical spatial resolution is @xmath0 1.5 kpc , but bulge parameters are prone to errors if its effective radius is small compared to the seeing radius , and might suffer from systematic effects .
i briefly discuss the consequences of these results to our knowledge of the stellar mass budget in the local universe , and finish by showing preliminary results from a large sdss sample on the dichotomy between classical and pseudo - bulges . |
* figure 1 : linearly polarized intensity @xmath29 at 2.3 ghz from s - pass * ( @xmath30 ) .
the thick dashed lines delineate the radio lobes reported in this letter , while the thin dashed lines delimit the @xmath0-ray fermi bubbles@xcite .
the map is in galactic coordinates , centred at the galactic centre with galactic east to the left and galactic north up ; the galactic plane runs horizontally across the centre of the map .
the polarized flux density is indicated by the scale bar given in unit of jy / beam with a beam size of 10.75 ( 1 jy @xmath31 w m@xmath32hz@xmath33 ) .
the lobe edges follow the @xmath0-ray border up to @xmath34 where the radio emission extends beyond .
the three polarized radio ridges discussed in the text are also indicated along with the two limb brightening spurs .
the ridges appear to be the front side of a continuous windings of collimated structures around the general biconical outflow of the lobes ( see text ) .
the galactic centre spur is nearly vertical at low latitude , possibly explained by a projection effect if it is mostly at the front of the northern lobe . at its higher latitudes ,
the galactic centre spur becomes roughly parallel with the northern ridge ( above ) which itself exhibits little curvature ; this is consistent with the overall outflow s becoming cylindrical above 4 - 5 kpc as previously suggested@xcite .
in such a geometry , synchrotron emission from the rear side of each cone is attenuated by a factor @xmath35 with respect to the front - side , rendering it difficult to detect the former against the foreground of the latter and of the galactic plane ( see supplementary information ) .
* figure 2 : lobes polarized intensity and @xmath0ray spurs . *
schematic rendering of the edges of two @xmath0-ray substructures evident in the 2 - 5 gev fermi data as displayed in figure 2 of ref.@xcite which seem to be counterparts of the galactic centre spur and the southern ridge .
the latter appears to be connected to the galactic centre by its @xmath0-ray counterpart . with
the flux densities and polarization fraction quoted in the text we can infer equipartition@xcite magnetic field intensities of @xmath36 g ( 1 @xmath2 g @xmath37 t ) if the synchrotron - emitting electrons occupy the entire volume of the lobes , or @xmath38 g if they occupy only a 300 pc thick skin ( the width of the ridges ) . for the southern ridge , @xmath39 g ; for the galactic centre spur @xmath40 g ; and , for the northern ridge , @xmath41 g .
note the large area of depolarization and small angular scale signal modulation visible across the galactic plane extending up to @xmath42 on either side of the galactic centre ( thin dashed line ) .
this depolarization is due to faraday rotation by a number of shells that match h@xmath28 emission regions@xcite , most of them lying in the sagittarius arm at distances from the sun up to 2.5 kpc , and some in the scutum - centaurus arm at @xmath123.5 kpc .
the small scale modulation is associated to weaker h@xmath28 emission encompassing the same hii regions and most likely associated with the same spiral arms .
thus 2.5 kpc constitutes a lower limit to the lobes near side distance and places the far side beyond 5.5 kpc from the sun ( cf . ref .
@xcite ) . along with their direction in sky
, this suggests the lobes are associated with the galactic bulge and/or centre .
* figure 3 : polarized intensity and magnetic angles at 23 ghz from wmap[@xcite]*. the magnetic angle is orthogonal to the emission polarization angle and traces the magnetic field direction projected on to the plane of the sky .
the three ridges are obvious while traces of the radio lobes are visible ( 2.3 ghz edges shown by the black solid line ) .
the magnetic field is aligned with the ridges and curves following their shape .
two spurs match the lobe edges northwest and southwest of galactic centre and could be limb brightening of the lobes .
a third limb brightening spur candidate is also visible north east of the galactic centre .
the map is in galactic coordinates , centred at the galactic centre .
grid lines are spaced by @xmath43 .
the emission intensity is in brightness temperature , the unit is k. data have been binned in 1@xmath44 pixels to improve the signal - to - noise ratio . from a combined analysis of microwave and
@xmath0-ray data ( see also the supplementary information ) we can derive the following magnetic fields limits ( complementary to the equipartition limits reported in the text and figure 2 ) : for the overall lobes / bubbles @xmath45 g and for the galactic centre spur @xmath46 g @xmath47 g . *
figure 4 : the vertical range of cosmic ray electrons as a function of their kinetic energy . *
( due to geometrical uncertainties , adiabatic losses can not be determined so that the plotted range actually constitutes an upper limit . )
electrons are taken to be transported with a speed given by the sum of the inferred vertical wind speed ( 1100 km / s ) and the vertical component of the alfven velocity in the magnetic field .
the former is inferred from the geometry of the northern ridge : if its footpoint has executed roughly half an orbit in the time the galactic centre spur has ascended to its total height of @xmath48 kpc , its upward velocity must be close to 1,000 km / s@xmath49[@xcite ] , where we have normalised to a footpoint rotation speed of 80 km / s at a radius of 100 pc from the galactic centre@xcite ( detailed analysis gives 1100 km / s : see the supplementary information ) . in a strong , regular magnetic field ,
the electrons are expected to stream ahead of the gas at the alfven velocity@xcite in either the ridges ( @xmath50 g , @xmath51 km / s ; this is a lower limit given that @xmath52 @xmath53 on the basis of the rosat data@xcite ) or in the large - scale field of the lobes ( @xmath54 g , @xmath55 km / s for @xmath56 @xmath53 in the lobes interior as again implied by the data ) .
also plotted are : the characteristic energies of electrons synchrotron radiating at 2.3 and 23 ghz ( for a @xmath57 g field ) and into 1 and 50 gev @xmath0-rays via inverse compton ( ` ic ' ) upscattering of a photon background with characteristic photon energy 1 ev ; and the approximate 7 kpc distance of the top of the northern ridge from the galactic plane . | the nucleus of the milky way is known to harbour regions of intense star formation activity as well as a super - massive black hole@xcite .
recent fermi space telescope observations have revealed regions of @xmath0-ray emission reaching far above and below the galactic centre , the so - called fermi bubbles@xcite .
it is uncertain whether these were generated by nuclear star formation or by quasar - like outbursts of the central black hole@xcite and no information on the structures magnetic field has been reported . here
we report on the detection of two giant , linearly - polarized radio lobes , containing three ridge - like sub - structures , emanating from the galactic centre .
the lobes each extend @xmath1 , bear a close correspondence to the fermi bubbles , are located in the galactic bulge , and are permeated by strong magnetic fields of up to 15 @xmath2 g .
our data signal that the radio lobes originate in a bi - conical , star - formation ( rather than black hole ) driven outflow from the galaxy s central 200 pc that transports a massive magnetic energy of @xmath3 erg into the galactic halo .
the ridges wind around this outflow and , we suggest , constitute a ` phonographic ' record of nuclear star formation activity over at least 10 myr . ettore carretti,@xmath4 roland m. crocker,@xmath5 lister staveley - smith@xmath6 , marijke haverkorn@xmath7 , cormac purcell@xmath8 , b. m. gaensler@xmath8 , gianni bernardi@xmath9 , michael j. kesteven@xmath10 , and sergio poppi@xmath11 csiro astronomy and space science , po box 276 , parkes , nsw 2870 , australia max - planck - institut f " ur kernphsik , p.o .
box 103980 heidelberg , germany research school of astronomy & astrophysics , australian national university , weston creek , act 2611 , australia international centre for radio astronomy research , m468 , university of western australia , crawley , wa 6009 , australia arc centre of excellence for all - sky astrophysics department of astrophysics / imapp , radboud university nijmegen , p.o .
box 9010 , 6500 gl nijmegen , the netherlands leiden observatory , leiden university , p.o .
box 9513 , 2300 ra leiden , the netherlands sydney institute for astronomy , school of physics , the university of sydney , nsw 2006 , australia harvard smithsonian center for astrophysics , 60 garden street , cambridge , ma , 02138 , usa csiro astronomy and space science , po box 76 , epping , nsw 1710 , australia inaf osservatorio astronomico di cagliari , st .
54 loc .
poggio dei pini , i-09012 capoterra ( ca ) , italy we use the images of the recently concluded s - band polarization all sky survey ( s - pass ) that has mapped the polarized radio emission of the entire southern sky with the parkes radio telescope at a frequency of 2307 mhz , with 184 mhz bandwidth , and 9 angular resolution@xcite . the lobes exhibit diffuse polarized emission ( figure [ fig_1 ] ) , an integrated total intensity flux of 21 kjy , and high polarization fraction of 25% .
they trace the fermi bubbles excepting the top western ( i.e. , right ) corners where they extend beyond the @xmath0-ray region .
depolarization by hii regions establish that the lobes are almost certainly associated with the galactic centre ( figure [ lobes : fig ] and supplementary information ) , implying their height is @xmath128 kpc .
archival data of wmap[@xcite ] reveal the same structures at the microwave frequency of 23 ghz ( figure [ wmap : fig ] ) .
the 2.3 to 23 ghz spectral index @xmath13 ( with flux density @xmath14 modelled as @xmath15 ) of linearly - polarized emission interior to the lobes spans the range @xmath13 = [ -1.0 , -1.2 ] generally steepening with projected distance from the galactic plane ( see the supplementary information ) . along with the high polarization fraction , this phenomenology indicates the lobes are due to cosmic ray electrons , transported from the plane , synchrotron - radiating in a partly ordered magnetic field .
three distinct emission ridges that all curve towards galactic west with increasing galactic latitude are visible within the lobes ( figure [ fig_1 ] ) ; two other substructures proceeding roughly north - west and south - west from around the galactic centre hint at limb brightening in the biconical base of the lobes .
these substructures all have counterparts in wmap polarization maps ( figure [ wmap : fig ] ) and one of them@xcite , already known from radio continuum data as the galactic centre spur@xcite , appears to connect back to the galactic centre ; we label the other substructures the northern and southern ridges .
the ridges magnetic field directions ( figure [ wmap : fig ] ) curve following their structures . the galactic centre spur and southern ridges also seem to have gev @xmath0-ray counterparts ( figure [ lobes : fig ] also cf .
ref.[@xcite ] ) .
the two limb brightening spurs at the biconical lobe base are also visible in the wmap map , where they appear to connect back to the galactic centre area .
a possible third spur develops north - east from the galactic centre .
these limb brightening spurs are also obvious in the stokes u map as an x - shape structure centred at the galactic centre ( figure s3 of supplementary information ) .
such coincident , non - thermal radio , microwave and @xmath0-ray emission indicates the presence of a non - thermal electron population covering at least the energy range 1 - 100 gev ( figure [ fig_4 ] ) that is simultaneously synchrotron radiating at radio and microwave frequencies and up - scattering ambient radiation into @xmath0-rays by the inverse compton process .
the widths of the ridges are remarkably constant at @xmath12 300 pc over their lengths .
the ridges have polarization fractions of 25 to 31% ( see supplementary information ) , similar to the average over the lobes . given this emission and the stated polarization fractions , we infer magnetic field intensities @xmath16 g for the lobes and @xmath17 g the ridges ( see figure [ lobes : fig ] and [ wmap : fig ] and the supplementary information ) .
an important question about the fermi bubbles is whether they are ultimately powered by star - formation or by activity of the galaxy s central , super - massive black hole .
despite their very large extent , the @xmath0-ray bubbles and the x - shaped polarized microwave and x - ray structures tracing their limb - brightened base@xcite have a narrow waist of only 100 - 200 pc diameter at the galactic centre .
this matches the extent of the star - forming molecular gas ring ( @xmath18 ) recently demonstrated to occupy the region@xcite . with 5 - 10% of the galaxy s molecular gas content@xcite ,
star - formation activity in this ` central molecular zone ' is intense , accelerating a distinct cosmic ray population@xcite and driving an outflow@xcite of hot , thermal plasma , cosmic rays , and ` frozen - in ' magnetic field lines@xcite .
one consequence of the region s outflow is that the cosmic ray electrons accelerated there ( dominantly energised by supernovae ) are advected away before they lose much energy radiatively in situ@xcite .
this is revealed by the fact that the radio continuum flux on scales up to 800 pc around the galactic centre is in anomalous deficit with respect to the expectation afforded by the empirical far - infrared - radio continuum correlation@xcite . the total 2.3 ghz radio continuum flux from the lobes of @xmath12 21 kjy , however , saturates this correlation normalising to the inner @xmath19 pc diameter region s 60 @xmath2 m flux of 2 mjy[@xcite ] .
together with the morphological evidence , this strongly indicates the lobes are illuminated by cosmic ray electrons accelerated in association with star - formation within this region ( see the supplementary information ) not as a result of black hole activity .
the ridges appear to be continuous windings of individual , collimated structures around a general biconical outflow out of the galactic centre .
the sense of galactic rotation ( clockwise as seen from galactic north ) and angular - momentum conservation mean that the ridges get ` wound - up'@xcite in the outflow with increasing distance from the plane explaining the projected curvature of the visible , front - side of the ridges towards galactic west .
polarized , rear - side emission is attenuated rendering it difficult to detect against the lobes front - side and the galactic plane s stronger emission ( figure [ fig_1 ] and the supplementary information ) . for cosmic ray electrons synchrotron - emitting at 2.3 ghz to be able to ascend to the top of the northern ridge at @xmath12 7 kpc in the time it takes them to cool ( mostly via synchrotron emission itself ) requires vertical transport speeds of @xmath20500 km / s ( for 15 @xmath2 g ; see figure [ fig_4 ] ) . given the geometry of the gc spur , the outflowing plasma is moving at @xmath21 km / s ( figure [ fig_4 ] and the supplementary information ) , somewhat faster than the @xmath22 km / s gravitational escape velocity from the galactic centre region@xcite , implying that 2.3-ghz - radiating electrons can , indeed , be advected to the top of the ridges in their loss time .
given the calculated fields and the speed of the outflow , the total magnetic energy for each of the ridges , @xmath23 erg ( see the supplementary information ) , is injected at a rate @xmath24 erg / s over a few @xmath25 years ; this is very close to the rate at which independent modelling@xcite suggests galactic centre star formation is injecting magnetic energy into the region s outflow .
on the basis of the ridges individual energetics , geometry , outflow velocity , timescales , and plasma content ( see supplementary information ) , we suggest that their footpoints are energised by and rotate with the super - stellar clusters inhabiting@xcite the inner @xmath12100 pc ( in radius ) of the galaxy .
in fact , we suggest that the ridges constitute ` phonographic ' recordings of the last @xmath1210 myr of galactic centre star - formation . given its morphology , the galactic centre spur likely still has an active footprint .
in contrast , the northern and southern ridges seem not to connect to the plane at 2.3 ghz .
this may indicate their footpoints are no longer active though the southern ridge may be connected to the plane by a gamma - ray counterpart ( see fig .
[ lobes : fig ] ) .
unfortunately , present data do not allow us to trace the galactic centre spur all the way down to the plane but a connection between this structure and one ( or some combination ) of the @xmath26-scale radio continuum spurs@xcite emanating north of the star - forming giant molecular cloud complexes sagittarius b and c or the bright , non - thermal ` radio arc'@xcite ( itself longitudinally coincident with the @xmath124 myr quintuplet@xcite stellar cluster ) , seems plausible .
the magnetic energy content of both lobes is much larger than the ridges , @xmath27 erg .
this suggests the magnetic fields of the lobes are the result of the accumulation of a number of star formation episodes .
alternatively , if the lobes field structure were formed over the same timescale as the ridges , it would have to be associated with recent activity of the super - massive black hole , perhaps occurring in concert with enhanced nuclear star - formation activity@xcite .
our data indicate the process of gas accretion on to the galactic nucleus inescapably involves star - formation which , in turn , energises an outflow .
this carries away low angular momentum gas , cosmic rays and magnetic field lines and has a number of important consequences : i ) the dynamo activity in the galactic centre@xcite , likely required to generate its strong@xcite in situ field , requires the continual expulsion of small - scale helical fields to prevent dynamo saturation@xcite ; the presence of the ridges high in the halo may attest to this process .
ii ) the lobes and ridges reveal how the very active star formation in the galactic centre generates and sustains a strong , large - scale magnetic field structure in the galactic halo .
the effect of this on the propagation of high - energy cosmic rays in the galactic halo should be considered .
iii ) the process of gas expulsion in the outflow may explain how the milky way s super - massive black hole is kept relatively quiescent@xcite despite sustained , inward movement of gas
. 1 morris , m. , & serabyn , e. the galactic centre environment , ann .
rev .
astron .
astrophys . , 34 , 645 - 702 ( 1996 ) su , m. , slatyer , t. r. , & finkbeiner , d. p.
giant gamma - ray bubbles from fermi - lat : active galactic nucleus activity or bipolar galactic wind ?
, , 724 , 1044 - 1082 ( 2010 ) su , m. , & finkbeiner , d. p. evidence for gamma - ray jets in the milky way , , 753 , 61 ( 2012 ) zubovas , k. , king , a. r. , & nayakshin , s. the milky way s fermi bubbles : echoes of the last quasar outburst ?
, , 415 , l21-l25 ( 2011 ) crocker , r. m. , & aharonian , f. fermi bubbles : giant , multibillion - year - old reservoirs of galactic center cosmic rays , physical review letters , 106 , 101102 ( 2011 ) crocker , r. m. non - thermal insights on mass and energy flows through the galactic centre and into the fermi bubbles , 423 , 3512 - 3539 ( 2012 ) carretti , e. , galactic foregrounds and cmb polarization , in : the dynamic ism : a celebration of the canadian galactic plane survey , eds .
r. kothes , t. l. landecker , and a. g. willis 6 - 10 june 2010 , naramata , bc , canada , asp conf . ser .
cs-438 , 276 ( 2011 ) hinshaw , g. , weiland , j. l. , hill , r. s. , et al .
five - year wilkinson microwave anisotropy probe observations : data processing , sky maps , and basic results , astrophys .
j.,suppl . , 180
, 225 - 245 ( 2009 ) jones , d. i. , crocker , r. m. , reich , w. , ott , j. , & aharonian , f. a. magnetic substructure in the northern fermi bubble revealed by polarized microwave emission , , 747 , l12-l15 ( 2012 ) sofue , y , reich , w. , & reich , p. the galactic center spur - a jet from the nucleus ?
, , 341 , l47-l49 ( 1989 ) beck , r. , & krause , m. revised equipartition and minimum energy formula for magnetic field strength estimates from radio synchrotron observations , astronomische nachrichten , 326 , 414 - 427 ( 2005 ) bland - hawthorn , j. , & cohen , m. the large - scale bipolar wind in the galactic center , , 582 , 246 - 256 ( 2003 ) molinari , s. , bally , j. , noriega - crespo , a. , et al . a 100 pc elliptical and twisted ring of cold and dense molecular clouds revealed by herschel around the galactic center , , 735 , l33-l39 ( 2011 ) aharonian , f. a. et al .
discovery of very - high - energy @xmath0-rays from the galactic centre ridge , , 439 , 695 - 698 ( 2006 ) crocker , r. m. , jones , d. i. , aharonian , f. , law , c. j. , melia , f. , oka , t. , & ott , j. wild at heart : the particle astrophysics of the galactic centre , , 413 , 763 - 788 ( 2011 ) law , c. j. a multiwavelength view of a mass outflow from the galactic center , , 708 , 474 - 484 ( 2010 ) crocker , r. m. , jones , d. i. , aharonian , f. , et al
. @xmath0-rays and the far - infrared - radio continuum correlation reveal a powerful galactic centre wind , , 411 , l11-l15 ( 2011 ) crocker , r. m. , jones , d. i. , melia , f. , ott , j. , & protheroe , r. j. a lower limit of 50 microgauss for the magnetic field near the galactic centre , , 463 , 65 - 67 ( 2010 ) yun , m. s. , reddy , n. a. , & condon , j. j. radio properties of infrared - selected galaxies in the iras 2 jy sample , , 554 , 803 - 822 ( 2001 ) launhardt , r. , zylka , r. , & mezger , p. g. the nuclear bulge of the galaxy iii .
large - scale physical characteristics of stars and interstellar matter , , 384 , 112 - 139 ( 2002 ) heesen , v. , beck , r. , krause , m. , & dettmar , r .- j .
cosmic rays and the magnetic field in the nearby starburst galaxy ngc 253 iii .
helical magnetic fields in the nuclear outflow , , 535 , a79 ( 2011 ) muno , m. p. , et al .
diffuse x - ray emission in a deep chandra image of the galactic center , , 613 , 326 - 342 ( 2004 ) kulsrud , r. , & pearce , w. p. the effect of wave - particle interactions on the propagation of cosmic rays , , 156 , 445 - 469 ( 1969 ) pohl ,
m. , reich , w. , & schlickeiser , r. synchrotron modelling of the 400 pc spur at the galactic center , , 262 , 441 - 454 ( 1992 ) humann , b. , stolte , a. , brandner , w. , & gennaro , m. the present - day mass function of the quintuplet cluster , astron.astrophys .
, 540 , a57 ( 2012 ) ferrire , k. interstellar magnetic fields in the galactic center region , , 505 , 1183 - 1198 ( 2009 ) brandenburg , a. , & subramanian , k. astrophysical magnetic fields and nonlinear dynamo theory , phys.rep . , 417 , 1 - 209 ( 2005 ) gaustad , j. e. , mccullough , p. r. , rosing , w. , & van buren , d. , a robotic wide - angle h - alpha survey of the southern sky publications of the astronomical society of the pacific , 113 , 1326 - 1348 ( 2001 ) almy , r. c. et al . , distance limits on the bright x - ray emission toward the galactic center : evidence for a very hot interstellar medium in the galactic x - ray bulge , , 545 , 290 - 300 ( 2000 ) is linked to the online version of the paper at www.nature.com/nature .
this work has been carried out in the framework of the s - band all sky survey collaboration ( s - pass ) .
we thank the parkes telescope staff for outstanding support both while setting up the non - standard observing mode and during the observing runs .
rmc thanks felix aharonian , rainer beck , geoff bicknell , david jones , casey law , mark morris , christoph pfrommer , wolfgang reich , andrea stolte , troy porter , and heinz vlk for discussions and the max - planck - institut f " ur kernphsik for supporting his research .
rmc also acknowledges the support of a future fellowship from the australian research council through grant ft110100108 .
bmg and cp acknowledge the support of an australian laureate fellowship from the australian research council through grant fl100100114 .
mh acknowledges the support of the research programme 639.042.915 , which is partly financed by the netherlands organisation for scientifc research ( nwo ) .
the parkes radio telescope is part of the australia telescope national facility which is funded by the commonwealth of australia for operation as a national facility managed by csiro .
ec performed the s - pass observations , was the leader of the project , developed and performed the data reduction package , did the main analysis and interpretation .
rmc provided theoretical analysis and interpretation .
lss , mh , and sp performed the s - pass observations .
mjk performed the telescope special setup that has allowed the survey execution .
lss , mh , bmg , gb , mjk , and sp were co - proposers and contributed to the definition of the project .
cp performed the estimate of the h@xmath28 depolarizing region distance .
ec and rmc wrote the paper together .
all the authors discussed the results and commented on the manuscript .
the authors declare that they have no competing financial interests .
correspondence and requests for materials should be addressed to e.c .
( email : ettore.carretti@csiro.au ) .
reprints and permissions information is available at npg.nature.com/reprintsandpermissions . |
theoretical stellar evolution models are of huge importance to stellar and galactic astrophysics because they are basically the only way of deriving the age , internal structure and composition of stars and galaxies from simple observational data ( e.g. meynet et al . 2005 ;
nordstrm et al .
the accuracy of the results depends on the predictive power of the models , but this is severely limited by the parameteric treatment of several effects , including convective core overshooting ( @xmath0 ) , the efficiency of convective energy transport ( @xmath1 ) , the effects of rotation , magnetic fields and mass loss , and the need to use theoretically - calculated opacities .
the main offender is @xmath0 , changes in which cause major modifications to the predicted lifetimes , chemical yields and luminosities of massive stars ( e.g. maeder & meynet 1989 ) .
this in turn has a large effect on the predicted properties and formation rates of evolved objects such as core - collapse supernovae ( eldridge & tout 2004 ) and black holes .
also , changes in @xmath1 can affect the derived ages of globular clusters by up to 2gyr ( chaboyer 1995 ) , whilst reasonable variation in @xmath0 can alter the derived ages of open clusters by a factor of two ( bragaglia & tosi 2006 ) .
it is clear that this must be improved .
theoretical models can be calibrated with observational constraints derived using detached eclipsing binaries ( debs ) ( e.g. pols et al .
1997 ; vandenberg et al .
the study of these objects allows us to accurately measure the masses , radii and @xmath2s of two stars of the same age and chemical composition ( andersen 1991 ) .
observational errors in mass and radius can be below 1% ( e.g. , southworth et al . 2004e , 2005b ) .
accurate @xmath2s can also be found , allowing luminosities and distances to be directly measured .
debs have been used to constrain @xmath0 ( andersen et al .
1990 ) and its dependence on mass ( ribas et al .
2000 ) ; @xmath1 was also studied by ludwig & salaris ( 1999 ) .
however , the stength of these results has been compromised by the lack of information available for each object . for a deb ,
the radii and effective temperatures are known for two specific masses .
when comparing to theory , two of these four datapoints ( usually the radii ) are required to deduce the age and metal abundance of the system .
the remaining two are generally not accurate enough to do anything more than indicate the helium abundance or , if you assume a normal helium abundance , perhaps the extent of convective overshooting .
further information is needed to derive accurate constraints on @xmath0 or @xmath1 .
one possibility is to measure the surface metal abundances of the stars from high - dispersion spectroscopy , but this is rarely done .
another possibility is to study debs which display apsidal motion ( rotation of the oritentation of an eccentric orbit due to tidal and relativistic effects ; claret & willems 2002 ) but these are less common and require observations over a long period of time .
.[eboc ] parameters of well - studied debs in open clusters . only systems with masses and radii known to within 5%
are included , sorted by decreasing primary star mass . [ cols="<,<,^,^,^,<",options="header " , ] the study of eclipsing binaries in stellar clusters allows more constraints to be placed on theoretical models ( e.g. thompson et al .
2000 ; lebreton et al .
as the cluster stars , including both components of the deb , were born in the same place at the same time , theoretical predictions must be able to match their observed properties for a single age and chemical composition . as a useful byproduct ,
the age and composition of the cluster can be derived from the theoretical models ( e.g. southworth et al .
2004ad ) and its distance can be measured empirically from the properties of the deb ( e.g. southworth et al .
fundamentally , this method requires a simultaneous fit of the morphology of the cluster in colour - magnitude diagrams and the properties of the deb in mass - radius - temperature diagrams .
we are currently undertaking a research project to study debs which are members of open clusters with a range of ages and metallicities , in order to study how @xmath0 and other theoretical model parameters vary with mass and composition . whilst results
so far have been very encouraging , it has still not been possible to match a well - studied deb to a well - studied cluster ; work to remedy this is in progress .
one concept which has , however , come to light is that studying several debs in open cluster allows you to put four or more stars with the same age and composition but with differing masses into one mass - radius or mass - temperature plot ( southworth et al .
this raises the possibility of obtaining `` standard sequences '' of eclipsing stars in one cluster with accurately known masses , radii , @xmath2s and surface gravities . to this end
we have obtained photometry and spectroscopy of the eclipsing binaries v1481cyg , v2261cyg and v2263cyg in the young open cluster ngc7128 .
preliminary light curves for these are shown in figs .
[ fig1 ] and [ fig2 ] .
preliminary ( no debiassing or flat - fielding ) strmgren @xmath3 light curve of the eclipsing binary v2263cyg in ngc7128 ( @xmath4 is at the top and @xmath5 at the bottom ) .
as it is semi - detached it can not be used to constrain single - star evolutionary theory , but it can provide an accurate distance to the cluster . ] | detached eclipsing binaries are very useful objects for calibrating theoretical stellar models and checking their predictions .
detached eclipsing binaries in open clusters are particularly important because of the additional constraints on their age and chemical composition from their membership of the cluster .
i compile a list containing absolute parameters of well - studied eclipsing binaries in open clusters , and present new observational data on the b - type systems v1481cyg and v2263cyg which are members of the young open cluster ngc7128 . |
in this paper we discuss the measurement of the w mass from direct reconstruction of the invariant mass of the decay products in the channels ww@xmath3qqqq ( 4q ) and ww@xmath4qq .
preliminary results are presented for data collected in aleph@xcite during 1998 with an integrated luminosity of 174.2@xmath5 at 188.63gev .
events are preselected to remove radiative returns to the z and clustered into four jets using the ` durham - pe ` algorithm , defining @xmath6 .
events are vetoed if a charged track in a jet carries more than 90% of the jet energy or if there is more than 95% of electromagnetic energy in a @xmath7 cone around any particle .
a neural network with fourteen input variables ( nn14 ) is used to perform the final selection .
training is performed with an independent sample of the standard monte - carlo ( ` koralw`@xcite hadronised with ` jetset`@xcite ) and comparable samples of qq@xmath8 and zz events , both generated using ` pythia`@xcite , to simulate the background .
events with nn@xmath9 are used to extract the w mass@xcite .
the total charged energy and multiplicity are used to preselect events with a further cut on the total longitudinal momentum and visible energy to remove radiative returns to the z. the lepton candidates are chosen to be more energetic and isolated than the other charged tracks and are identified as an electron or muon in the detector .
the energy of electron candidates are corrected for possible bremsstrahlung photons detected in the electromagnetic calorimeter .
the ` durham - pe ` algorithm is used to force two jets from objects not used to reconstruct the lepton defining @xmath12 .
a probability for an event to come from a signal process is determined from monte carlo reference samples using the lepton energy and isolation and the event total transverse momentum .
selected events are required to have a probability greater than 0.4 .
a similar preselection to that used for electron and muon events is applied with additional constraints to remove events with i ) energy around the beam line , ii ) isolated , energetic photons and iii ) those already selected as electron or muon candidate events .
a tau jet is constructed from one or three charged tracks and two other jets are forced using the ` jade ` algorithm .
the tau jet must be that jet most anti - parallel to the missing momentum vector and isolated from the other jets . as with electron and muon candidate events , a probability is calculated and the same cut applied .
to improve the invariant mass resolution a four constraint kinematic fit is applied to the four jets to conserve energy ( as provided by lep ) and momention .
corrections are applied to the jets to take into account particle losses in the detector .
the masses from the three combinations of di - jets formed from the fitted jets are rescaled according to @xmath14 , where @xmath15 and @xmath16 are the measured jet energies .
a pairing algorithm is applied to the di - jet combinations to select that which most closely corresponds to a ww pair .
the combination with the smallest mass difference between rescaled masses is chosen provided one mass lies in the window 60 to 86 gev/@xmath2 and the other 74 to 86 gev/@xmath2 .
a binned monte - carlo reweighting procedure is employed to find the value of @xmath0 which best fits the mass distributions .
events from a ` koralw`@xcite sample with equivalent background are reweighted with a cc03 matrix element to provide a two - dimensional probability density function for the minimisation using a single parameter , @xmath0 .
variable binning controlled by the density of monte - carlo is employed optimised to produce a stable result .
the w - width is allowed to vary with @xmath0 according to the standard model . in order to check that the procedure does not introduce any biases ,
monte carlo samples are generated with @xmath0 in the range 79.35 and 81.35 gev/@xmath2 . treating these samples as data , no significant offsets in the masses measured are found .
a two constraint fit@xcite is applied to each event by minimising a @xmath18 constructed from the deviations of selected parameters of the jets and leptons from their true values and demanding that the hadron and lepton invariant masses are equal .
the single fitted mass obtained for each event must lie in the window 74 to 94.5 gev/@xmath2 . a reweighting procedure similar to that employed in the four quark channel is used to fit the mass distribution .
fixed binning is used for the electron and muon channels and variable binning is retained for the tau channel .
@p5.0cmlllll source & 4q & e & @xmath19 & @xmath20 + + calorimeter calibrations & 30 & 27 & 14 & 19 + charged particle tracking & & 7 & 3 & 3 + jet corrections & 8 & 14 & 4 & 7 + parton fragmentation & 35 & 25 & 25 & 30 + initial state radiation & 10 & 5 & 5 & 5 + lep energy & 17 & 17 & 17 & 17 + + reference mc statistics & 10 & 16 & 15 & 23 + background contamination & 10 & 8 & 1 & 25 + colour reconnection & 25 & & & + bose - einstein effects & 50 & & & + total & 77 & 47 & 37 & 53 + +
the systematic errors summarised in table 1 .
uncertainties due to the detector are determined using data taken at the z at intervals during the high energy running .
particles not seen by the detector cause discrepancies in the jet finding , the effect is estimated by matching jets built from monte carlo tracks before and after passing them through the detector simulation .
the error due to parton fragmentation effects is measured by determining the mass shift when ` herwig`@xcite rather than ` jetset ` is used for hadronisation .
the effect of initial state radiation is estimated by comparing the use of 1st and second order matrix elements .
the lep energy error is that given by lep .
colour reconnection between parton pairs in the qqqq channel is studied using variants on ` jetset ` or ` herwig ` .
the bose - einstein effect has been studied using z - peak data@xcite , the systematic error is determined from the shift in the mass measured when the parameters obtained at the z peak are applied to monte carlo events using a modified ` jetset ` .
this effect is applied between to w decay products in the qqqq channel . .w mass measurement results at 189 gev [ cols="<,<,<,<,<,<",options="header " , ] +
the mass distributions obtained are shown in figure 1 .
the preliminary results for 189 gev are given in table 2 for each channel where the be - cr error is that for the bose - einstein and colour reconnection systematics added in quadrature .
results for data taken at 172 and 183 gev have been published @xcite , combining these and the results above gives @xmath21 = 80.561 @xmath1 0.095(stat . )
@xmath1 0.050(syst . )
@xmath1 0.056(be - cr ) gev/@xmath2 @xmath22 = 80.343 @xmath1 0.089(stat . )
@xmath1 0.041(syst . )
gev/@xmath2 . 9 aleph collaboration , _ aleph : a detector for electron - positron annihilations at lep _ , nucl inst .
a294 ( 1990 ) 121 .
m.skrzypek , s.jadach , w.placzek and z.was , comp.phys.commun .
94 ( 1996 ) 216 .
t.sjstrand , comp.phys.commun .
82 ( 1994 ) 74 .
aleph collaboration , _ measurement of w - pair production in @xmath23 collisions at 189 gev _ ,
contribution to hep99 , abstract 6_405 ; http//alephwww.cern.ch/. aleph collaboration , _ measurement of the w - mass by direct reconstruction in @xmath23 collisions at 172 gev _
, phys.lett .
b 422 ( 1998 ) 384 . aleph collaboration , _ measurement of the w - mass in @xmath23 collisions at 183 gev _ , phys.lett .
b 453 ( 1999 ) 121 .
g.marchesini et al .
, , comp.phys.commun . 67 ( 1992 ) 465 .
aleph collaboration , _ measurement of the w mass in @xmath23 collisions at production threshold _ ,
b 401 ( 1997 ) 347 .
aleph collaboration , _ bose einstein correlations in w pair decays _
, contribution to hep99 , abstract 1_388 ; http//alephwww.cern.ch/. | the w - boson mass has been measured using the aleph detector at lep .
preliminary results from data taken in 1998 are added to previous measurements to give @xmath0
= 80.411 @xmath1 0.064(stat . )
@xmath1 0.037(syst . )
@xmath1 0.022(be - cr ) @xmath1 0.018(lep ) gev/@xmath2 .
glas - ppe/199919november 1999 |
the heisenberg ferromagnet is defined by the partition function @xmath0 = \int \prod [ d \omega(x ) \exp(-s)\label{eq:1}\ ] ] where @xmath1 ^ 2 \qquad \vec n^2(x ) = 1\label{eq:2}\ ] ] and @xmath2 is the element of solid angle for the orientation of @xmath3 in colour space .
the model presents a 2nd order phase transition at @xmath4@xcite . for @xmath5
there is an ordered phase , with order parameter the magnetization @xmath6 ; for @xmath7 , @xmath8 ( disordered phase ) .
we shall describe the system from a dual point of view , and show that in the disordered phase vortices condense .
the model will be viewed as a @xmath9 dimensional euclidean field theory .
vortices will be labelled by the integer valued topological charge of the 2 dimensional spacial configurations , which is a conserved quantity , and defines a @xmath10 symmetry of the system .
a disorder parameter @xmath11 will be constructed , which detects spontaneous breaking of this @xmath10 symmetry , or condensation of vortices .
the situation is analogous to the condensation of monopoles in the confining phase of gauge theories@xcite or to the condensation of abelian vortices in @xmath12@xcite . to check our construction
we shall extract from the numerical determination of @xmath11 at the phase transition the known critical indices .
usually the colour frame to which the direction of @xmath3 is referred is a fixed frame , independent of @xmath13 @xmath14 a body fixed frame can be defined@xcite by three unit vectors @xmath15 @xmath16 and @xmath17 .
the frame is defined up to an arbitrary rotation around @xmath18 . since @xmath19 @xmath20 or @xmath21 @xmath22 are the generators of the @xmath23 symmetry group .
eq.([eq:3 ] ) is nothing but the definition of parallel transport . from eq.([eq:3 ] ) it follows @xmath24\vec\xi_i = 0 $ ] or , by completeness of @xmath25 @xmath26 = \vec t\cdot\vec f_{\mu\nu}(\omega ) = 0 \label{eq:4}\ ] ] @xmath27 @xmath28 is a pure gauge , apart from singularities .
the general solution of eq.([eq:3 ] ) is then , for @xmath18 @xmath29 where @xmath30 is the value of @xmath31 at infinity , and the dependence on the path @xmath32 is trivial , because @xmath33 is a pure gauge , eq.([eq:4 ] ) .
this is true apart from singularities .
we will show that such singularities exist .
the current @xmath34 is identically conserved @xmath35 if we look at the theory as the euclidean version of a field theory , with euclidean time on the 3 axis , the corresponding conserved quantity is @xmath36 which is nothing but the topological charge of the 2 dimensional configurations of the theory .
@xmath37 can assume positive and negative integer values .
by use of eq.([eq:3 ] ) and eq.([eq:4 ] ) it is easy to show that @xmath38 where the path @xmath32 is the contour of the region in the 2 dimensional space ( @xmath39 = const . )
where eq.([eq:4 ] ) holds . since @xmath40 eq.([eq:5 ] ) shows that @xmath41 is not always a pure gauge .
this can be explicitely checked on a configuration corresponding to a static 2 dimensional instanton propagating in time ( vortex ) .
the conserved current @xmath42 identifies a @xmath10 symmetry .
we will show that this symmetry is wigner in the ordered phase @xmath5 , and is spontaneously broken in the disordered phase .
let @xmath43 be a @xmath44 dependent singular rotation creating a vortex of charge @xmath45 at the site @xmath46 in a 2 dimensional configuration .
@xmath47 the creation operator of a vortex @xmath48 at site @xmath46 , time @xmath49 , will be defined as @xmath50\bigr\ } \label{eq:7}\end{aligned}\ ] ] we measure the correlator @xmath51 by cluster property @xmath52 @xmath53 signals spontaneous breaking of the @xmath10 symmetry ( [ eq:4a ] ) , or condensation of vortices . by use of the definition ( [ eq:7 ] )
it is easy to see that @xmath54}{z[s]}\ ] ] where @xmath55 is obtained from @xmath56 , eq.([eq:2 ] ) by the replacement @xmath57 ^ 2 \hskip-5pt&\to&\hskip-5pt \left[r_q^{-1}(\vec x,0)\vec n(\vec
x,1 ) - \vec n(\vec x,0)\right]^2 \\
\left[\delta_0\vec n(\vec x , x_0)\right]^2 \hskip-5pt&\to&\hskip-5pt \left[r_q^{-1}(\vec x,0)\vec n(\vec x , x_0 + 1 ) - \vec n(\vec x , x_0)\right]^2\end{aligned}\ ] ] and that this really amounts to have a vortex propagating from @xmath58 to @xmath59@xcite . instead of @xmath60 itself it proves convenient@xcite to study the quantity @xmath61 .
as @xmath62 from eq.([eq:8 ] ) we have for @xmath63 , @xmath64 . since @xmath65 , @xmath66 $ ] .
@xmath67 is easier to measure and contains all the information on the transition .
the behaviour of @xmath67 is shown in fig.1 . for @xmath68 , @xmath69 finite limit consistent with zero , or @xmath70 , which means condensation of vortices . for @xmath71 @xmath67
can be evaluated in perturbation theory and behaves as @xmath72 @xmath73 is the lattice size .
eq.([eq:9 ] ) implies that @xmath74 for @xmath71 in the thermodynamical limit @xmath75 . around @xmath76 a finite size scaling analysis
can be performed @xmath77 0.1 in * fig.1 * 0.1 in and since @xmath78 , we get the scaling law@xcite @xmath79 the scaling law is verified , fig.2 , and allows to extract @xmath76 and @xmath80 @xmath81\\ \nu & = & 0.70 \pm 0.02\ ; [ 0.698]\end{aligned}\ ] ] they agree with the values determined from @xmath82 , which are indicated in parentheses@xcite .
-10pt 0.1 in * fig.2 *
the phase transition to disorder in 3d heisenberg model is produced by condensation of topological solitons .
a disorder parameter can be defined and out of it the critical indices can be determined .
this work has partially supported by murst .
a. di giacomo is grateful to ec , tmr project , erbfmx - ct97 - 0122 for financing the partecipation to the conference .
9 e. brezin , j. zinn - justin , _ nucl .
phys . _ * b257 * , 867 , ( 1985 ) .
a. di giacomo , g. paffuti , _ phys .
rev . _ * d56 * , 6816 , ( 1997 ) .
l.del debbio , a.di giacomo , g.paffuti and p.pieri , _ phys .
lett._*b 355 * ( 1995 ) 255 . g. di cecio , a. di giacomo , g. paffuti , m. trigiante , _ nucl .
phys . _ * b489 * , 739 , ( 1997 ) . a. di giacomo , m. mathur , _ phys .
_ * b400 * , 129 , ( 1997 ) .
p. peczak , a.l .
ferrenberg , d.p .
landau , _ phys .
rev . _ * 43 * , 6087 , ( 1991 ) . | the 3d heisenberg model is studied from a dual point of view in terms of 2d solitons ( vortices ) .
it is shown that the disordered phase corresponds to condensation of vortices in the vacuum , and the critical indices are computed from the corresponding disorder parameter . |
fly is the tree n - body code we design , develop and use to run very big simulations of the large scale structure of the universe using parallel systems mpp and smp .
fly uses the leapfrog numerical integration scheme for performance reasons , and incorporates fully periodic boundary conditions using the ewald method .
the i / o data format is integrated with the astromd package .
+ astromd is an analysis and visualization tool specifically designed to deal with the visualization and analysis of astrophysical data .
astromd can find structures having a not well defined shape or symmetries , and performs quantitative calculations on a selected region or structure .
astromd makes use of virtual reality techniques which are particularly effective for understanding the three dimensional distribution of the fields , their geometry , topology and specific patterns .
the display of data gives the illusion of a surrounding medium into which the user is immersed .
the result is that the user has the impression of travelling through a computer - based multi - dimensional model which could be directly hand - manipulated .
the fly code , written in fortran 90 and c languages , uses the one - side communication paradigm : it has been developed on the cray t3e using the shmem library .
fly is based on the following main characteristics .
it adopts a simple domain decomposition , a grouping strategy and a data buffering that allows us to minimize data communication .
fly does not split the domain with orthogonal planes , but the domain decomposition is done by assigning an equal number of particles to each processor .
the input data particles is a sorted file containing the fields of position and velocity , so that particles with a near tag number are also near in the physical space , and the arrays containing the tree properties are distributed using a fine grain data distribution . during the tree walk procedure ,
fly builds a single interaction list ( il ) to be applied to all particles inside a grouping cell ( @xmath1 ) .
this reduces the number of the tree accesses to build the il .
we consider a hypothetical particle we call _ virtual body _ ( vb ) placed in the center of mass of the @xmath1 : the vb interaction list @xmath2 is formed by two parts : @xmath3 where @xmath4 includes the elements more distant than a threshold parameter from vb and @xmath5 includes the elements near vb . using the two lists it is possible to compute the force @xmath6 of each _ p _ particle in @xmath1 as the sum of two components : @xmath7
the component @xmath8 is computed only once for vb , and it is applied to all the _ p _ particles , while the @xmath9 component is computed separately for each particle .
the size of the @xmath1 , and the tree - level where it can be considered , is constrained by the maximum allowed value of the overall error of this method . in this sense
the performance of fly is a level - based code .
the data buffer is managed with a policy of a simulated cache in the local ram .
every time the pe has to access a remote element , at first it looks for the local simulated cache and , if the element is not found , the pe executes the get calls to down - load the remote element and stores it in the buffer . in a simulation with 16-million - particles
clustered , with 32 pes and 256 mbytes of local memory , without the use of the simulated cache , the pes execute about @xmath10 remote gets .
this value , using the data buffering , decreases at @xmath11 remote gets , with an enormous advantage in terms of scalability and performance .
1 shows the code performance on cray t3e system , obtained by running simulations with 32 and 64 pes , and fly scalability , considering the case of 16,777,216 particles , where a speed - up factor of 118 is reached using 128 pes .
the highest performance obtained in a clustered configuration is a positive effect of the grouping characteristic .
the obtained results show that fly has a very good scalability and a very high performance and it can be used to run very big simulations .
astromd is developed using the visualization toolkit ( vtk ) by kitware , a freely available software portable on several platforms which range from the pc to the most powerful visualization systems , with a good scalability .
data are visualized with respect to a box which can describe the whole computational mesh or a sub - mesh .
astromd can find structures having a not well defined shape or symmetries , and performs quantitative calculations on a selected region or structure .
the user can choose the sample of the loaded particle type ( i.e. stars , dark matter and gas particles ) , the size of the visualization box and the starting time from which he wants to show the evolution of the simulation .
density _ entries control the visualization of the iso - surfaces .
these are calculated on a grid whose resolution can be user - selectable . to allow the user to investigate with more accuracy a subset of the visualized system it is possible to use a cubic sampler .
if the sampler is selected ( _ show / hide _ menu ) , visualized in the scene and enabled ( _ sampler _ menu ) , all the computations are performed only inside the region of the sampler ( fig .
astromd can also show the evolution in time of the simulated system over all the interval of time for which the data are available , performing interpolations at intermediate frames . during the evolution the updated time of evolution
is displayed in the _ time _ entry of the _ cloud _ section .
finally snapshots of the images displayed can be created using the button _ take it _ in the _ screenshot _ menu .
astromd is developed by the visit ( visual information technology ) laboratory at cineca ( casalecchio di reno - bologna ) in collaboration with the astrophysical observatory of catania .
antonuccio - delogu , v. , becciani , u. , pagliaro , a. , van kampen , e. , colafrancesco , s. , german , a. and gambera , m. 2000 , submitted to barnes , j.e . and hut , p. 1986 , nature , 324 , 446schroeder , w. , ken , m. , lorensen , b. 1999 , `` the visualization toolkit '' , prentice hall becciani , u. , antonuccio - delogu , v. 2000 , j. comput .
phys . , 163 , 118 earnshaw , r.a . , watson , d. 1993 , `` animation and scientific visualization '' , academic press ltd .
qinn , t. , stadel , c. tipsy http://www-hpcc.astro.washington.edu/tools/tipsy salmon , j. and warren , m.s .
1997 , proc . of the eight conf . on parallel processing for scientific computing , siam 1997 | we present a new code allowing to evolve three - dimensional self - gravitating collisionless systems with a large number of particles @xmath0 . *
fly * ( fast level - based n - body code ) is a fully parallel code based on a tree algorithm .
it adopts periodic boundary conditions implemented by means of the ewald summation technique .
fly is based on the one - side communication paradigm to share data among the processors that access remote private data avoiding any kind of synchronism .
the code was originally developed on a cray t3e system using the _ shmem _ library and it was ported on sgi origin 2000 and on ibm sp ( on the latter making use of the _ lapi _ library ) .
version 1.1 is an open source _ freely available code_. + fly data output can be analysed with astromd , an analysis and visualization tool specifically designed to deal with the visualization and analysis of astrophysical data .
astromd can manage different physical quantities
. it can find out structures without well defined shape or symmetries , and perform quantitative calculations on selected regions .
is a _ freely available _ code . |
our paper contains a direct elementary proof of the following series transformation : ( * landen s transformation * ) if @xmath0 , then@xmath1{x}}{1+\sqrt{x}}\right)^{2}-\frac{1^{2}\cdot 3}{2^{2}\cdot 4^{2}}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{4}-\frac{1^{2}\cdot 3^{2}\cdot 5}{2^{2}\cdot 4^{2}\cdot 6^{2}}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{6}-\cdots\right\}= & \\ & \\={\displaystyle}1+\left(\frac{1}{2}\right)^{2}x+\left(\frac{1\cdot 1}{2\cdot 4}\right)^{2}x^{2}+\left(\frac{1\cdot 1\cdot 3}{2\cdot 4\cdot 6}\right)^{2}x^{3}+\left(\frac{1\cdot 1\cdot 3\cdot 5}{2\cdot 4\cdot
6\cdot 8}\right)^{2}x^{4}+\cdots & \\\end{array } $ } \ ] ] @xmath2 the interest in this theorem is that it gives a direct proof the equality of the following two formulas for the perimeter of an ellipse with semi - axes @xmath3 and @xmath4 .
( * the perimeter of an ellipse * ) the perimeter , @xmath5 , of an ellipse with semi - major axes @xmath3 and @xmath4 and eccentricity @xmath6 is:@xmath7@xmath2 the first formula for @xmath5 is due to maclaurin @xcite in 1742 while the second is due to ivory @xcite in 1796 .
berndt ( @xcite , p. 147 ) points out that ivory s formula can be obtained from a form of landen s transformation to be found in erdlyi s compendium ( @xcite , p.111 , formula ( 5 ) ) , but we have not been able to encounter a direct elementary proof in the literature which transforms the first of the two formulas for @xmath5 into the second one , and which does not appeal to general transformation formulas .
ivory s own proof cleverly finesses this difficulty by showing that both series are equal to an integral .
the following identity is valid for all integers @xmath8 and real numbers @xmath9.@xmath10 the following identities between binomial coefficients are well known:@xmath11 for example , see knuth ( @xcite pp .
71 and 46 , resp . )
now solve the first identity for @xmath12 , write @xmath13 in place of @xmath9 everywhere , use the second identity to get rid of the negative sign inside the binomial coefficients , and finally multiply and divide by @xmath14 this next lemma is the novelty in our proof .
the following relation is valid for all integers @xmath15 @xmath16 we construct , in _ two different ways _ , a certain polynomial , @xmath17 , whose coefficient of @xmath18 is the sum @xmath19 defined in ( 3 ) .
observe that the _ coefficient of _ @xmath20 in @xmath21is equal to ( put @xmath22)@xmath23therefore , _ the coefficient of _
@xmath24in@xmath25is equal to@xmath26thus , _ the sum _ we are seeking to evaluae , viz.@xmath27is the _ coefficient _ of @xmath18 in the _ _ sum__@xmath28this is the * _ first form _ * of the polynomial @xmath29 but @xmath17 can also be written@xmath30which is the * _ second form _ * of @xmath17 . expanding it by the binomial theorem we obtain@xmath31we see that all the powers of @xmath32 are _
even_. thus , if @xmath9 is _ odd _ , the coefficient of @xmath18 is _ zero _ , while if it is _ even _ , the coefficient of @xmath33is equal to@xmath34 the following result is well known ( @xcite ) : ( * vandermonde s theorem * ) the following relation holds for all real numbers @xmath3 and @xmath4:@xmath35 @xmath2
our proof of * theorem 1 * is based on an idea of carlson @xcite .
however we use the fundamental * lemma 2 * , of which we have given a direct elementary proof based on the elementary properties of the binomial coefficients ( see 2 ) , while carlson proves the transformation on the basis of general expansion theorems for r - functions . "
our proof consists of two steps : the left - hand side of * theorem 1 * is rearranged into the following power series in @xmath36:@xmath37we achieve this via the binomial theorem , * lemma 1 * and * lemma 2*. the power series @xmath38 is rearranged into a power series in @xmath32 alone via the binomial theorem . applying * lemma 1 * and vandermonde s theorem , the coefficients of this series collapse down to the coefficients of the right hand side of * theorem 1*.
all subsequent series converge absolutely and uniformly for @xmath0 , so that the following series manipulations are valid in that range.@xmath39{x}}{1+\sqrt{x}}\right)^{2}-\frac{1^{2}\cdot 3}{2^{2}\cdot 4^{2}}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{4}-\frac{1^{2}\cdot 3^{2}\cdot 5}{2^{2}\cdot 4^{2}\cdot 6^{2}}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{6}-\cdots\right\}\\ & = { \displaystyle}(1+\sqrt{x})\sum_{m=0}^{\infty}\frac{-1}{2m-1}\left\{\frac{1}{4^{m}}\binom{2m}{m}\right\}^{2}\left\{{\displaystyle}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{2}\right\}^{m}\\ & = { \displaystyle}(1+\sqrt{x})\sum_{m=0}^{\infty}\frac{-1}{2m-1}\left\{\frac{1}{4^{m}}\binom{2m}{m}\right\}^{2}{\displaystyle}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{2 m } \\ & = { \displaystyle}\sum_{m=0}^{\infty}\frac{-1}{2m-1}\left\{\frac{1}{4^{m}}\binom{2m}{m}\right\}^{2}4^{m}(\sqrt{x})^{m}(1+\sqrt{x})^{-2m+1 } \\ & = { \displaystyle}\sum_{m=0}^{\infty}\frac{-1}{2m-1}\left\{\frac{1}{4^{m}}\binom{2m}{m}\right\}^{2}4^{m}(\sqrt{x})^{m}(1 + 2\sqrt{x}+x)^{-m+\frac{1}{2}}\\ & = { \displaystyle}\sum_{m=0}^{\infty}\frac{-1}{2m-1}\left\{\frac{1}{4^{m}}\binom{2m}{m}\right\}^{2}4^{m}(\sqrt{x})^{m}(1+x)^{\frac{1}{2}}(1+x)^{-m}\left(1+\frac{2\sqrt{x}}{1+x}\right)^{-m+\frac{1}{2}}\\ & = -\sum_{m=0}^{\infty}\frac{1}{2m-1}\left\{\frac{1}{4^{m}}\binom{2m}{m}\right\}^{2}4^{m}\left(\frac{\sqrt{x}}{1+x}\right)^{m}(1+x)^{\frac{1}{2}}\sum_{k=0}^{\infty}\binom{-m+\frac{1}{2}}{k}\left(\frac{2\sqrt{x}}{1+x}\right)^{k}\\ & = -(1+x)^{\frac{1}{2}}\sum_{m=0}^{\infty}\frac{1}{2m-1}\left\{\frac{1}{4^{m}}\binom{2m}{m}\right\}^{2}2^{m}\sum_{k=0}^{\infty}\binom{-m+\frac{1}{2}}{k}\left(\frac{2\sqrt{x}}{1+x}\right)^{k+m}\\ & = -(1+x)^{\frac{1}{2}}\sum_{m=0}^{\infty}\sum_{k=0}^{\infty}\frac{2^{m}}{2m-1}\left\{\frac{1}{4^{m}}\binom{2m}{m}\right\}^{2}\binom{-m+\frac{1}{2}}{k}\left(\frac{2\sqrt{x}}{1+x}\right)^{k+m}\\ & = -(1+x)^{\frac{1}{2}}\sum_{m=0}^{\infty}\sum_{k=0}^{\infty}\frac{2^{m}}{2m-1}\left\{\frac{1}{4^{m}}\binom{2m}{m}\right\}^{2}\frac{2m-1}{2m-1 + 2k}\binom{-m-\frac{1}{2}}{k}\left(\frac{2\sqrt{x}}{1+x}\right)^{k+m}\\ & \left(\text{since $ \binom{r}{k}=\dfrac{r}{r - k}\binom{r-1}{k}$}\right)\\ & = -(1+x)^{\frac{1}{2}}\sum_{m=0}^{\infty}\sum_{k=0}^{\infty}\frac{2^{m}}{4^{2m}}\binom{2m}{m}^{2}\frac{1}{2m+2k-1}\frac{{\displaystyle}\binom{2m+2k}{m+k}\binom{m+k}{k}}{{\displaystyle}\binom{2m}{m}}\frac{(-1)^{k}}{4^{k}}\left(\frac{2\sqrt{x}}{1+x}\right)^{k+m}\\ & ( \text{by \textbf{lemma 1}})\\ & = ( 1+x)^{\frac{1}{2}}\sum_{m=0}^{\infty}\sum_{k=0}^{\infty}\frac{2^{m}}{4^{2m}}\binom{2m}{m}\frac{1}{2m+2k-1}{\displaystyle}\binom{2m+2k}{m+k}\binom{m+k}{k}{\displaystyle}\binom{2m}{m}\frac{(-1)^{k}}{4^{k}}\left(\frac{2\sqrt{x}}{1+x}\right)^{k+m}\\ & ( \text{now put $ k:=n - m$ and interchange the order of summation})\end{aligned}\ ] ] @xmath40 @xmath41 \left(\frac{2\sqrt{x}}{1+x}\right)^{n } ( \text{by \textbf{lemma 2}})\\ & = ( 1+x)^{\frac{1}{2}}\sum_{m=0}^{\infty}\frac{-1}{4m-1}\frac{1}{4^{2m}}\binom{4m}{2m}{\displaystyle}\frac{1}{4^{m}}\binom{2m}{m}\left(\frac{2\sqrt{x}}{1+x}\right)^{2 m } ( \text{putting $ n=2m$}.)\end{aligned}\ ] ] putting together the two extreme members of this chain of equalities , * _ we have shown : _
* @xmath42{x}}{1+\sqrt{x}}\right)^{2}-\frac{1^{2}\cdot 3}{2^{2}\cdot 4^{2}}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{4}-\frac{1^{2}\cdot 3^{2}\cdot 5}{2^{2}\cdot 4^{2}\cdot 6^{2}}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{6}-\cdots\right\}\\ & = ( 1+x)^{\frac{1}{2}}\sum_{m=0}^{\infty}\frac{-1}{4m-1}\frac{1}{4^{2m}}\binom{4m}{2m}{\displaystyle}\frac{1}{4^{2m}}\binom{2m}{m}\left(\frac{2\sqrt{x}}{1+x}\right)^{2m}. \end{aligned}\ ] ] @xmath2 this completes the proof of * step 1*.
we expand the term @xmath43 by the binomial theorem .
therefore , the rhs of the equation in * theorem 3 * becomes@xmath44again , we put @xmath45 , interchange the order of summation , and observe that * _ the coefficient of _ * @xmath46 * * _ is_**@xmath47where we have used both the conclusion and the proof of * lemma 1*. so , if we now substitute this last expression:@xmath48into the rhs of ( 5 ) we obtain@xmath49{x}}{1+\sqrt{x}}\right)^{2}-\frac{1^{2}\cdot 3}{2^{2}\cdot 4^{2}}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{4}-\frac{1^{2}\cdot 3^{2}\cdot 5}{2^{2}\cdot 4^{2}\cdot 6^{2}}\left(\frac{2\sqrt[4]{x}}{1+\sqrt{x}}\right)^{6}-\cdots\right\}\\ & = \sum_{n=0}^{\infty}\sum_{m=0}^{n}\frac{(-1)^{n-1}}{2n-1}\frac{1}{4^{n}}\binom{2n}{n}\binom{-n+\frac{1}{2}}{m}\binom{n}{n - m}x^{n}\\ & = \sum_{n=0}^{\infty}\frac{(-1)^{n-1}}{2n-1}\frac{1}{4^{n}}\binom{2n}{n}\left\{\sum_{m=0}^{n}\binom{-n+\frac{1}{2}}{m}\binom{n}{n - m}\right\}x^{n}\\ & ( \text{and by \textsc{vandermonde } 's theorem this is equal to } ) \end{aligned}\ ] ] | we prove landen s transformation by direct elementary transformation of infinite series . |
solar activity can be seen through the evolution of sunspots number in quasi - periodic oscillatory series with periods going from 8 to 15 years and with a mean period of 11 years . due to the change of magnetic field polarity in solar hemispheres alternatively
each cycle , the period is rather 22 years .
the quasi - periodic evolution of many activity phenomena is still a unsolved key problem in solar physics ( along with , e.g. , heating of the solar chromosphere and corona , and solar flares ) .
an important issue of this understanding is due to the influence of solar activity over the terrestrial climate ( ( * ? ? ?
* archibald 2006 ) ) .
many physical models were proposed to understand the basic mechanisms ( e.g. , ( * ? ? ?
* benevolenskaya 1998 ) ) producing solar / stellar activity and its quasi - cyclic evolution . from sunspots time series , mathematical approaches have highlighted several other hidden periods other that the well - apparent 11-years period .
these works contributed to provide some observed parameters to constraint theoretical models , and to predict the future evolution of the sunspots number ( e.g. , ( * ? ? ?
* clilverd 2003 ) ; ( * ? ? ?
* sello 2003 ) ) . in this work
we follow another mathematical approach , investigating the influence of the past evolution of the sunspots number over the present one .
a natural and simple way to carry out this analysis is to assume that the susnpots number have a temporal delay behaviour .
thus , the relationship between present and past values becomes non - linear and could prove that the past amplitude influence the present one . as for the abovementioned methods , this one also allows some predictions about future solar cycles by using intermediate parameters to characterize the general past evolution .
we consider a temporal delay behavior ( eq . [ eq1 ] ) to rely the present evolution of a phenomena with some particular events in its past evolution .
the variation of @xmath0 in time is not only related with its current value @xmath1 but also with its past values @xmath2 , where @xmath3 is our temporal delay .
the simplest way is to assume only one past temporal influence and some proportionality between the variables ( e.g. , ( * ? ? ?
* murray 1993 ) ) , as follows : @xmath4 because we use yearly values of the relative sunspots number , given by sdic ( http:// www.sidc.be/sunspot-data/ ) , @xmath5 is equal to @xmath6 .
the present and past values of @xmath0 are already known and we assumed some values for the parameter @xmath3 ( @xmath7 ; fig .
[ fig : ratiofactor ] , left panel ) .
so we can determine constants @xmath8 and @xmath9 ( eq . [ eq2 ] ) from the correlation between the sunspots number ratio and the past sunspots number ( fig .
[ fig : ratiofactor ] right panel ) .
the @xmath3 values which minimize the correlation between the sunspots number ratio and the past spots number , are 7 or 8 years ( fig .
[ fig : ratiofactor ] ) . to test the accuracy of our method
, we applied it on the solar cycle 23 ( table [ tab : cycle23 ] and fig .
[ fig : evolspots ] , left panel ) .
our predictions are consistent with the observations , except for the unusually long period of low activity at the end of this cycle .
we also characterized the next solar cycle @xmath11 ( table [ tab : prediction ] and fig .
[ fig : evolspots ] ) using our modelling of the solar cycle @xmath12 as well as the spots number observed until @xmath13 and @xmath14 .
the next maximum sunspots number would take place between @xmath15 and @xmath16 and should be close to 60 ( fig .
[ fig : evolspots ] , right panel ) as for the solar cycle @xmath17 . using
the solar minimum occurred in @xmath18 ( @xmath19 from sdic ) , the predicted maximum is consistent with the value from the linear least - square fit on the both axis ( red line on fig .
[ fig : rminrmax ] ) and is a few smaller than the range given by ( * ? ? ?
* brajsa ( 2009 ) ) .
moreover the next solar minimum should not occur before 2019 or even 2020 .
lcccccc panel of & & & + fig .
[ fig : evolspots ] & & & + & epoch & number & epoch & number & epoch & number + left & @xmath13 & @xmath27 & @xmath28 & @xmath29 & @xmath30 & @xmath31 + middle & @xmath13 & @xmath32 & @xmath33 & @xmath34 & @xmath35 & @xmath36 + right & @xmath37 & @xmath38 & @xmath33 & @xmath39 & @xmath40 & @xmath41 + these preliminary results are encouraging because we find a similar delay as that observed between the geomagnetic activity and solar cycle peaks ( * ? ? ?
* ( hathaway & wilson 2006 ) ) linked probably with magnetic activity by some kind of histeresis mechanism . at present , we can successfully reproduce some previous solar cycles ( e.g. , epoch and solar maximum ) .
we plan to improve our predictive method including the influence of delays for which there is a good correlation .
this more detailed description could allow to solve the overestimation of the next solar minimum and to reproduce the asymmetries observed during the previous cycles .
our final aim is to obtain a reliable prediction of the whole solar activity by identifying the fundamental lower and high activity precursors of its present and future evolution .
all these improvements are still needed to be able to predict future low solar activity periods ( e.g. , maunder / dalton minimum ) . | the so - called is generally characterized by the quasi - periodic oscillatory evolution of the photospheric spots number .
this quasi - periodic pattern has always been an intriguing question .
several physical models were proposed to explain this evolution and many mathematical data analysis were employed to determine the principal frequencies noticeable in the measured data .
both approaches try to predict the future evolution of the solar activity and to understand the physical phenomena producing these cycles . here
we present the analysis of the sunspots number evolution using the time - delay approach .
our results show than the solar cycle can also be characterized by this behavior implying the influence of the past evolution over the present one , suggesting an histeresis mechanism , linked probably with magnetic activity . |
blazars have been shown to exhibit a sequence of properties as a function of source power ( fossati et al .
1998 ) . as the source power increases , the emission line luminosity and the ratio of compton to synchrotron luminosity increase , while the synchrotron peak frequency @xmath0 and the ic peak frequency decrease .
recent multiwavelength studies support this scheme ( e.g. kubo et al .
1998 ) , although the result that the ratio of the compton to synchrotron luminosity increases with source luminosity suffers from limited statistics , and should be only considered tentative .
the initial division of blazars into flat spectrum radio quasars ( fsrqs ) and bl lacertae objects ( bls ) was based on the equivalent width ( ew ) of the broad emission lines .
sources with ew @xmath1 5 @xmath2 were classified as fsrqs and sources with ew @xmath3 5 @xmath2 as bls .
this difference in the ew of the emission lines has been interpreted as absence of a substantial blr in bls , and has been used to advance the idea that in bls the gev - tev emission is due to ssc , while in fsrqs the gev emission is due to ec .
however , the ew criterion does not correspond to a dichotomy ( scarpa & falomo 1997 ) , because a weak blr is present in bls as well .
additionally , it is not the blr luminosity @xmath4 that is relevant for the ec luminosity , but the blr photon energy density @xmath5 that is measured in the comoving frame of the non - thermal source .
one needs to know not only @xmath4 , but also the blr radius @xmath6 and the location of the non - thermal emitter relative to the blr in order to quantify the relative importance of ssc versus ec emission .
the size of the blr has been measured only for radio quiet agns through reverberation mapping ( kaspi et al .
2000 ) , and it has been found to scale with the ionizing luminosity @xmath7 of the acrretion disk as @xmath8 . it was additionally found that , assuming keplerian motions for the blr clouds , the mass of the central object scales with the ionizing luminosity as @xmath9 .
here we assume the scalings apply also to radio loud agn and examine the implications for blazars .
following the formalism of internal shocks propagating in a conical jet ( rees 1978 ) , we scale the location @xmath10 and the radius @xmath11 of the non - thermal spherical emitter with the mass @xmath12 of the central object .
we assume that @xmath4 is a fraction of @xmath7 and scale the kinetic luminosity and the poynting flux of the blob with @xmath7 .
under this scheme , the radius of the blr scales as @xmath13 , and the distance of the blob from the center of the system scales as @xmath14 .
therefore , we assume that for powerful sources the blob radiates from inside the blr , @xmath15 .
however , if we consider increasingly weaker sources , @xmath6 falls faster than @xmath10 and , below some critical luminosity , the blob radiates from outside the blr . for a blob inside the blr , @xmath16 , where @xmath17 is the bulk motion lorents factor of the blob . for a blob outside the blr , the solid angle subtended by the blr , as seen by the blob ,
is reduced .
this affects @xmath5 in two ways .
the first is the usual geometric @xmath18 factor , and the second is a relativistic de - boosting that , for @xmath19 , gives @xmath20 ( dermer & schlickeiser 1994 ) . the second effect dominates if the blob is located less than a few @xmath6 away from the blr .
for example , for @xmath21 , @xmath22 at a distance of @xmath23 is smaller than @xmath22 inside the blr by a factor of @xmath24 due to the usual @xmath18 and by a factor of @xmath25 due to relativistic de - boosting .
we apply this scaling using a model ( georganopoulos & kirk 2000 ) for the blob which includes both particle acceleration and radiative losses with ic scattering losses treated in the thomson regime .
particles are accelerated in an acceleration zone and escape into a radiation zone , before they eventually escape out of the system .
this simplified picture is intended to represent particles which are accelerated by a shock front , escape it , and radiate downstream before the compressed plasma re - expands .
whilst undergoing acceleration , particles simultaneously suffer synchrotron losses and losses by compton scattering of both photons of external origin ( ec ) and synchrotron photons ( ssc ) from the radiation zone . in the radiation zone ,
ec , ssc and synchrotron losses occur until the particle finally escapes after a time @xmath26 . the electron energy distribution ( eed ) is computed self - consistently , taking account of these processes . our assumption about the scaling of the poynting flux implies a constant magnetic field , which we take to be @xmath27 g. the blob
is assumed to move with a lorentz factor @xmath28 at an angle @xmath29 with respect to the line of sight .
low energy particles ( @xmath30 ) are injected into the blob at a rate of @xmath31 @xmath32 s@xmath33 .
also @xmath34 . for @xmath35 erg s@xmath33 ,
reverberation mapping gives @xmath36 cm .
we assume that at this luminosity @xmath37 and @xmath38 cm . in fig.1 , we let @xmath7 vary from @xmath39 erg s @xmath33 to @xmath40 erg s@xmath33 , and follow the behavior of the system . in the lower panel @xmath6 , @xmath10 , and @xmath11
are plotted as a function of @xmath7 . for weak sources ,
the blob is located outside the blr ( @xmath41 ) . as the source power increases , the blob gradually approaches and eventually enters the blr . in the middle panel of fig.1
we see how this affects @xmath22 ( the magnetic field energy density @xmath42 is constant under the adopted scaling ) . for weak sources ,
@xmath22 is much smaller than both @xmath42 and the self - consistently derived synchrotron photon density @xmath43 .
gradually @xmath22 increases , and eventually , for bright sources , dominates over both @xmath42 and @xmath43 . in the upper panel of fig.1
we plot the self - consistently derived break @xmath44 in the eed .
note that @xmath44 decreases as the power of the source decreases . in fig.2
we plot basic observable quantities as a function of @xmath7 . in the lower panel
we plot the synchrotron luminosity @xmath45 , the ssc luminosity @xmath46 , and the ec luminosity @xmath47 . at low powers
, @xmath48 is much weaker than @xmath46 and @xmath45 that are roughly equal .
as the source power increases , @xmath48 gradually dominates over @xmath46 and @xmath45 , and we end up with an ec dominated source . in the middle panel we plot the peak frequencies of the three emission components . note how the synchrotron peak frequency @xmath49 decreases as the source power increases .
similar behavior is also seen for the ssc peak frequency @xmath50 and the ec peak frequency @xmath51 .
finally in the upper panel of fig.1 we plot the ratio @xmath52 ( solid line ) of the synchrotron to accretion disk luminosity and the ratio @xmath53 of the ic luminosity to synchrotron luminosity .
@xmath45 dominates over @xmath7 in weak sources in agreement with the lack of a thermal component and weak emission lines in weak sources like bls .
@xmath7 becomes more significant for powerful sources , again in agreement with the strong emission lines of fsrqs and the accretion disk signature observed in some fsrqs ( e.g. in 3c 279 , pian et al 1999 ) .
the dominance of the compton over the synchrotron emission increases as the source power increases , in agreement with observations ( e.g. kubo et al .
note , however , that the observational case for an increasing compton dominance with source power is based on poor statistics due to the limited sensitivity of the _
cgro_. in fig.3 we plot the synchrotron luminosity @xmath54 versus the synchrotron peak frequency @xmath55 for the blazars studied by sambruna , maraschi & urry ( 1996 ) and kubo et al .
( 1998 ) . on top of the data points we plot the model tracks as a function of @xmath7 for a range of observing angles .
note that these tracks represent two model derived quantities , @xmath45 and @xmath49 as @xmath7 varies .
the model covers rather well the observed parameter space .
given the track of the model under an angle @xmath56 , we do not expect that any powerful ( @xmath57 erg s@xmath33 ) sources with high peak frequencies @xmath58 hz exist .
the discovery of such sources would pose a serious problem for this model .
in fig.4 we plot the peak luminosities of the three emission mechanisms for 5 model sources with @xmath7 ranging from @xmath39 up to @xmath40 erg s@xmath33 .
the behavior of the model is in good agreement with the general characteristics of the observed luminosity sequence ( compare with fig.12 of fossati et al .
the synchrotron peak frequency decreases from @xmath59 hz down to @xmath60 hz , as the synchrotron power increases .
the compton peak frequency in weak sources is in the tev regime ( @xmath61 hz ) and it is due to ssc , while in powerful sources it is in the gev regime ( @xmath62 hz ) and it is due to ec .
according to the model , although in these bright sources the energy losses are dominated by ec , the hard x - ray emission is due to ssc , in agreement with resent observations ( kubo et al .
1998 ) .
we note here that fig.4 corresponds to sources that are oriented at an angle @xmath29 . in reality one should expect a range of angles , which will give rise to significant scattering around the presented trend .
this scattering is visible in the work of fossati et al .
( 1998 ) and indicates that a proper unification scheme for blazars should include the effects of orientation . | we present preliminary results of our work on blazar unification .
we assume that all blazars have a broad line region ( blr ) and that the size of the blr scales with the power of the source in a manner similar to that derived through reverberation mapping in radio quiet active galactic nuclei ( agns ) . using a self - consistent emission model that includes particle acceleration
we show that according to this scaling , in weak sources like mkn 421 , the inverse compton ( ic ) scattering losses are dominated by synchrotron - self compton scattering ( ssc ) , while in powerful sources , like 3c 279 , they are dominated by external compton ( ec ) scattering of blr photons . in agreement with other workers , we show that even in the powerful sources that are dominated by ec scattering , the hard x - ray emission is due to ssc . finally , we show that this scaling reproduces well the observed sequence of blazar properties with luminosity . |
within the framework of quantum chromodynamics ( qcd ) , inelastic scattering between a proton and antiproton is described as a hard collision between their constituents ( partons ) .
after the collision , the outgoing partons manifest themselves as localized streams of particles or `` jets '' . predictions for the inclusive jet cross section have improved in the early nineties with next - to - leading order ( nlo ) perturbative qcd calculations @xcite and new , accurately measured parton density functions ( pdf)@xcite .
d has recently measured and published @xcite the cross section for the production of jets as a function of the jet energy transverse to the incident beams , @xmath7 .
the measurement is based on an integrated luminosity of about 92 pb@xmath1 of @xmath2 hard collisions collected with the d detector @xcite at the fermilab tevatron collider .
this result allows a stringent test of qcd , with a total uncertainty substantially reduced relative to previous results @xcite .
we also measure the ratio of jet cross sections at two center - of - mass energies : 630 ( based on an integrated luminosity of about 0.537 pb@xmath1 ) and 1800 gev @xcite .
experimental and theoretical uncertainties are significantly reduced in the ratio .
this is due to the large correlation in the errors of the two cross section measurements , and the suppression of the sensitivity to parton distribution functions ( pdf ) in the prediction .
the ratio of cross sections thus provides a stronger test of the matrix element portion of the calculation than a single cross section measurement alone .
previous measurements of cross section ratios have been performed with smaller data sets by the ua2 and cdf @xcite experiments .
jets are reconstructed using an iterative jet cone algorithm with a cone radius of @xmath8=0.7 in @xmath9@xmath10 space , ( pseudorapidity is defined as @xmath11 $ ] ) @xcite . the offline data selection procedure , which eliminates background caused by electrons , photons , noise , or cosmic rays , follows the methods described in refs . @xcite .
the jet energy scale correction , described in @xcite , removes instrumentation effects associated with calorimeter response , showering , and noise , as well as the contribution from spectator partons ( underlying event ) .
the energy scale corrects jets from their reconstructed @xmath7 to their `` true '' @xmath7 on average .
an unsmearing correction is applied later to remove the effect of a finite @xmath7 resolution @xcite .
the resulting inclusive double differential jet cross sections , @xmath12 , for @xmath13 and @xmath14 ( the second region for comparison to ref .
@xcite ) , are compared with a nlo qcd theoretical prediction @xcite .
discussions on the different choices in the theoretical calculation : pdfs , renormalization and factorization scales ( @xmath15 ) , and clustering algorithm parameter ( @xmath16 ) can be found in refs .
@xcite .
figure [ fig_3 ] shows the ratios @xmath17 for the data ( @xmath18 ) and jetrad nlo theoretical ( @xmath19 ) predictions based on the cteq3 m , cteq4 m and mrst pdf s [ 4,5 ] for @xmath13 .
( the tabulated data for both @xmath13 and @xmath14 measurements can be found in ref .
@xcite . )
the predictions are in good quantitative agreement with the data , as verified with a @xmath20 test , which incorporates the uncertainty covariance matrix @xmath21 . here
@xmath22 and @xmath23 represent the @xmath24-th data and theory points , respectively .
the overall systematic uncertainty is largely correlated .
table [ tab : table2 ] lists @xmath25 values for several jetrad predictions using various parton distribution functions @xcite .
the predictions describe both the @xmath13 and @xmath14 cross section very well .
the measurement by d and cdf are also in good quantitative agreement within their systematic uncertainties @xcite .
-0.8 cm .
@xmath25 comparisons between jetrad and @xmath26 and @xmath27 data for @xmath28 , @xmath29=@xmath30 , and various pdfs .
there are 24 degrees of freedom . [ cols="^,>,>",options="header " , ] -1.2 cm [ tab : table2 ] -1 cm -0.8 cm [ fig_3 ] -2 cm
d has made a preliminary measurement of the pseudorapidity dependence of the inclusive jet cross section .
figure [ fig : forward ] shows the ratios @xmath17 for the data ( @xmath18 ) and jetrad nlo theoretical ( @xmath19 ) predictions using the cteq3 m pdf set for @xmath32 and @xmath33 .
the measurements and the predictions are in good qualitative agreement .
a detailed error analysis is currently being completed .
a simple parton model would predict a jet cross section that scales with center - of - mass energy . in this scenario , @xmath34 , plotted as a function of jet @xmath35 , would remain constant with respect to the center - of - mass energy .
figure [ fig : ratmu ] shows the d measurement of @xmath36 ( stars ) compared to jetrad predictions ( lines ) .
there is poor agreement between data and nlo qcd calculations using the same @xmath15 in the numerator and the denominator ( probability of agreement not greater than 10% ) .
the agreement improves for predictions with different @xmath15 at the two center - of - mass energies @xcite . in conclusion
, we have made precise measurements of jet production cross sections . at @xmath0=1800 gev
, there is good agreement between the measurements and the data .
the ratio of cross sections at @xmath0=1800 and 630 gev , however , differs from nlo qcd predictions , unless different renormalization scales are introduced for the two center - of - mass energies .
w. t. giele , e. w. n. glover , and d. a. kosower , phys .
letters * 73 * , 2019 ( 1994 ) ; s. d. ellis , z. kunszt , and d. e. soper , phys .
letters * 64 * , 2121 ( 1990 ) ; f. aversa _ et al .
_ , phys . rev .
letters * 65 * , ( 1990 ) | we have made a precise measurement of the inclusive jet cross section at @xmath0=1800 gev . the result is based on an integrated luminosity of 92 pb@xmath1 collected at the fermilab tevatron @xmath2 collider with the d detector .
the measurement is reported as a function of jet transverse energy ( 60 gev @xmath3 500 gev ) , and in the pseudorapidity intervals @xmath4 0.5 and 0.1@xmath50.7 .
a preliminary measurement of the pseudorapidity dependence of inclusive jet production ( @xmath4 1.5 ) is also discussed .
the results are in good agreement with predictions from next to leading order ( nlo ) quantum chromodynamics ( qcd ) .
d has also determined the ratio of jet cross sections at @xmath0=630 gev and @xmath0=1800 gev ( @xmath6 ) .
this preliminary measurement differs from nlo qcd predictions . |
99 g. marchesini et al . ,
_ comput . phys
. commun . _ * 67 * ( 1992 ) 465 .
g. corcella and m.h .
seymour , hep - ph/9908335 .
d collaboration , b. abbott et al .
lett . _ * 80 * ( 1998 ) 5498 .
cdf collaboration , t. affolder et al .
, fermilab - pub-99/220-e . | we show vector boson transverse momentum distributions at the tevatron , obtained by running the herwig monte carlo event generator with matrix - element corrections .
we compare our results with some recent d and cdf data .
ur1589 + er/40685/939 + hep - ph/9911536 + november 1999 vector boson production at hadron colliders is a fundamental process to test quantum chromodynamics and the standard model of the electroweak interactions .
the lowest order processes @xmath0 and @xmath1 are not sufficient to perform reliable phenomenological predictions , but the initial - state radiation has to be taken into account . a possible way to deal with such multiple emissions consists in running a monte carlo event generator .
standard monte carlo algorithms @xcite describe parton cascades in the soft / collinear approximation , with ` dead zones ' in the phase space which can be filled by the using of the exact first - order matrix element .
in @xcite we implemented matrix - element corrections to the herwig simulation of drell yan interactions : we filled the missing phase space using the exact @xmath2 matrix element ( hard corrections ) and corrected the shower in the already - populated region using the exact amplitude for every hardest - so - far emission ( soft corrections ) . for @xmath3 production at the tevatron , about 4% of the events
are generated in the dead zone , about half of which are @xmath4 events .
similar results hold for @xmath5 production as well . an interesting observable
to study is the vector boson transverse momentum @xmath6 , which is the object of many theoretical and experimental analyses .
while in the parton shower approximation it has to be @xmath7 , after matrix - element corrections a fraction of events with larger values of @xmath6 is to be expected . in fig .
[ wqt ] ( a ) , we plot the @xmath3 @xmath6 spectrum at the tevatron according to herwig 5.9 , the latest public version , and to herwig 6.1 , the new version including matrix - element corrections to drell yan processes .
herwig has the option to vary the intrinsic transverse momentum @xmath8 of the incoming partons , which is set to zero , its default value , in the distributions shown in fig .
[ wqt ] ( a ) .
we observe a remarkable impact of the corrections : after some @xmath6 the 5.9 version does not give events anymore , while herwig 6.1 still has some events generated via the exact matrix element . in fig .
[ wqt ] ( b ) we compare some recent d data @xcite on @xmath3 production at the tevatron with the herwig 6.1 results , which we corrected in order to take the detector smearing effects into account .
we find good agreement overall ; we also consider the option of @xmath9 gev , but do not see any relevant effect after the detector corrections . as far as @xmath5 production is concerned ,
we have some preliminary cdf data @xcite , already corrected for detector effects , which we compare with herwig 6.1 in fig .
[ zqt ] , where the options @xmath8=0 , 1 and 2 gev are investigated .
the agreement is acceptable and the role of the implemented matrix - element corrections is crucial in order to succeed in fitting in with the data for @xmath10 gev . at very low @xmath6 ,
the best fit is obtained by setting @xmath11 gev . in fig
. [ ratio ] , we plot the ratio of the @xmath3 and the @xmath5 transverse momentum spectra , both normalized to unity , for different values of @xmath8 .
although it can be seen from fig .
[ zqt ] ( b ) that the @xmath5 @xmath6 spectrum depends strongly on @xmath8 at low @xmath6 , the ratio of the @xmath3 and @xmath5 spectra is insensitive to it .
this is good news for the @xmath3 mass measurement in hadron collisions , as this ratio is one of the main theory inputs that is needed .
a strong dependence on unknown non - perturbative parameters like @xmath8 could limit the accuracy of the @xmath3 mass measurement at the tevatron and , ultimately , at the lhc .
we have added matrix - element corrections to herwig s treatment of vector boson production in hadron collisions .
they make an enormous difference at high transverse momentum @xmath6 , but little at low @xmath6 .
although the dependence of the results on the non - perturbative intrinsic @xmath6 of partons in the proton ( @xmath8 ) is quite strong at low @xmath6 , it is very similar in the @xmath3 and @xmath5 cases , so that the ratio of the two @xmath6 spectra is almost independent of @xmath8 . |
the hera collider facility in hamburg , germany , was a unique machine for lepton - proton scattering at highest energies .
for the two experiments h1 and zeus protons with an energy of up to @xmath2 gev and electrons or positrons with an energy of @xmath3 gev were collided .
this is equivalent to a maximal centre of mass energy of @xmath4 gev . at the end of june 2007
the data taking finished . in deep inelastic scattering ( dis ) of leptons off nucleons the substructure of the nucleons
was discovered .
dis continues to be the tool for exploring the substructure of the nucleons with high precision , i.e. measuring their quark and gluon content in the form of so called parton distribution functions ( pdfs ) .
the evolution of pdfs is a sensitive test of our understanding of qcd dynamics , which is expressed in the form of pdf evolution equations .
furthermore a precise knowledge of pdfs is vital for measurements at hadron colliders , such as the lhc .
the kinematics of the scattering are described in terms of the lorentz invariant quantities : the bjorken scaling variable @xmath5 , the inelasticity @xmath6 , and the virtuality @xmath7 .
the hera experiments have made measurements of the proton structure for @xmath7 values of up to @xmath8gev@xmath9 and @xmath5 values down to @xmath10 .
one of the most fundamental measurements to be performed is that of the neutral current ( nc ) inclusive cross section for the reaction @xmath11 , which can be expressed in the form @xmath12 with @xmath13 and the structure functions @xmath14 , @xmath15 and @xmath16 . at leading order
, the structure functions relate to the pdfs as @xmath17 additional information can be obtained from charged current ( cc ) cross section for the reaction @xmath18 : @xmath19 the gluon density @xmath20 , which does not enter the inclusive cross section calculations at leading order , is constrained by the @xmath14 scaling violations , jet cross sections and the measurement of @xmath15 .
both zeus and h1 have performed inclusive cross section measurements with comparable precision and covering a similar kinematic range . therefore the results of the two experiments may be combined to provide a single set containing all inclusive hera cross sections and to be used for further qcd analyzes .
the averaging procedure , described in detail in @xcite , is without theoretical assumptions .
only small theoretical corrections are needed for swimming points to a common @xmath21 grid and for adjusting earlier measurements performed at a proton beam energy of @xmath22 gev .
the precision cross section data from the hera experiments are typically reported with three different components of the measurement uncertainty : statistical and systematic uncertainties , where the latter consist of parts uncorrelated or correlated between different kinematic domains .
the correlated uncertainties , which are due to effects like the luminosity measurement or shifts in the electron energy calibration need to be treated correctly in the averaging procedure . as a result , not only the uncorrelated and statistical part of the uncertainties are reduced .
because the measurements by the two experiments have different sensitivities to the correlated uncertainties , these can be constrained further and thus reduced .
the combination procedure is performed separately for the sets of @xmath23 and @xmath24 scattering and using both nc and cc data @xcite .
the original data and the combination are shown for a few exemplary values of @xmath5 of the @xmath23 nc data set in figure [ fig : h1zcombfit ] , left .
a remarkable reduction of the uncertainties is apparent .
figure [ fig : h1zcombfit ] , right , shows the full @xmath23 data set , which is seen to cover four orders of magnitude in @xmath5 and @xmath7 with very high precision .
the compatibility of the two experiments is observed to be very good with a total @xmath25 for @xmath26 averaged points .
the combined data is in the following used to perform a qcd analysis at nlo using hera data only . for the analysis , which is called herapdf @xmath1 ,
the dglap evolution equations are used to evolve the pdfs , which are parametrized at the starting scale of @xmath27gev@xmath9 .
a full evaluation of experimental and theory model uncertainties is performed .
the resulting pdfs are shown in figure [ fig : qcdfits ] at a scale of @xmath28gev@xmath9 and compared to earlier separate analyzes of the h1 and zeus collaborations @xcite .
a reduction of the uncertainties is seen , which is due to the improved combined data used as input .
this is most notable on the gluon density , which dominates all other partons at low @xmath5 whose uncertainty is typically also larger than the quark pdfs , which are directly accessed in dis .
while data taking at hera has stopped , more precise measurements have become available recently or are expected for the near future . in general , analyzes at low and intermediate @xmath29gev@xmath9 can be performed using relatively small data sets .
therefore the new high precision analyzes of h1 @xcite were performed using data from the hera - i running period , which ended in the year 2000 .
the total measurement uncertainties were reduced to as low as @xmath30 per point , which is about a factor of two better than previous data covering this kinematic domain @xcite . as an example , the new results on the structure function @xmath14 from @xcite are shown in figure [ fig : newdata ] , left . the analyzes at higher @xmath31gev@xmath9 are in general more constrained by the available statistics .
therefore improvements are expected from the analysis of the hera - ii data , where nearly @xmath32pb@xmath33 were collected per experiment after the hera luminosity upgrade starting from the year 2003 .
the data sample is about balanced between @xmath23 and @xmath24 .
a new feature of the hera - ii data is also beam polarization , where typical average values of @xmath34 are reached .
zeus has recently published new results on the inclusive nc and cc @xmath24 cross section @xcite .
figure [ fig : newdata ] , right , shows the cc cross sections and highlights their dependence on different quark flavours in the proton .
these are the first double differential inclusive measurements using the polarized electron beam .
also the employed @xmath24 hera - ii data samples have an integrated luminosity ten times larger than the previously used hera - i sample .
the hera experiments measure the proton structure in a wide range of @xmath5 and @xmath7 , thus providing stringent tests of qcd and valuable input for the lhc .
a new procedure combines the already published data to obtain one hera data set with improved uncertainties .
a combined qcd fit , herapdf 0.1 , is performed using this combined data set .
it is able to describe the data and provides pdfs with much reduced uncertainties compared to previous fits performed separately by the h1 and zeus collaborations .
in addition new measurements are available with significantly increased experimental precision .
99 c. adloff _ et al . _
[ h1 collaboration ] , eur .
j. c * 30 * ( 2003 ) 1 [ arxiv : hep - ex/0304003 ] .
s. chekanov _ et al . _
[ zeus collaboration ] , eur .
j. c * 42 * ( 2005 ) 1 [ arxiv : hep - ph/0503274 ] .
[ h1 collaboration ] , arxiv:0904.3513 [ hep - ex ] . c. adloff _ et al . _
[ h1 collaboration ] , eur .
j. c * 21 * ( 2001 ) 33 [ arxiv : hep - ex/0012053 ] .
s. chekanov _ et al . _
[ zeus collaboration ] , eur .
j. c * 21 * ( 2001 ) 443 [ arxiv : hep - ex/0105090 ] .
s. chekanov _ et al . _
[ zeus collaboration ] , arxiv:0901.2385 [ hep - ex ] .
s. chekanov _ et al . _
[ zeus collaboration ] , arxiv:0812.4620 [ hep - ex ] . | new and previously published measurements on the deep inelastic @xmath0 scattering cross section by the h1 and zeus collaborations are presented .
the uncertainties can be significantly reduced by a model independent combination procedure , which treats the systematic error correlations in a coherent way .
the combined h1 and zeus measurements of the inclusive neutral and charged current cross sections are used to perform a common nlo qcd fit , called herapdf @xmath1 .
the resulting set of parton density functions ( pdfs ) have a much improved experimental uncertainty compared to previous extractions using the uncombined h1 or zeus data . |
the analysis of the klm collaboration data @xcite for pb(158 gev / nucleon)-ag / br collisions indicated the existence of events with `` strong dynamical fluctuations '' . the use of factorial moments as a tool for preliminary selection of events was suggested . in our previous paper @xcite we analyzed the cluster structure of events resulting from the heavy ion collision data and from the monte carlo ( mc ) generators .
we investigated the dependence of the cluster distributions on the parameter defining a cluster size .
the quantity we worked with was the second scaled factorial moment as a function of averaged multiplicity @xmath0 with `` two subtracted '' ( i.e. @xmath0 - 2 ) : @xmath1 we gave also a motivation for the choice of such a discrimination tool . in full agreement with the suggestions following from ref .
@xcite we have found two different patterns in the first four published experimental events . in this note
we would like to present some further analysis concerning the same subject .
we again employ the cluster definition used in the procedure implementing the bose - einstein ( be ) effect in mc @xcite and in what follows only clusters containing at least two hadrons are taken into account .
as before , we work in a two - dimensional momentum space ( @xmath2 ) since in the data set @xcite only the pseudorapidity @xmath3 and the azimuthal angle @xmath4 are given .
as a distance measure for clustering we use @xmath5 which provides also rather stable results under some coefficient change in front of these two terms defining @xmath6 . in our procedure originally each particle is considered as a single cluster .
we fix the value of a `` cluster size parameter '' @xmath7 ( the upper limit of @xmath6 , for which two particles are joined into one cluster ) and perform the clustering procedure for all pairs of particles .
our procedure is different from the clustering procedure applied in @xcite .
details are given in @xcite .
here we would only like to point out that our results are significant if we have a sufficiently large number of clusters ( with at least two particles ) .
this limits the possible range of @xmath8 values , which must neither be too small nor too large .
twenty values of @xmath8 ( @xmath9 ) were taken for each of the events under consideration .
thus for each value of @xmath8 for a given event we have * a number of particles in each cluster @xmath10 * a number of clusters with @xmath11 , @xmath12 . obviously in the following @xmath13 . with this information
we may also calculate for subsequent values of @xmath8 the entropy @xcite @xmath14 where the summation runs over all clusters in an event ( leaving aside one particle clusters ) .
the quantity @xmath15 is a probability to find a particle in the k - th cluster .
as well known , the jaynes - shannon entropy introduced in this way is a good measure of the `` amount of uncertainty '' represented by a discrete probability distribution
. therefore one may expect that it will help ( in a natural way ) to distinguish between different heavy ion collision events .
here we do not use in our clustering procedure the principle of event entropy maximisation .
a futher study of this interesting subject is in progress .
we performed the clustering procedure for * the `` random events '' of similar multiplicities obtained by using a plain uniform random generator of @xmath16 points ( serene events ) * the four klm events presented in @xcite * the events obtained from the venus generator @xcite . we have chosen randomly for presentation 5 out of 20 events generated for both the serene and venus classes .
the results for cluster distribution are presented in figs .
1a)-3a ) .
the number of clusters for all the serene events has a rather broad maximum for @xmath17 between 5 and 10 ( @xmath18 ) with the value around 200 . for venus events the maximum occurs at smaller @xmath17 and
the subsequent decrease is much faster .
two of the experimental events resemble venus events , the other two are more similar to serene events . the striking structure seen in figs .
1a)-3a ) appears again if we now plot ( fot the same range of @xmath8 ) the entropy defined in eq .
( 3 ) , as shown in figs .
1b)-3b ) .
the maximum for all the serene events is very flat , whereas for all the venus events the values of entropy decrease rather fast for higher values of @xmath8 .
the experimental events are again much more differentiated .
more quantitative comparison of the events is possible if we define for each event * the ratio @xmath19 of the maximal number of clusters in each event to the number of clusters for the last bin in @xmath8 in this event ( cf . figs .
1a)-3a ) ) * the ratio @xmath20 of the maximal value of the entropy in each event to its `` last bin '' value ( cf
1b)-3b ) ) .
the values of these ratios are given in tab.1 .
we checked that omitting clusters with only two particles we get similar results as shown in tab.2 , although the number of clusters and the values of entropy ( especially for small values of @xmath8 ) are strongly reduced .
the values of considered ratios for all serene events are very similar . for venus events the values are much bigger and
more differentiated .
for two experimental events we find the values similar to those of serene events and for two others the values are more similar to venus events . [ cols="^,^ " , ]
comparing the results presented in fig.1 and fig.2 and the numbers given in tab.1 and tab.2 we may conclude that : * all the serene events follow one ( `` quiet '' ) pattern , where the fall of the number of clusters and entropy from its maximal value is rather slow ; the broad entropy distribution reflects the randomness of these events structure * on the contrary , all the venus events exhibit a completely different behaviour ; the majority of particles goes into one or a few clusters for larger values of @xmath8 , which results in a fast fall of the number of clusters and entropy * two of the experimental events ( the same as in ref .
@xcite and ref .
@xcite ) are serene like , the other two resemble more the venus like pattern .
thus , using a slightly different language , we confirmed our previous results @xcite .
the events from data seem to be more differentiated than those from the generators .
data with full momentum measurements and particle identification would be of great help in further analysis , improving our understanding of multiple production in heavy ion collisions .
we used the data kindly provided to us by b. wosiek ( ref .
@xcite ) and the data prepared from the `` venus '' generator .
an interesting conversation with p. bogu concerning the application of the j - s entropy in medical data bases should be noticed . the financial support of kbn grants # 2 p03b 086 14 and # 2p03b 010 15 is gratefully acknowledged .
one of us ( rw ) is grateful for a partial financial support by the kbn grant # 2 p03b 019 17 .
k. fiakowski and r. wit , _ acta phys .
polon . _ * 30 * , 2759 ( 1999 ) .
k. fiakowski , r. wit and j. wosiek , _ phys .
rev . _ * d58 * , 094013 ( 1998 ) .
jaynes , _ phys
. rev . _ * 106 * , 620 ( 1957 ) .
k. werner , _ phys .
rep . _ * 232 * , 87 ( 1995 ) . + | we analyse the cluster structure of the final multihadron states resulting from heavy ion collisions using the concept of jaynes - shannon entropy .
further evidence for an interesting differentiation of events is provided . 23.0 cm 16.0 cm -2.0 cm -1.0 cm -1.0 cm k. fiakowski , r. wit _ m. smoluchowski institute of physics + jagellonian university + 30 - 059 krakw , ul.reymonta 4 , poland _ pacs : 25.70.-z + _ keywords : _ heavy ion collisions , cluster analysis , monte carlo + 4 october , 1999 + |
the top quark is the heaviest known elementary particle of the standard model ( sm ) .
it has a life - time shorter than the hadronization time and offers a window to search for new physics . with large numbers of top events produced at lhc in run-1
, it is possible to study its properties in detail .
these proceedings present measurements of top production , top properties and searches at the center of mass energy of 7 , 8 and 13 tev by the atlas experiment @xcite .
the atlas experiment has performed measurements of the inclusive top - antitop production cross section of @xmath3 production at center of mass energy of 7 , 8 and 13 tev in the dilepton channel @xcite .
the measurement at 8 tev represents the most precise measurement to date , even more precise than next - to - next - to - leading order ( nnlo ) predictions @xcite . at 13 tev
, the cross section is found to be @xmath4 . in the three analyses , a simultaneous fit of the cross section
, b - jet reconstruction and tagging efficiency is performed in the @xmath5 channel .
all the measurements are in agreement with sm predictions , as shown in figure [ fig : a ] . 0.50 pair production in pp collisions as a function of centre - of - mass energy .
the results at @xmath6 , @xmath7 and @xmath8 tev are compared to the theory predictions @xcite .
( b ) summary of atlas measurements of the single top production cross sections in various channels as a function of the center of mass energy compared to theoretical calculations @xcite.,title="fig : " ] 0.40 pair production in pp collisions as a function of centre - of - mass energy .
the results at @xmath6 , @xmath7 and @xmath8 tev are compared to the theory predictions @xcite .
( b ) summary of atlas measurements of the single top production cross sections in various channels as a function of the center of mass energy compared to theoretical calculations @xcite.,title="fig : " ] new physics could affect the shape of the differential cross section as a function of top kinematics . in this conference , measurements performed in two different topologies were presented : the resolved and the boosted topologies , which are optimized for tops with transverse momentum @xmath9 and and @xmath10 gev respectively . in the resolved topology , the measurement of the top - antitop differential cross section is performed as a function of the mass , @xmath11 and rapidity of the top pair system at @xmath8 tev @xcite .
these measurements are performed in a fiducial region closely matching the detector acceptance and using tops observables based on stable particles in the @xmath5 channel .
r0.4 the observed spectra are softer than the monte carlo ( mc ) predictions . in the boosted topology ,
the differential cross section as a function of the @xmath11 of the @xmath3 system is measured in the semileptonic decay channel at @xmath7 tev @xcite .
the measurements are performed in both a fiducial and total phase space .
the measurements are also found to be softer than the mc predictions .
several measurements of the inclusive single top cross section in the @xmath12 , @xmath13 and @xmath14 channel at 7 and 8 tev have been performed by atlas .
the latest 8 tev results were presented in this conference .
figure [ fig : b ] shows a summary of these measurements @xcite .
the inclusive cross sections for @xmath13-channel is found to be @xmath15 pb , showing a good agreement with the nlo+nnll predictions @xcite , as well as the inclusive measurement in the @xmath14 channel where the measured value is @xmath16 pb @xcite .
an upper limit for the @xmath12-channel cross section was established @xcite .
the @xmath17 and @xmath18 cross sections were measured in final states with two , three or four leptons @xcite . in this analysis , a simultaneous fit is performed in 20 signal and control regions .
the control regions are defined by varying the number jets and lepton charge in the event .
the results agree with the sm prediction as shown in figure [ fig : ttwttv ] .
measurements of the top mass , performed in @xmath3 events in the semileptonic and the dileptonic channels , were presented @xcite . the analysis in the semileptonic channel uses a 3-dimensional template fit which determines simultaneously the top quark mass , the jet and @xmath19-jet energy scale factor .
this measurement is the most precise mass measurement performed by atlas to date .
the dilepton channel uses a one dimensional template fit and the combined result is found to be @xmath20 gev . in single
top decays , the measurement is performed through a one dimensional template fit using the invariant mass of the lepton and @xmath19-jet , in order to reduce the modelling uncertainties @xcite .
neural networks are used to optimize the purity of the selection to @xmath21 .
the measured value is found to be @xmath22 .
moreover , a measurement of the pole mass using the normalized differential cross section for @xmath23-jet as a function of the inverse of the invariant mass of system was performed @xcite .
the selected events are identified using the lepton+jets top - quark pair decay channel , where lepton refers to either an electron or a muon .
the measured value is found to be @xmath24 .
top pairs produced via the strong interaction are produced unpolarized at leading order .
their spins are correlated and information transferred to decay products .
a measurement of the @xmath3 spin correlation at @xmath7 tev was performed @xcite . in this analysis ,
the @xmath3 spin correlation is extracted from dilepton events by using the difference in the azimuthal angle of the two selected leptons .
the measured value is consistent with the sm predictions .
moreover , the measurement of the angular distribution of the decay products is sensitive to super symmetric top squark ( stop ) pair production .
the top squarks with masses between the top quark mass 172.5 gev and 191 gev are excluded at the @xmath25 confidence level .
in this conference , limits in searches for flavor changing neutral currents ( fcnc ) were presented @xcite .
fcnc are predicted by the sm but are largely suppressed by the gim mechanism . in beyond the standard model ( bsm ) models the fcnc are enhanced , giving a window to search for new physics .
one search is performed in @xmath3 events with one top quark decaying to a @xmath26-boson and a light quark and the other to a @xmath27-boson and a @xmath19-quark .
both bosons are required to decay leptonically .
no evidence of fcnc is found and an observed upper limit is established .
another search for fcnc is performed in single top production via @xmath28 with the top decaying to a @xmath26-boson and a light quark @xcite .
only the leptonic channel is considered and upper limits are established on the cross section times branching ratio and on the coupling constants of the processes .
atlas has performed multiple measurements in the top physics domain .
the measurements of cross sections and properties are in agreement with the sm predictions .
some top quark properties were used to exclude bsm models and limits were established for fcnc searches .
99 atlas collaboration , 2008 jinst 3 s08003 .
atlas collaboration , eur .
j. c 74 ( 2014 ) , no .
10 , 3109 .
m. czakon , p. fiedler and a. mitov , phys .
lett . 110 ( 2013 ) , 252004 . atlas collaboration , atlas - conf-2015 - 033
. atlas collaboration , jhep 1506 ( 2015 ) , 100 . | these proceedings summarize the latest measurements on top production , top properties and searches using the atlas detector at the lhc .
the measurements are performed on @xmath0 collision data with a center of mass energy @xmath1 and @xmath2 tev . |
the lhc is expected to directly probe possible new physics beyond the standard model ( sm ) up to a scale of a few tev . while its data should provide answers to several of the major open questions in the present picture of elementary particle physics
, it is important to start examining how this sensitivity can be further extended at a next generation of colliders .
today we have a number of indications that new physics could be of supersymmetric nature .
if this is the case , the lhc will have a variety of signals to discover these new particles and the linear collider ( lc ) will be required to complement the probe of the susy spectrum with detailed measurements .
however , beyond supersymmetry there is a wide range of other scenarios invoking new phenomena at , and beyond , the tev scale .
they are aimed at explaininig the origin of electro - weak symmetry breaking , if there is no light elementary higgs boson , at stabilising the sm , if susy is not realised in nature , or at embedding the sm in a theory of grand unification .
many of such scenarios predict the existence of new particles that would be manifested as rather spectacular resonances in @xmath0 collisions , if the achievable centre - of - mass energy is sufficient .
a high energy lc represents an ideal laboratory for studying this new physics @xcite .
it also retains an indirect sensitivity , through a precision study of the virtual corrections to electro - weak observables , when their mass exceeds the available centre - of - mass energy .
this paper summarises the results of a series of studies aimed at quantifying the potential of a high energy , high luminosity @xmath0 lc in extending to high scales the probe for new physics .
while a significant activity has already addressed the issues related to a tev - class collider , we now review the potential of a multi - tev lc , such as clic .
the analysis of the lep and slc data has provided a significant experience in the extraction of electro - weak observables , optimising their statistical sensitivity and controlling their systematic uncertainties . at larger centre - of - mass energies ,
the relevant @xmath1 cross sections are significantly reduced and the experimental conditions at the interaction region need to be taken into account in validating the anticipated accuracies on the cross section @xmath2 , forward - backward asymmetries @xmath3 and left - right asymmetries @xmath4 determination at @xmath5 = 1 tev - 5 tev . since the two - fermion cross section is of the order of only 10 fb , it is imperative to achieve high luminosity by reducing the beam - spot sizes . in this regime
the beam - beam effects are important and the primary @xmath0 collision is accompained by several @xmath6 interactions .
being mostly confined in the forward regions , this @xmath7 background reduces the polar angle acceptance for quark flavour tagging and dilutes the jet charge separation using jet charge techniques .
these experimental conditions require efficient and robust algorithms to ensure sensitivity to flavour - specific @xmath8 production .
the statistical accuracy for the determination of @xmath2 , @xmath3 and @xmath4 has been studied , for @xmath9 and @xmath10 , taking the clic parameters at @xmath5 = 3 tev .
the simdet parametrised detector simulation has been used and the @xmath6 background , corresponding to 10 overlayed bunch crossings , has been added to @xmath11 , @xmath10 events .
@xmath10 final states have been identified using an algorithm based on the sampling of the decay charged multiplicity of the highly boosted @xmath12 hadrons at clic energies @xcite .
similarly to lep analyses , the forward - backward asymmetry has been extracted from a fit to the flow of the jet charge @xmath13 defined as @xmath14 , where @xmath15 is the particle charge , @xmath16 its momentum , @xmath17 the jet thrust axis and the sum is extended to all the particles in a given jet . here the presence of additional particles , from the @xmath18 background , causes a broadening of the @xmath13 distribution and thus a dilution of the quark charge separation .
the track selection and the value of the power parameter @xmath19 needed to be optimised as a function of the number of overlayed bunch crossings .
the results are summarised in terms of the relative statistical accuracies @xmath20 in table [ tab : res ] .
another important issue is the accuracy on the luminosity determination , that needs to be controlled to 0.5% , or better .
.relative statistical accuracies on electro - weak observables , obtained for 1 ab@xmath21 of clic data at @xmath5 = 3 tev , including the effect of @xmath6 background .
[ cols="<,^ " , ] fermion compositeness or exchange of very heavy new particles can be described in all generality by four - fermion contact interactions @xcite .
these parametrise the interactions beyond the sm by means of an effective scale , @xmath22 , @xmath23 the strength of the interaction is set by convention as @xmath24 and models can be considered by choosing either @xmath25 or @xmath26 as detailed in table ii .
the contact scale @xmath27 can be interpreted as effect of new particles at a mass @xmath28 , @xmath29 . in order to estimate the sensitivity of electro - weak observables to the contact interaction scale @xmath27
, the statistical accuracies discussed in section ii have been assumed for the @xmath30 and @xmath31 final states .
the systematics of the assumed 0.5% include the contributions from model prediction uncertainties .
results are given in terms of the lower limits on @xmath27 which can be excluded at 95% c.l .
, in figure [ fig : ci ] .
it has been verified that , for the channels considered in the present analysis , the bounds for the different @xmath22 are consistent .
high luminosity @xmath0 collisions at 3 tev can probe @xmath27 at scales of 200 tev , and beyond . for comparison , the corresponding results expected for a lc operating at 1 tev are also shown .
beam polarisation represents an important tool in these studies .
first , it improves the sensitivity to new interactions , through the introduction of the left - right asymmetries @xmath32 and the polarised forward - backward asymmetries @xmath33 in the electro - weak fits .
if both beams can be polarised to @xmath34 and @xmath35 respectively , the relevant parameter is the effective polarisation defined as @xmath36 . in addition to the improved sensitivity , the uncertainty on the effective polarization , can be made smaller than the error on the individual beam polarization measurements .
secondly , in the case of a significant deviation from the sm prediction would be observed , @xmath37 and @xmath38 polarization is greatly beneficial to determine the nature of the new interactions .
this has been studied in details for a lc at 0.51.0 tev @xcite and those results also apply , qualitatively , to a multi - tev collider .
extending the sensitivity to new physics beyond the anticipated reach of the lhc , is a prime aim of future colliders . by accurately measuring electro - weak observables , a lc able to achieve @xmath0 collisions at and beyond 1 tev , with high luminosity ,
can indirectly probe scales extending from tens to several hundreds tev .
giudice , r. rattazzi and j.d .
wells , nucl .
b544 * ( 1999 ) 3 ; e. a. mirabelli , m. perelstein and m. e. peskin , phys .
* 82 * ( 1999 ) 2236 ; t. han , j.d .
lykken , r .- j .
zhang , phys .
* d59 * ( 1999 ) 105006 .
see , for example , t.g .
rizzo and j.d .
wells , phys . rev . *
d61 * 016007 ( 2000 ) ; p.
nath and m. yamaguchi , phys . rev . * d60 * ( 1999 ) 116006 ; m. masip and a. pomarol , phys . rev .
* d60 * ( 1999 ) 096005 ; r. casalbuoni , s. de curtis , d. dominici and r. gatto , phys .
b462 * ( 1999 ) 48 ; a. strumia , phys . lett .
* b466 * ( 1999 ) 107 . | extending the sensitivity to new physics beyond the anticipated reach of the lhc is a prime aim of future colliders .
this paper summarises the potential of an @xmath0 linear collider , at and beyond 1 tev , using a realistic simulation of the detector response and the accelerator induced background .
the possible lc energy - luminosity trade - offs offered in probing multi - tev scales for new phenomena with electro - weak observables are also discussed . |
financial support by the austrian science fund ( projects i543-n20 and j3732-n27 ) and the german research foundation within the dach framework is acknowledged .
40ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1103/physrevlett.94.026803 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop ( ) \doibase http://dx.doi.org/10.1038/43403 [ * * , ( ) ] , @noop * * , ( ) \doibase http://dx.doi.org/10.1063/1.4819397 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1017/s1431927614000610 [ * * , ( ) ] @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) _ _ , @noop ph.d . thesis , ( ) @noop _ _ ( , ) \doibase http://dx.doi.org/10.1016/s0968-4328(99)00112-2 [ * * , ( ) ] link:\doibase 10.1080/13642819908214851 [ * * , ( ) ] , @noop _ _ , advences in electronics and electron physics ( , ) @noop * * , ( ) @noop @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1107/s0365110x57002194 [ * * , ( ) ] @noop _ _ ( , ) \doibase http://dx.doi.org/10.1016/j.ultramic.2013.11.010 [ * * , ( ) ] | transmission electron microscopy has been a promising candidate for mapping atomic orbitals for a long time . here , we explore its capabilities by a first principles approach .
for the example of defected graphene , exhibiting either an isolated vacancy or a substitutional nitrogen atom , we show that three different kinds of images are to be expected , depending on the orbital character . to judge the feasibility of visualizing orbitals in a real microscope , the effect of the optics aberrations is simulated .
we demonstrate that , by making use of energy - filtering , it should indeed be possible to map atomic orbitals in a state - of - the - art transmission electron microscope .
the possibility to _ see _ atomic orbitals has always attracted great scientific interest . at the same time , however , the real meaning of `` measuring orbitals '' has been a subject that scientists have long and much dwelt upon ( see , e.g. , @xcite and references therein ) . in the past , significant efforts have been devoted to the development of experimental approaches and theoretical models that allow for orbital reconstruction from experimental data @xcite .
based on the generation of higher harmonics by femtoseconds laser pulses , a tomographic reconstruction of the highest occupied molecular orbital ( homo ) for simple diatomic molecules in the gas phase was proposed @xcite .
direct imaging of the homo and the lowest - occupied molecular orbital ( lumo ) of pentacene on a metallic substrate was theoretically predicted and experimentally verified with scanning - tunnelling microscopy ( stm ) @xcite .
more recently , real - space reconstruction of molecular orbitals from angle - resolved photoemission data has been demonstrated @xcite .
this method has been subsequently further developed to retrieve both the spatial distribution @xcite and the phase of electron wavefunctions of pentacene and perylene-3,4,9,10-tetracarboxylic dianhydride ( ptcda ) adsorbed on silver @xcite .
the reconstruction of charge densities and chemical bonds using transmission electron microscopy ( tem ) has been considered @xcite , but only recently the possibility of probing selected transitions to specific unoccupied orbitals by using energy - filtered tem ( eftem ) was demonstrated theoretically .
a first example for the capability of this approach was provided with the oxygen k - edge of rutile tio@xmath0 @xcite .
however the interpretation of experimental tem images for systems like rutile would be complicated because of the multiple elastic scattering of electrons that occurs in thick samples . in this letter , we suggest defective graphene @xcite as the prototypical two dimensional ( 2d ) material to demonstrate the possibility of mapping atomic orbitals using eftem .
we break the ideal @xmath1 hybridization by introducing two different kinds of defects , namely a single isolated vacancy and a substitutional nitrogen atom .
this lifts the degeneracy of the @xmath2-states , inducing strong modifications to the electronic properties compared to the pristine lattice @xcite . by selecting certain scattering angles ,
dipole - allowed transitions dominate the electron energy loss spectroscopy ( eels ) signal @xcite .
a single - particle description can be safely adopted , since many - body effects do not play a major role in the excitation process .
overall , tem images of these systems can be interpreted in terms of bare @xmath3 transitions . in an eftem experiment ,
an incoming beam of high - energy electrons ( of the order of 100 kev ) is directed to the target where it scatters at the atoms either elastically or inelastically .
the outgoing electron beam is detected and analyzed .
state of the art image simulations generally only include elastic scattering of the electrons using the multi - slice approach @xcite . in the case of eftem for a thin sample ,
the influence of elastic scattering becomes negligible , and inelastic scattering gives the dominant contribution to the formation of the images . the key quantity to describe the inelastic scattering of electrons , which is probed by eels , is the mixed dynamic form factor ( mdff ) .
it can be interpreted as a weighted sum of transition matrix elements between initial and final states @xmath4 and @xmath5 of the target electron @xcite : @xmath6 with energies @xmath7 and @xmath8 .
@xmath9 is the energy - loss of the fast electron of the incident beam , @xmath10 and @xmath11 are the wavevectors of the perturbing and induced density fluctuations , respectively .
if many - body effects can be neglected , this picture can be simplified for dipole - allowed transitions . in this case , using the spherical harmonics as basis for the target states and referring to transitions originating from a single state ( as in @xmath3 excitations ) , the mdff is @xcite @xmath12 where @xmath13 are spherical harmonics , @xmath14 is an integral of the spherical bessel function @xmath15 weighted over the initial and final radial wavefunctions . @xmath16 and @xmath17 indicate the azimuthal and magnetic quantum number of the final state of the target electron , and @xmath18 and @xmath19 are the angular momenta transferred during the transition .
@xmath20 is a quantity that describes crystal - field effects and is proportional to the cross - density of states ( xdos ) @xmath21 where @xmath22 is the angular part of the final wave function , @xmath23 is the band index , and @xmath24 is a k - point in the first brillouin zone . compared to the density of states ( dos ) , the xdos includes also non - diagonal terms connecting states with different angular momenta . as @xmath25 is a hermitian matrix @xcite , the mdff can be diagonalized .
therefore , assuming that the target s final states of the @xmath3 excitation are not degenerate , the transition matrix elements reflect the azimuthal shape of the final single - particle states and can thus be separated by using energy - filtering .
ground - state calculations are performed using density - functional theory and the full - potential augmented planewave plus local - orbital method , as implemented in exciting @xcite . introducing a vacancy or a substitutional atom , a 5@xmath265 supercell
is set up , hosting 49 and 50 atoms , respectively ( fig . 1 and 2 in the supplemental material @xcite ) . the space group and thus the number of inequivalent carbon atoms ( 13 ) is the same in both cases .
we adopt a lattice parameter of @xmath27=4.648 bohr , corresponding to a bond length of 2.683 bohr , while the cell size perpendicular to the graphene plane is set to c=37.794 bohr in order to prevent interactions between the periodically repeated layers .
exchange - correlation effects are treated by the pbe functional @xcite .
the brillouin zone is sampled with an 8@xmath268@xmath261 k - point grid .
the structures are relaxed down to a residual force lower than 0.0005 ha / bohr acting on each atom .
interatomic distances between atoms of the relaxed structures , up to the seventh nearest neighbor , are given in table [ tab1 ] .
upon relaxation , the atoms surrounding the vacancy move slightly away from it , thus shortening the bond lengths with the next nearest neighbors , @xmath28 , compared to the unperturbed system .
the effect of the vacancy extends up to the fourth neighbours , whereas it is almost negligible for more distant atoms ( more information about the relaxed structures can be found in the supplemental material @xcite ) . in the case of nitrogen doping , the substitutional atom does not strongly influence the atomic configuration of the system .
this happens because the nitrogen - carbon bond length is just slightly shortened with respect to the carbon - carbon bond length in pristine graphene . for all the systems , we have investigated dipole - allowed transitions at the k - edge of carbon , assuming an incoming electron beam perpendicular to the graphene plane .
.[tab1 ] bond lengths between atoms up to the seventh nearest neighbor , @xmath29 , @xmath28 , @xmath30 , @xmath31 , @xmath32 , and @xmath33 , for graphene doped with nitrogen ( top row ) and with a vacancy ( bottom row ) .
@xmath34 are the relative deviations from those of pristine graphene .
@xmath35 indicates the defect site .
( [ cols="<,^,^,^,^,^,^,^",options="header " , ] in fig .
[ fig_dos ] , the projected density of states ( pdos ) of pristine graphene ( upper panel ) and of the first nearest - neighbor atom for nitrogen - doped graphene ( middle panel ) and graphene with a single vacancy ( bottom ) , respectively , is plotted for empty states up to 12 ev above the fermi energy . here , @xmath36 , @xmath37 , and @xmath38 represent the local cartesian coordinates at the individual atomic sites as determined by the point - group symmetry .
in particular , @xmath38 is the axis perpendicular to the graphene , i.e. , ( @xmath36 , @xmath37 ) plane .
all the other atoms of the defective systems exhibit a pdos with very similar character as in pristine graphene , besides the second and third nearest neighbors which are slightly affected by the defect @xcite .
local projected density of states ( pdos ) of carbon in pristine graphene ( upper panel ) , and of the first nearest - neighbor atom for nitrogen - doped graphene ( middle panel ) and graphene with a single vacancy ( bottom ) .
@xmath39 , @xmath40 , and @xmath41 states are indicated by the red , green , and black lines , respectively .
note that , in the lower panel , the peak close to the fermi energy exceeds the boundary of the box , with a maximum at about 2 states / ev . in the case of pristine graphene , the red line indicates the sum of @xmath42 and @xmath43 .
the three colored areas labeled as a , b , and c indicate the energy ranges for which the tem images have been calculated.,scaledwidth=48.0% ] in pristine graphene , antibonding @xmath44 and @xmath45 states are clearly recognizable at about 2 ev and 9 ev , respectively .
as already reported in literature @xcite , the introduction of a vacancy or a substitutional nitrogen has a significant influence on the electronic structure .
a consequence of the doping atom is lifting the degeneracy of @xmath39 and @xmath40 that is significant for the first nearest neighbors ( middle panel in fig .
[ fig_dos ] ) .
this effect is particularly evidenced by the appearance of bands at about 5 ev , which exhibit @xmath40 character . here ,
three different regions can be easily identified : a ) from 0 ev to 4 ev , the bands have only @xmath41 character ; energy ranges that present such dos character will be referred to as @xmath46 .
b ) for energies higher than 6 ev , there are contributions from @xmath39 , @xmath40 , and @xmath41 .
the only difference to ideal graphene is the lifted degeneracy of @xmath39 and @xmath40 .
this defines a new kind of region , named @xmath47 .
c ) between 4 ev and 6 ev , the @xmath39 character of the first nearest neighbor is much less pronounced than that of @xmath40 , while all the other atoms have only @xmath41 character ; this region will be referred to as @xmath48 . in the case of graphene with a vacancy
, the same kinds of regions can be identified , but corresponding to different energy ranges . here , the @xmath49 type is found between 0.5 ev and 7 ev ; @xmath47 encompasses energies above 7 ev ; @xmath48 is a small energy window , just few tenths of ev close to the fermi energy .
we find similar kinds of dos characters also for damaged nitrogen - doped graphene , i.e. , graphene with a substitutional nitrogen and a vacancy located near it ; such defects have beed recently reported in tem measurements of nitrogen - doped graphene @xcite .
details of this calculation and the corresponding simulated tem images can be found in the supplemental material @xcite . to investigate the impact of the local electronic structure ( pdos ) on the eftem images , we first consider the ideal case of a perfect microscope with an acceleration voltage of 300 kev . in this case , the recorded images correspond to the intensity of the exit wavefunction in the multislice simulation @xcite .
the finite resolution of the spectrometer is taken into account by simulating images every 0.05 ev in 2 ev - broad energy ranges ( regions a , b , and c in fig .
[ fig_theo ] ) and then summing them up to get the final images .
each image is shown in contrast - optimized grayscale .
simulated real - space intensity of the electron s exit wave function after propagation of an incident planewave through a graphene layer in presence of a nitrogen substitutional atom ( upper panels ) and a vacancy ( bottom panels ) .
the colored lines indicate the energy regions highlighted in fig .
[ fig_dos].,scaledwidth=48.0% ] first , we analyze graphene with nitrogen doping ( fig . [ fig_theo ] , upper panels ) . here , in the region close to the fermi level ( a in fig .
[ fig_dos ] ) there are only contributions from @xmath41 orbitals . the image is then formed by disk - like features where their arrangement clearly visualizes the missing atoms ( upper left panel in fig . [ fig_theo ] ) . at an energy loss between 4 and 6 ev above the carbon k - edge
( region b in fig .
[ fig_dos ] ) , there is a @xmath48-like region . we expect to see contributions from @xmath40 of the atom closest to the nitrogen , but no ( or very little ) signal coming from the other atoms .
this happens because @xmath40 lies on a plane perpendicular to the incoming electron beam and its magnitude is more intense than the one of @xmath41 ; thus its contribution to the final signal overcomes the one from @xmath41 states .
consequently , only the @xmath40 orbitals of the three atoms surrounding the nitrogen are visible , which are pointing towards the defect , as imposed by the local @xmath50 symmetry ( upper middle panel in fig .
[ fig_theo ] ) . at an excitation energy between 8 and 10 ev above the k - edge ( region c in fig .
[ fig_dos ] ) , instead , there are contributions from all the @xmath2 states . since , however , @xmath39 and @xmath40 lie in a plane perpendicular to the beam axis , their contribution to the final signal dominates over the one from @xmath41 states . as a consequence ,
the image is composed of ring - like features , stemming solely from @xmath39 and @xmath40 states , arranged in hexagons ( upper right panel in fig .
[ fig_theo ] ) . due to symmetry
breaking , the intensity is not uniform , neither along a ring ( since @xmath39 and @xmath40 states are non - degenerate ) nor among different rings ( due to non - equivalent atomic sites ) . the corresponding images for the system with a vacancy ( bottom panels in fig .
[ fig_theo ] ) appear nearly identical to the ones above , but at different energy ranges .
this can be understood by comparing the pdos of the two systems . between 0 and 2 ev ,
for instance , we have a @xmath49-like region in the case of nitrogen - doped graphene , and both @xmath48 and @xmath49 in the case of graphene with a vacancy .
due to the similarity of the two systems , we will , in the following , focus on doped graphene and show the corresponding analysis for graphene with a single vacancy in the supplemental material @xcite . in order to predict the outcome of real experiments , we now visualize the effect of the optics aberrations and of a more realistic acceleration voltage on these images .
we have simulated an electron - beam acceleration voltage of 80 kev and the operating parameters of two different kinds of microscopes , the fei tecnai g@xmath51 f20 and fei titan g@xmath51 60 - 300 .
the former has a spherical aberration @xmath52 = 1.2 mm , corresponding to a an extended scherzer defocus of 849 @xmath53 , while the latter is a last - generation aberration - corrected microscope , i.e. , exhibiting no spherical and chromatic aberrations . in view of that
, chromatic aberrations are not included in the calculations .
the images corresponding to the energy regions a , b , and c are shown in fig .
[ fig_exp_n ] . simulated tem image of nitrogen - doped graphene .
the coloured lines indicate the energy regions highlighted in fig .
[ fig_dos ] .
80 kev incident beam energy and lenses as in a titan ( upper panels ) and a tecnai microscope ( bottom panels ) were assumed.,scaledwidth=48.0% ] because of the lower resolution of the tecnai microscope , all the features are blurred ( lower panels ) compared to the ideal images . therefore ,
neither the atomic positions , nor the orbital shapes can be retrieved from them . on the other hand , images simulated by taking into account the aberration - corrected optics of the titan microscope are very sharp and let us identify all the features already observed for the idealized situation previously described .
this can be easily seen , comparing the upper panels of figs .
[ fig_exp_n ] and [ fig_theo ] .
in particular , at an energy loss of 5 ev ( region b ) , the @xmath40 orbitals are visible , as in the ideal images .
this clearly demonstrates the potential ability of aberration - corrected microscopes to visualize atomic orbitals with eftem , especially in a system like graphene .
this conclusion also holds when considering noise caused by the finite electron dose ( see supplemental material @xcite for corresponding images ) . in summary , we have predicted the possibility of performing orbital mapping in low - dimension systems using eftem and we have demonstrated it with the prototypical example of defective graphene . in particular , we have shown that , as far as the optics is concerned , reasonable image resolution may already nowadays be experimentally achievable with last generation aberration - corrected microscopes like a fei titan g@xmath51 60 - 300 and even more with improved instruments of the next generation .
however , additional work is necessary to reduce artifacts such as noise , drift , instabilities and damage .
the inelastic cross section for the carbon k - edge ionisation is about a factor of 10 smaller than the elastic scattering cross section on a carbon atom @xcite .
the intensity collected within an energy window of 2 ev as in fig .
[ fig_theo ] is @xmath545% of the total k - edge intensity .
so , order - of - magnitude - wise , in order to obtain the same snr as in elastic imaging , we need at least 200 times more incident dose which means a dwell time of the order of several minutes for last generation tems in eftem mode .
there is no fundamental law that would forbid such an experiment with today s equipment ; however , it is hampered by drift ( which must be well below the interatomic distance during the exposure time ) , instabilities , and radiation damage .
a new route to circumvent radiation damage based on an eftem low - dose technique was proposed recently @xcite .
this may solve the problem in future .
we have identified three different kinds of images that are expected to be acquired in an eftem experiment , depending on the character of the dos : when only @xmath41 states are present in the electronic structure , the corresponding images are composed of disk - like features .
when the dos is characterized by contributions from all @xmath2 states , ring - like features are seen that , however , only originate from a convolution of @xmath39 and @xmath40 states , while the @xmath55 character is not visible .
when the @xmath40 character strongly exceeds the one of @xmath39 , only a single orbital is recorded .
we expect this work to trigger new experiments on defective graphene and similar systems . |
rs cvn - type stars are binary systems where the most massive primary component is a g - k giant or subgiant and the secondary is a subgiant or dwarf of spectral classes g to m. these systems are well known due to their strong chromospheric plages , coronal x - ray emission , and strong flares in the optical , uv , radio , and x - ray .
most long - term stellar activity studies of rs cvn stars are derived from the easily detected optical photometric variations produced by their long - lived large spots . in most cases ,
the mean magnitude reflects a stellar activity cycle similar to the 11-year solar one . on the other hand
, the peak - to - peak magnitude shows a shorter cycle , called flip - flop cycle , which reflects the non axisymmetrical redistribution of the spotted area on the stellar surface .
the iue database provides a large number of uv high and low resolution spectra of these type of stars . furthermore , the iue satellite monitored these stars continuously during several seasons . in the present work
, we have measured the mg ii line - core fluxes on the iue low and high resolution spectra of three rs cvn - type stars ( ii peg , ux ari and v711 tau ) and then converted the fluxes to the mount wilson index @xmath1 . for each star
, we analyzed the mean annual index @xmath2 with the lomb - scargle periodogram @xcite to search for a long - term chromospheric cycle .
following daz et al . , we obtained the rotational modulation of the @xmath1-index for several seasons by fitting the light - curves with a harmonic function .
we analyzed the amplitude of each curve with the lomb - scargle periodogram to search for a chromospheric flip - flop cycle .
ii peg ( hd 224085 ) is a single - lined rs cvn - binary system composed by a k2iv star and an unseen companion of an estimated spectral class m0-m3v . in fig .
[ fig.hd224085 ] we plot the mount wilson index @xmath1 derived from the iue high and low resolution spectra obtained between 1979 and 1995 .
derived from the iue high resolution spectra ( @xmath3 ) , and from the iue low resolution spectra ( @xmath4 ) .
arrows indicate the seasons for which we analyzed the modulation .
, scaledwidth=65.0% ] to search for cyclic patterns in the chromospheric data , we first studied the mean annual index @xmath5 of the data plotted in fig .
[ fig.hd224085 ] as a function of time with the lomb - scargle periodogram .
we obtained a peak at 7741 days ( @xmath021 years ) with a false alarm probability ( fap ) of 35% .
secondly , we analyzed the rotational modulation of the index @xmath1 during the seasons indicated with arrows in fig .
[ fig.hd224085 ] . to do so
, we phased each season s light - curve @xmath1 vs. time with the 6.724-day rotation period ( see fig .
[ fig.hd224085_curvas ] ) and we fitted each set of data with the harmonic function : @xmath6 .
we analyzed the amplitude @xmath7 against time with the lomb - scargle periodogram and we obtained a cyclic pattern of 3310 @xmath8 253 days ( 9.07 @xmath8 0.69 years ) with a fap of 31% .
this periodic behaviour seems to be well correlated with the flip - flop cycle with a period of 9.30 years obtained by berdyugina and tuominen for the spot activity .
ux ari ( hd 21242 ) is a rs cvn - type system composed by a k0iv star and a g5v companion in a 6.483-day orbit . in fig .
[ fig.hd21242 ] we plot the index @xmath1 obtained for this star between 1978 and 1996 .
, scaledwidth=65.0% ] we analyzed the mean annual @xmath2 of the indexes plotted in fig .
[ fig.hd21242 ] as a function of time with the lomb - scargle periodogram .
we obtained a period of 2180 @xmath8 32 days ( @xmath06 years ) with a fap of 29% .
v711 tau ( hr 1099 , hd 22468 ) is one of the most active rs cvn non - eclipsing spectroscopic binary system , consisting of a k1 subgiant primary and a g5 dwarf secondary in a 2.837 day - orbit @xcite . in fig .
[ fig.hd22468 ] we plot the index @xmath1 for this star between 1978 and 1995 .
we analyzed the mean annual @xmath2 as a function of time with the lomb - scargle periodogram and we obtained a peak at 6589@xmath81170 days with a fap of 11% .
this period of @xmath9 years is in agreement with the ones reported in the literature . on the other hand
, we analyzed the amplitude of the rotational modulation of the datasets indicated with arrows in fig .
[ fig.hd22468 ] and we obtained a cyclic pattern in the amplitude @xmath10 of the curves plotted in fig .
[ fig.hd22468_curvas ] of period 1207@xmath8 45 days ( @xmath0 3.3 years ) of 23% fap , which is consistent with the one obtained by lanza et al . for the spot activity . | we study the mount wilson indices we obtained indirectly from iue high and low resolution spectra of the rs cvn - type systems ii peg ( k2iv ) , ux ari ( k0iv+g5v ) and v711 tau ( k1iv+g5v ) , extensively observed by iue from 1978 to 1996 .
we analyze the activity signatures , which correspond to the primary star , with the lomb - scargle periodogram . from the analysis of v711 tau data
, we found a possible chromospheric cycle with a period of 18 years and a shorter @xmath03 year cycle , which could be associated to a chromospheric flip - flop cycle .
the data of ii peg also suggest a chromospheric cycle of @xmath021 years and a flip - flop cycle of @xmath09 years .
finally , we obtained a possible chromospheric cycle of @xmath06 years for ux ari .
address = instituto de astronoma y fsica del espacio , conicet - uba , buenos aires , argentina . |
because stars are well - spaced , even the inner parts of galaxies can appear faint , comparable in surface brightness to the darkest of night skies . not surprisingly , then , when we start exploring the full six - dimensional phase space of velocities and positions that stars occupy in galaxies , the signal per phase space element becomes almost vanishingly small . in the case of the milky way ,
for example , the fascinating stellar streams in the halo @xcite have widths of only @xmath0 , and velocity dispersions of maybe @xmath1 .
if we were to divide the galaxy , with a linear dimension of @xmath2 and velocities spanning @xmath3 , into resolution elements this small , we would end up with @xmath4 of them , many more than there are stars in the milky way , so the average occupation number per element would be very small indeed .
thus , if we are to study the detailed kinematics of galaxies , we need to do two things .
first , we must be able to detect stellar populations at extremely low phase densities , which essentially means detecting individual stars .
second , we need to come up with ways to combine the information from these individual detections in order to bring together enough signal to say anything about the properties of the galaxy , and hence reconstruct its detailed dynamical structure in order to learn about its evolution .
planetary nebulae ( pne ) offer an ideal tracer of such faint stellar populations , as they are readily individually detectable from their emission lines , even in quite distant galaxies , and the doppler shifts in these lines can be used to measure their line - of - sight velocities .
to make such measurements efficiently in a single step , we have designed and built a customized instrument , the planetary nebula spectrograph or pn.s @xcite . in this paper , we present examples from a couple of the projects that we have been undertaking with this instrument , to illustrates the principles of investigating galaxies in the ultimate low - density regime of phase space .
when one traces edge - on stellar disks away from the plane out to very low surface brightnesses , an excess of light above the extrapolation of the normal disk population is frequently found @xcite .
the nature of such `` thick disks '' remains highly controversial : they could just be the extreme tail of the normal disk population , or they could represent some more dramatic event , such as the debris from a merger .
one exciting new clue to help distinguish between these possibilities was uncovered when it was found that the thick disk in the edge - on system fgc 227 appears to be rotating in the opposite direction to the normal thin - disk population , indicating that it would have to be a distinct component such as might be formed in a merger @xcite .
however , the surface brightness of this component is so faint that , even with ten hours of integration on an 8-metre telescope , conventional spectroscopy had such large error bars that the data were also consistent with co - rotating thin and thick disks .
[ fig : ngc891 ] as figure [ fig : ngc891 ] illustrates , we can do a great deal better with a rather shorter integration on a 4-metre telescope using pn.s .
the upper panel shows the number counts of pne detected in the edge - on spiral ngc 891 as a function of distance from its plane .
the lines show a possible decomposition of the disk into thin and thick exponential components @xcite .
the data drop below the model close to the plane , as pne are difficult to detect against the high surface brightness of the galaxy in this region , and some pne will also be lost in ngc 891 s strong dust lane . however , in the region we are interested in away from the plane , the pn number counts trace the light distribution very well , underlining their nature as generic tracers of the stellar population .
further , we are clearly detecting them in significant numbers out to beyond the transition where the thick disk becomes the dominant component .
the lower panel in this figure shows the observed mean rotation speed for these pne as a function of distance from the plane .
there is plenty of signal to distinguish between co- and counter - rotating thin and thick disk components , and in this system the two are clearly rotating in the same direction . indeed , we can go further and fit a simple single - component kinematic model to the data .
this heuristic model is of the form @xmath5 where @xmath6 provides the factor that allows for the line - of - sight projection effects that reduce the line - of - sight velocity below the mean rotational velocity @xcite , while @xmath7 parameterizes all the terms related to the shape of the velocity ellipsoid in the asymmetric drift equation @xcite ; here it is assumed to be a constant .
the circular speed of the galaxy , @xmath8 , can be inferred from gas kinematics , while the vertical velocity dispersion , @xmath9 , is estimated by solving the jeans equation for a self - gravitating sheet whose density distribution is given by the double exponential model in the upper panel of figure [ fig : ngc891 ] .
clearly , the data are essentially consistent with this simple single - component model : there is no kinematic evidence that the thick disk in ngc 891 is in any way a distinct entity .
as a further illustration of the way in which faint kinematic components can be detected , figure [ fig : m31 ] shows the results of an analysis of the 2615 pne that were found using pn.s in a survey of m31 @xcite . in an inclined disk system like this , the phase space is essentially reduced to four dimensions , two spatial and two velocity .
we can measure three of these components , two spatial and the line - of - sight velocity , so each pn has only one unknown coordinate .
thus , while one can not measure the energy and angular momentum of any single pn , there is only a one - dimensional family of possibilities , as illustrated by the line sections in the figure .
if group of pne share a common orbit ( and hence energy and angular momentum ) , then their lines will all intersect at a single point , creating a local excess in this plane .
such an excess of crossing lines is , indeed , found in this figure , at the point indicated by the box .
the location of the orbit to which it corresponds does not appear in any way special in an optical image of m31 , but , as the inset image in the figure shows , mid - infrared data reveal a bright ring of emission at this radius , indicating that it lies at one of the major orbital resonances .
thus , either we have detected the population of stars born in this ring of star formation , or , more likely since pne come from old stars , we are picking out the relatively small population of objects that have become dynamically trapped at this resonance .
whatever their origin , these data again illustrate the power of pn.s to identify kinematic components that are at far too low a density in phase space to be detectable by more conventional means .
k. gordon , et al . , `` the multiwavelength view of m31 including new spitzer / mips infrared images '' in _ bulletin of the american astronomical society _ , 2004 , vol .
36 of _ bulletin of the american astronomical society _ , 1579 . | galaxies are faint enough when one observes just their light distributions , but in studying their full dynamical structure the stars are spread over the six dimensions of phase space rather than just the three spatial dimensions , making their densities very low indeed .
this low signal is unfortunate , as stellar dynamics hold important clues to these systems life histories , and the issue is compounded by the fact that the most interesting information comes from the faintest outer parts of galaxies , where dynamical timescales ( and hence memories of past history ) are longest . to extract this information ,
we have constructed a special - purpose instrument , the planetary nebula spectrograph , which observes planetary nebulae as kinematic tracers of the stellar population , and allows one to study the stellar dynamics of galaxies down to extremely low surface brightnesses .
here , we present results from this instrument that illustrate how it can uncover the nature of low surface - brightness features such as thick disks by studying their kinematics , and trace faint kinematic populations that are photometrically undetectable .
address = school of physics & astronomy , university of nottingham , uk , email=michael.merrifield@nottingham.ac.uk address = http://www.astro.rug.nl/~pns/ |
we thank d. saumon for helpful discussions , and making available unpublished calculations , and d.j .
stevenson for constructive referee comments . this work was supported by the european community through a training and mobility of researchers grant to t.g .
\1989 . abundances of the elements : meteoritic and solar . _ geochim .
cosmochim . acta _ * 53 * , 197 - 214 . 1995 . solar models with helium and heavy elements diffusion .
modern physics _ * 67 * , 781808 . 1992 .
the molecular - metallic transition of hydrogen and the structure of jupiter and saturn . _ _ * 391 * , 817826 .
the abundance and distribution of water vapor in the jovian troposphere as inferred from voyager iris observations .
_ _ * 388 * , 648 - 688 . 1984 . the helium abundance of saturn from voyager measurements . _ _ * 282 * , 807 - 815
the c / h ratio in jupiter from the voyager infrared investigation . _ _ * 257 * , 901912 .
are the giant planets fully convective ? _ icarus _ , * 112 * , 337353 .
non - adiabatic models of jupiter and saturn . _ icarus _ , * 112 * , 354367 .
condensation of methane , ammonia and water and the inhibition of convection in giant planets .
_ science _ * 269 * , 16971699 . 1982 .
effects of differential rotation on the gravitational figures of jupiter and saturn .
_ icarus _ * 52 * , 509515 . 1989 .
structure and composition of giant planets interiors . in _ origin and evolution of planetary and satellite atmospheres _ ,
s. k. atreya , j. b. pollack , and m. s. matthews , eds . , university of arizona press , tucson , pp .
539563 . 1989 .
optimized jupiter , saturn and uranus interior models .
_ icarus _ * 78 * , 102118 .
1989 . a new analysis of the jovian 5-@xmath36 m voyager iris spectra .
_ icarus _ * 77 * , 457468 .
molecular dissociation in hot , dense hydrogen .
_ * 76 * , 12401243 .
formation of the giant planets .
phys . _ * 64 * , 544557 .
seismological observations with a fourier transform spectrometer : detection of jovian oscillations . _ _ * 267 * , 604622 .
metallization and electrical - conductivity of hydrogen in jupiter .
_ science _ * 273 * , 936938 .
comets , impacts and atmospheres .
_ icarus _ * 116 * , 215226 .
planetesimal dissolution in the envelopes of the forming giant planets .
_ icarus _ * 67 * , 409443 .
prediction of neon depletion in jupiter s atmosphere _
eos _ * 76 * , 343 .
an equation of state for low - mass stars and giant planets .
_ astrophys .
ser . _ * 99 * , 713741 .
structure of jupiter : galileo probe measurements . _ science _ * 272 * , 844845 .
interiors of the giant planets .
earth planet .
sci _ * 10 * , 257295 .
cosmochemistry and structure of the giant planets and their satellites .
_ icarus _ * 62 * , 415 . 1990 .
aneos analytic equations of state for shock physics codes , sandia natl . lab .
sand89 - 2951 .
metallization of fluid molecular - hydrogen at 140 gpa ( 1.4 mbar ) .
lett . _ * 76 * , 1860 - 1863 . 1938 . on the state of matter in the interior of planets .
_ astrophys .
j _ * 87 * , 508516 .
1996 . the helium mass fraction in jupiter s atmosphere .
_ science _ * 272 * , 849851 .
interior structure of the earth and planets ( translated by w.b .
hubbard & r.a .
masteler ) .
harwood academic pub .
modern models of giant planets . in _ high pressure research : application to earth and planetary sciences _ ( y. syono and m.h .
manghgnani , eds . ) , pp . 393401 .
* figure 1 * : + density profiles in models of jupiter with a fixed composition ( y=0.30 ) , using an adiabatic temperature profile and the @xmath8-eos ( plain line ) , adiabatic and ppt - eos ( plain line with discontinuity ) , non - adiabatic @xmath8-eos ( dashed line ) , and non - adiabatic ppt - eos ( dotted line ) . the thin plain and dashed lines correspond to adiabatic and non - adiabatic 2.5 mbar ppt - eos , respectively ( see text ) .
the temperatures of the models range between 2050 and 2450k at a pressure of 10kbar , 53006300k at 1 mbar , 1000013000k at 10 mbar and 1400021000k at 30 mbar .
upper curves are @xmath37k density profiles for water ice and olivine ( from thompson 1990 ) .
the dashed region represents the assumed uncertainty on the eos for heavy elements ( @xmath38 ) . within this region
, the continuous line corresponds to our `` preferred '' profile for @xmath25 .
_ inset _ : differences of the decimal logarithm of the jupiter density profiles with the same profile using the @xmath8-eos and an adiabatic structure .
the presence of a radiative region leads to a colder and denser model in the kbar region and deeper .
the presence of a ppt yields a denser metallic region . :
+ constraints on jupiter s @xmath39 ( mass of the central core ) , @xmath40 ( total mass of heavy elements ) , @xmath41 ( mass fraction of heavy elements in the molecular envelope ) , and @xmath24 ( mass fraction of heavy elements in the metallic envelope ) from interior models .
each colored surface represents models calculated with a given hydrogen - helium eos : ppt - eos ( red ) , ppt - eos with ppt at 2.5 mbar ( green ) , @xmath8-eos ( blue ) ( see text ) .
the central regions with a slightly lighter hue have been calculated with the `` preferred '' heavy elements eos ( see figure 1 ) , and can be used to estimate the uncertainty related to the eos of heavy elements ( @xmath25 ) .
plain and hatched surfaces correspond to adiabatic and non - adiabatic temperature profiles , respectively .
arrows indicate the magnitude and direction of uncertainties on @xmath42 ( mass fraction of ices in the core , from 0.5 to 1.0 ) , @xmath28 ( mass fraction of helium in the protosolar nebulae , from 0.275 to 0.28 ) and @xmath43 .
the latter corresponds to an increase by 1@xmath7 of @xmath44 , and to the assumption that jupiter rotates on cylinders and not as a solid planet .
the second effect is responsible for about half of the uncertainty , but only in one direction . for clarity ,
arrows are only shown for the ppt - non adiabatic models .
the mass mixing ratios of c , n , o and all other elements ( except h and he ) in abundances such that c / h=3@xmath45(c / h)@xmath46 , n / h=3@xmath45(n / h)@xmath46 , o / h=3@xmath45(o / h)@xmath46 , _ ... etc _ ( the solar abundances are from anders & grevesse 1989 ) are shown in the bottom right corner of the figure . the value of @xmath17 for any other composition can be inferred from this `` ruler '' . the molecular envelope represents about 15% ( 20% in the case of the 2.5 mbar ppt eos ) of the total mass of the planet ( @xmath47 ) .
we used @xmath35=0.0192 . | * using the helium abundance measured by galileo in the atmosphere of jupiter and interior models reproducing the observed external gravitational field , we derive new constraints on the composition and structure of the planet . we conclude that , except for helium which must be more abundant in the metallic interior than in the molecular envelope , jupiter could be homogeneous ( no core ) or could have a central dense core up to 12@xmath0 .
the mass fraction of heavy elements is less than 7.5 times the solar value in the metallic envelope and between 1 and 7.2 times solar in the molecular envelope . the total amount of elements other than hydrogen and helium in the planet is between 11 and 45@xmath0 .
* : _ icarus _ number of manuscript pages : 15 + number of tables : 0 + number of figures : 2 + keywords : jupiter , + interiors , planets + chemical abundances running head : composition of the interior of jupiter as shown by wildt ( 1938 ) , jupiter is mainly composed with hydrogen and helium .
however , the question of the abundance and partitioning of the other species ( `` heavy elements '' ) throughout the planet is still unsolved .
answering this question would yield much better constraints on models of formation of the giant planets .
it would also give insight into the behavior of chemical species at high pressures and generally into physical processes in the planet s interior .
a precise determination of the seismic properties of the planet would certainly be the best way to determine accurately its internal composition .
global oscillations of jupiter seem to have been detected ( mosser et al .
1993 ) , but the accuracy of the measurements have yet to be improved and the vibration modes more clearly identified . to date , constraints on the interior structure of the planet can be provided solely by interior models matching the observed gravitational field ( i.e. the radius , mass and gravitational moments @xmath1 , @xmath2 and @xmath3 ) and surface conditions ( temperature , luminosity , atmospheric helium abundance ) .
studies of the interior of giant planets ( hubbard & marley 1989 ; zharkov & gudkova 1992 ; chabrier et al .
1992 ; guillot et al .
1994b ) have generally been focused on calculating one possible interior model rather than calculating the ensemble of all possible models .
it is therefore difficult , from these models , to give constraints on the amount or distribution of elements in the interior of the planet .
furthermore , the new determination of the abundance of helium in the upper troposphere by the galileo probe ( niemann et al .
1996 ) requires a revision of these quantities .
previous calculations using the voyager data indicated that : @xmath4 ( gautier et al .
1982 ; conrath et al .
1984 ) , where x and y are the mass fractions of hydrogen and helium , respectively .
the mass fraction _ directly _ measured by the probe is now : @xmath5 ( von zahn & hunten 1996 ) .
these values have to be compared to the protosolar value estimated to @xmath6 ( bahcall and pinsonneault , 1995 ) . since no significant escape of the original
hydrogen and helium could occur over the lifetime of the planet , the interior of the planet must then be richer in helium than the upper regions in order to insure that the global hydrogen / helium ratio is equal to the protosolar one
. this conclusion holds for both the voyager and galileo measurements . however , the higher atmospheric helium mass fraction measured by galileo results in a smaller abundance of heavy elements in this region than previously estimated .
we have calculated new optimized jupiter models using the method described by guillot et al .
( 1994b ) .
we refer the reader to that article for details on the calculations and references for the data used .
we have used the galileo helium / hydrogen ratio , and have included the following uncertainties : 1 . on the equations of state ( eos ) , for hydrogen , helium and heavy elements 2 .
on the temperature profile ( convective / radiative ) 3 . on the internal rotation ( solid / differential ) 4 . on the distribution of helium in the interior
.
these uncertainties are discussed in detail below .
in addition , we have included the observational 1-@xmath7 uncertainties on the gravitational moments , atmospheric helium abundance and protosolar helium abundance .
the equation of state of hydrogen and helium is certainly the most important source of uncertainty in the calculations .
a large part of the jovian interior encompasses a pressure / temperature region where interactions between particles are important , and molecules , atoms , ions and electrons coexist .
in such a region , the behavior of even the simplest molecule , hydrogen , is poorly understood .
it undergoes a phase _ transition _ from a molecular to a metallic phase at pressures of the order of one to a few megabar , but it is not known whether this transition is of first order ( i.e. includes a discontinuity of the specific entropy ) or not .
the characterization of the two phases is also not obvious : experimental and theoretical evidence suggest that , at pressures of two megabars or less , a fraction of the electrons become itinerant while molecules still exist , before hydrogen eventually reaches a monoatomic truly metallic state at higher pressures ( of the order of a few megabars ) .
uncertainties in the equation of state are thus both quantitative and qualitative . in this work ,
we choose to estimate these uncertainties by using two hydrogen - helium eoss calculated by saumon , chabrier & van horn ( 1995 ) .
the first one ( @xmath8-eos ) assumes that the transition is continuous and is calculated by smoothly interpolating between the low - pressure molecular fluid and the high - pressure ionized plasma .
their second eos ( ppt - eos ) is consistently calculated and predicts the presence of a first order plasma phase transition between molecular and metallic hydrogen , the so - called ppt .
this transition occurs around 1.7 mbar for a typical jovian interior profile . in the molecular region
, the densities calculated with these eoss along isentropes characteristic of the jovian interior agree with those experimentally determined by weir et al .
( 1996 ) to better than 2% ( saumon & xie , in preparation ) , even though the adiabatic temperature gradients ( and hence temperatures ) differ .
however , the electrical conductivities measured indicate a continuous transition around 1.4 mbar ( nellis et al . 1996 ) , and no ppt , at least for pressures lower than 1.8 mbar . on the other hand , monte - carlo simulations by magro et al .
( 1996 ) indicate that a ppt occurs at slightly larger pressures .
we have therefore considered a third case , using the ppt - eos , but displacing the ppt to @xmath9 mbar .
although the resulting eos is thermodynamically inconsistent in the 1.72.5 mbar region , this approach yields a well - behaved density profile ( see figure 1 ) and therefore provides another useful estimation of the uncertainty of the hydrogen - helium eos .
finally , we choose to ignore the complexity of the molecular / metallic hydrogen transition itself , but this is mostly a semantic issue , assuming that the corresponding uncertainty on the density profile is properly represented by the different eoss . * insert figure 1 here * the partitioning of elements in jupiter s atmosphere , and in particular of helium , represents the second main uncertainty .
there are two mechanisms affecting equilibrium partitioning of elements in jupiter s hydrogen .
stevenson ( 1982 ) showed that in the metallic - hydrogen phase , pressure - ionized elements with @xmath10 have limited solubility . however , only helium is abundant enough to be directly affected by such limited solubility ( noble gases such as ne might be indirectly affected by he - immiscibility roulston & stevenson , 1995 ) . the standard explanation of jupiter s ( slightly ) reduced atmospheric helium abundance relies on such a phase separation via immiscibility in the metallic phase at pressures just above the molecular - metallic transition .
on the other hand , if a true ppt is present as a first - order phase transition , then the gibbs phase rule requires that the concentrations of _ all _ elements in hydrogen be discontinuous across this boundary . such partitioning between the metallic and molecular phases of hydrogen
would be in _ addition _ to any possible phase separation of helium due to limited miscibility in the metallic phase , and would in principle affect all elements rather than helium alone .
however , helium and most heavy elements are expected to be partitioned preferentially into the molecular phase .
the galileo probe results for elemental concentrations do not particularly argue for the predominance of one partitioning mechanism over the other , but they do confirm that helium is not enriched in the molecular region .
we emphasize that a composition change due to the ppt or that caused by limited helium miscibility are expected to occur in the same pressure region and therefore can not be distinguished by our models .
were it not the case ( for example if a helium - rich core was formed at pressures much larger than a few megabars ) , a slightly wider range of ice / rock core masses ( see below ) would be found .
although it bears little consequences for the structure of the interior models themselves , our poor knowledge of the equation of state of heavy elements in jupiter directly affects the abundance of heavy elements that is inferred from these models in order to conserve the protosolar helium / hydrogen ratio . as described by chabrier et al .
( 1992 ) and guillot et al .
( 1994b ) , the mass fraction of heavy elements is obtained after optimization of a model using : @xmath11 where @xmath12 and @xmath13 are the equivalent and real mass fraction of helium , respectively , and @xmath14 , @xmath15 and @xmath16 are the density of pure hydrogen , pure helium , and heavy elements respectively , along a pressure - temperature profile .
note that @xmath17 is uniform ( independent of @xmath18 and @xmath19 ) only in the limit @xmath20 , or if the ratios @xmath21 and @xmath22 are independent of @xmath18 and @xmath19 .
these variations of @xmath17 having no physical meaning , we used a mass average over the molecular and metallic regions , @xmath23 and @xmath24 , respectively . in order to estimate the uncertainty on @xmath25 , we calculated a low , a high and an intermediate @xmath16 profile . in the case of the low one , we assumed a small mean molecular weight at low pressures , and interpolated to high pressures where we used a zero temperature eos for pure h@xmath26o ice adding thermal effects using zharkov ( 1986 ) .
the high @xmath16 was calculated using a larger mean molecular weight at low pressures , including refractory elements ( rocks ) above 10kbar , assuming a 10 times solar rocks / ices mass mixing ratio and interpolating with zero temperature eoss for olivine ( mg@xmath26sio@xmath27 ) and h@xmath26o at high pressures .
an intermediate profile was calculated in the same way , but assuming solar ices / rocks ratio . at the molecular / metallic transition
, @xmath25 was allowed to jump from the low to the high profile , and vice - versa .
the corresponding profiles are shown in figure 1 as a hatched region , which represents the uncertainty on @xmath25 , both due to the unknown composition and to the poorly known eoss of these elements .
the possibility that the interior temperature gradient strongly departs from adiabaticity yields another important source of uncertainty in the model .
the temperature profile retrieved by the galileo probe is close to an adiabat at least down to the 20 bar level ( seiff et al .
1996 ) but condensation could yield brief subadiabatic or superadiabatic events ( guillot 1995 ) .
the possibility that a radiative region exists in the kbar region ( guillot et al .
1994b ) represents the largest source of uncertainty by far .
this was estimated by calculating rosseland opacities as in guillot et al .
( 1994a ) , but using new available opacity data for h@xmath26o and h@xmath26s ( see marley et al .
1996 ) .
in other regions ( except at the ppt ) we assumed the temperature structure to be adiabatic , as any departure from adiabaticity in the interior ( e.g. due to a compositional gradient ) would be indistinguishable from uncertainties in the eos itself .
a comparison of the density profiles calculated from the different equations of state and temperature profiles is given in figure 1 .
the presence of a radiative region induces an uncertainty of the order of 5% on the density in the 10-kbar region of the planet .
the uncertainty in the h - he eos is small at both low pressures and at very high pressures , but reaches as much as 10% in the intermediate pressure range of around one to five or so megabars , a pressure range that involves around a third of the planetary mass .
the @xmath8-eos is , on average , significantly less dense than the ppt - eos , and therefore requires a larger amount of heavy elements in order to reproduce the observed mean density of the planet .
the presence of a radiative region has the opposite effect , as it leads to a cooler planet . as in guillot
et al .
( 1994b ) , we assumed that a dense central core was present and included possible variations in composition ( pure ices / pure rocks ) .
its mass was allowed to vary in order to fit the observational constraints .
the presence of such a core is important for constraining formation theories ( e.g. mizuno 1980 ) .
although it is often thought that its mass is constant after the hydrogen - helium envelope has been captured , it is quite possible that convection redistributes it towards external regions , therefore yielding a smaller core , if any ( see stevenson 1985 ) .
we emphasize that the presence of a well defined core is _ assumed _ , and is not a consequence of the observed gravitational field of the planet .
very similar results would be obtained by distributing the core over the inner half of the planet .
there is therefore little difference between heavy elements in the core and in the metallic region .
finally , a small uncertainty arises from the unknown rotational state of jupiter s interior . as shown by hubbard ( 1982 ) , assuming that the planet is differentially rotating on cylinders ( with angular velocities constrained by observations ) yields slightly different gravitational moments @xmath1 , @xmath2 and @xmath3 than those inferred from a solid rotation model .
this uncertainty was also included in the present work .
the observed gravitational moments provide no constraints on density changes which encompass small masses , in particular on the structure of regions of pressures lower than kbars .
similarly , no real constraints exist on the structure of the core or its composition ( hubbard 1989 ; guillot et al
. 1994b ) . moreover , we find that the resulting models are very _ insensitive _ to the location of the helium abundance discontinuity , as long as it is between about 0.5 and 5 mbar . on the contrary ,
the models are fairly sensitive to changes in the location of the ppt because it induces significant changes of the density profile ( see figure 1 ) .
the resulting constraints on the abundance and distribution of heavy elements in jupiter are given in figure 2 .
the colored surfaces represent possible solutions for given hydrogen - helium eoss and temperature profile . within each patch all other uncertainties were included , as discussed previously .
the most significant are : ( i ) the eos for heavy elements ; ( ii ) the value of @xmath2 ; ( iii ) the value of @xmath28 ; and ( iv ) the unknown composition of the core .
the observational error on the atmospheric helium abundance measured by the galileo probe is small , but it is interesting to note that calculations using the voyager value would have yielded values of @xmath23 larger by 2 or 3 solar values .
the difference between adiabatic and non - adiabatic models is smaller than in guillot et al .
( 1994b ) because improved h@xmath26o opacities have increased the rosseland opacities by a factor @xmath29 ( see the discussion of the problem of hot bands in guillot et al .
1994a ) . * insert figure 2 here * a first important result is that the mass of the core can be equal to zero . in that case , we find it even possible for jupiter to be homogeneous ( @xmath30 ) , if we except small - scale phenomena and variations of the abundance of helium .
this requires that the density of the metallic phase is not too large compared to that of the molecular phase ( @xmath8-eos ) , and an important enrichment in heavy elements ( 4 to 7 times the solar value ) . in the case of the more realistic ppt - eos
, we find that the presence of a central core is necessary .
for all cases , the core is relatively small : less than 12@xmath0 ( and less than 8.5@xmath0 in the case of a pure rock core ) .
again , we stress that the elements that form the core could be distributed over the inner half of the planet , and that the distinction between heavy elements in the core and heavy elements in the metallic region is not obvious . other constraints on the amount of heavy elements present in the planet
suffer mainly from our relatively poor knowledge of the equation of state of hydrogen ( and helium ) at pressures of around one to a few megabars .
figure 2 shows that the total mass of heavy elements ( core + metallic + molecular envelope ) lies between 11 and 45@xmath0 .
the upper limit corresponds to an enrichment of a factor 7.4 compared to the solar value , which is quite large .
we estimate that it is probable that the density in the metallic region lies closer to that predicted by the ppt - eos than by the @xmath8-eos , as in fact favored by saumon , chabrier and van horn ( 1995 ) .
it is thus more likely that @xmath31 .
similarly , we obtain that in the metallic region , @xmath32 , or , when we disregard the @xmath8-eos , @xmath33 .
the constraint found on the mass fraction of heavy elements in the molecular envelope , @xmath34 , can be compared to the measurements of galileo s mass spectrometer ( niemann et al . , 1996 ) .
those confirmed that jupiter s atmosphere is enriched in ch@xmath27 by a factor 2.9 compared to the solar value of anders and grevesse ( 1989 ) , and in h@xmath26s by about the same factor .
the n / h ratio has not yet been evaluated from galileo , but voyager infrared data suggest an enhancement of 2.2 to 2.4 ( lellouch et al . , 1989 ; carlson et al . , 1992 ) .
the case of h@xmath26o is not clear because it condenses relatively deep in the atmosphere , but it is probably at least in solar abundance .
fig .
2 shows that an enrichment in all heavy elements by a factor 2 or 3 in the molecular region is certainly consistent with all possible interior models .
reciprocally , it is possible to show from our models that , even though o is responsible for almost 50% of the value of @xmath35 , large values of the o / h ratio can be consistent with the observed gravitational moments .
for example , assuming that all other elements are enriched by a factor 3 in the molecular region , we infer that the enrichment in h@xmath26o can be as high as 12 times the solar value .
however , this requires a relatively hard ( low density ) h - he eos in the molecular region . using the ppt - eos only
, we find that it is more likely that h@xmath26o is less abundant than 8 times solar in the molecular envelope . in any case
, these results do not permit to choose between very different assumptions concerning the enrichment of jupiter s outer envelope by meteorites and comets ( e.g. pollack et al .
1986 ; owen & bar - nun 1995 ) .
it is difficult to infer a lower limit to the abundance of water in the molecular envelope of the planet , but it appears that it would be difficult to reconcile an abundance less than solar with the values of @xmath23 found , as this would require significant enrichments in all other elements .
most of the uncertainties in the results shown in figure 2 are due to the relatively poor knowledge of the equation of state of hydrogen in the megabar region .
recent improvements in shock - wave experiments ( nellis et al . 1996 ) let us hope that a more accurate representation of the molecular / metallic transition of hydrogen will be achieved in the near future .
these improvements could easily yield abundances of heavy elements in jupiter more accurate by 50% .
similarly , a more precise value of @xmath2 would lead to better constraints on the structure of the planet .
the optimal precision that should be attained on @xmath2 is about 3 times the actual one , as one is limited by the uncertain internal rotation rate of the planet ( see hubbard 1989 for a discussion ) . in order to be a useful constraint ,
@xmath3 should be measured with a 10 times higher accuracy .
even so , the problem of differential rotation is even more acute than for @xmath2 , and a detailed study of the internal rotation of the planet should be done in order for such a measurement to be useful .
finally , more accurate high pressure opacities and generally a better understanding of transport processes in the planet are also required in order to determine precisely the abundance and partitioning of elements in jupiter s interior . |
1 . comparison of power - balance prediction ( solid curve ) and bessel - function prediction ( dashed curve ) with numerical integration result ( diamonds ) , at fundamental frequency ( @xmath42 ) .
parameters : ( a ) @xmath44 ; ( b ) @xmath45 . | the inverse ac josephson effect involves rf - induced ( shapiro ) steps that cross over the zero - current axis ; the phenomenon is of interest in voltage standard applications .
the standard analysis of the step height in current , which yields the well - known bessel - function dependence on an effective ac drive amplitude , is valid only when the drive frequency is large compared with the junction plasma frequency or the drive amplitude is large compared with the zero - voltage josephson current . using a first - order krylov - bogoliubov power - balance approach we derive an expression for the threshold value of the drive amplitude for zero - crossing steps that is not limited to the large frequency or large amplitude region .
comparison with numerical solutions of the rsj differential equation shows excellent agreement for both fundamental and subharmonic steps .
the power - balance value for the threshold converges to the bessel - function value in the high - frequency limit .
the term ` inverse ac josephson effect ' was coined by levinsen _
et al .
_ @xcite to describe shapiro steps @xcite in the current - voltage characteristic of a small josephson junction that cross over the zero - current axis .
the phenomenon was recognized as being potentially important for voltage - standard applications inasmuch as the elimination of the dc bias current would eliminate one possible pathway for the entry of noise into the system .
it was studied extensively experimentally , analytically , and computationally by a number of authors ( see , _
e.g. _ , kautz @xcite plus references therein ) .
the ` standard ' analysis that emerged from these studies expressed the height in current of phase - locked shapiro steps in terms of bessel functions of an effective drive amplitude ; this analysis was shown to be appropriate when the frequency of the ac drive is large compared with the junction plasma frequency or when the amplitude of the ac drive is large compared with the zero - voltage josephson current .
our analysis , instead , is based on the power - balance formalism developed by krylov and bogoliubov @xcite ; it is not limited to the large frequency or the large amplitude regions .
comparison of the predictions of the power - balance approach with results obtained by direct numerical integration of the model differential equation typically show agreement to at least three significant digits . in the high - frequency limit
they approach those predicted by the bessel - function expressions .
the starting point of our analysis is the usual shunted - junction model of the small josephson junction , subjected to a dc - bias current and an ac - driving current ; the corresponding differential equation , in normalized form , is @xmath0 where @xmath1 and @xmath2 are , respectively , the dc- and ac - driving currents . the corresponding unperturbed equation , _
i.e. _ , with @xmath3 , @xmath1 , and @xmath2 set to zero , has two types of solutions , _ viz .
_ , oscillatory and rotary . since we are interested in non - zero - voltage states of the junction we focus on the latter , which have the form @xmath4 where am ( ) is the jacobian elliptic amplitude function of modulus @xmath5 , and @xmath6 is an arbitrary constant . the instantaneous junction voltage in this case is thus given by @xmath7 we now return to the original model given by eq
( 1 ) .
an obvious physical requirement for the junction voltage to be a stationary , periodic function similar to that given by eq .
( 3 ) is that the average power dissipated , _
i.e. _ , the conductance times the mean - square voltage , be equal to the average power furnished by the drive currents , _
i.e. _ , the mean - value of the drive current times the voltage . assuming that eq .
( 2 ) can be used as a first approximation to the solution of eq .
( 1 ) in the presence of dissipation and drive , we can write , using results from , the time - average power dissipated as @xmath8 where @xmath9 and @xmath10 are , respectively , the complete elliptic integrals of first and second kinds . assuming first the presence of only a dc - bias current , _
i.e. _ , setting @xmath11 , we can write the time - average input power as @xmath12 equating eq . ( 4 ) to eq .
( 5 ) gives an expression for the mccumber branch of the current - voltage characteristic of the junction in the following parametric form @xmath13 @xmath14 in the zero - bias configuration , instead , _
i.e. _ , with @xmath15 and @xmath16 , we can write the input power as @xmath17 which , by expressing the jacobian dn ( ) function in terms of its fourier - series expansion , we can write as @xmath18\ ! > \ , , \
] ] where @xmath19 , in which @xmath20 is the complementary modulus .
from eq .
( 9 ) we see that @xmath21 only if @xmath22 for some integer @xmath23 , and , assuming eq . ( 10 ) to be satisfied , that @xmath24 can vary smoothly from zero to @xmath25 depending on the value of the phase - shift term @xmath6 ( we have @xmath26 when @xmath27 ) .
the threshold value , @xmath28 , of the drive amplitude is the minimum value for which it is possible to satisfy the equation @xmath29 ; this yields the value @xmath30 for @xmath31 , the constant @xmath6 adjusts itself according to the relation @xmath32=\frac{\gamma_{thr}}{\gamma } \ , .\ ] ] finally , in the general case in which both @xmath33 and @xmath34 , the dissipation defined by eq .
( 4 ) is balanced by both dc and ac inputs .
this permits , _
e.g. _ , calculating the minimum bias - current value to which a phase - locked step extends : assuming eq .
( 10 ) to be satisfied , we find @xmath35 which , for @xmath36 [ see eq . ( 11 ) ] , is a negative number .
the ` standard ' bessel function expression for the height in current of a phase - locked shapiro step is @xcite @xmath37 where @xmath38 ( ) is the bessel function of order @xmath39 .
thus , from eqs .
( 6 ) and ( 13 ) , the threshold value of the drive amplitude in this approach is @xmath40 at this point it must be mentioned that the integer @xmath39 in eq . (
14 ) is _ not _ the same as the integer @xmath23 in eq .
( 10 ) : in fact , the bessel function index @xmath39 refers to a _ super_harmonic number whereas the power balance index @xmath23 refers to a _ sub_harmonic number . to be perfectly clear on this point , the corresponding shapiro steps in the current - voltage characteristic of the junction occur at normalized voltages @xmath41 thus , the only place where the two expressions , eq . ( 11 ) and eq . ( 15 ) , can be compared directly is at the fundamental frequency , where @xmath42 .
our results are summarized in fig .
1a , b . in these figures ,
the solid curve is the power - balance threshold , calculated from eq . ( 11 ) , the dashed curve is the bessel - function threshold , calculated from eq . (
15 ) , and the diamonds are values obtained from the direct numerical integration of eq .
( 1 ) . except for the highest point in fig . 1b , where the numerical result begins to diverge slightly from the power - balance prediction
, these two typically agree to at least three significant digits .
a similar agreement between power - balance prediction and numerical experiment is obtained at the second subharmonic ( @xmath43 ) . for higher frequencies
than those shown in fig .
1a , the two predicted threshold values , eq .
( 11 ) and eq .
( 15 ) , converge to a common asymptotic limit . in order to calculate numerically the points indicated by diamonds in fig . 1
, we often found it necessary to ` tune ' fairly precisely the initial conditions used for eq .
( 1 ) .
this fact suggests that , at least in some cases , the basin of attraction of the phase - locked state is rather small , perhaps indeed vanishing , a fact that would have important implications for the stability of the locked state , _
e.g. _ , against thermal fluctuations .
the technique of cell mapping @xcite might be a useful tool for exploring this question .
braiman _ et al .
_ @xcite have extended the bessel function approach to subharmonic frequencies .
in fact , their eq .
( 2 ) has just the form of the fourier - series expansion of the jacobian am ( ) function of our eq .
( 2 ) .
this approach gives expressions for the step height in current corresponding to eq .
( 14 ) for superharmonic steps in terms of sums of products of bessel functions .
the approach , however , clearly becomes rather unwieldy if more than the first few terms in the fourier expansion are employed .
the power - balance approach can also be extended beyond the lowest level of approximation that we have employed here @xcite ; this would presumably permit a description of superharmonic steps , which presently is lacking from our analysis . however , superharmonic steps occur at progressively higher voltages , which implies progressively higher frequencies , where the simple bessel - function expression , eq .
( 15 ) , is known to give a reasonable description of the situation .
thus , the reward to be obtained here might not be worth the effort .
finally , we must offer one _ caveat _ : as is apparent from fig .
1a , the power - balance prediction becomes progressively better than the bessel - function prediction as the ac drive frequency is reduced below unity ( which is the plasma frequency , with our normalization ) .
this , however , is a region where , in addition to simple periodic solutions of eq .
( 1 ) , exemplified by the ansatz of eq . ( 2 ) , there are known to exist also complicated quasi - periodic and chaotic trajectories @xcite . consequently , whereas eq .
( 11 ) does give a good estimate of the threshold value of the drive amplitude _ if _ a simple step exists , it does _ not _ guarantee the existence of such a step .
we wish to thank roberto monaco for a critical reading of the manuscript and niels grnbech - jensen for illuminating discussions and technical assistance .
b.a.m .
thanks the physics department of the university of salerno for hospitality during the visit that originated this work . financial support from the ec under contract no .
sc1-ct91 - 0760 ( tsts ) of the `` science '' program and from the human capital and mobility " program , from murst ( italy ) , and from the progetto fianalizzato `` tecnologie superconduttive e criogeniche '' del cnr ( italy ) is gratefully acknowledged .
99 m. t. levinsen , r. y. chiao , m. j. feldman , and b. a. tucker , appl .
. lett .
* 31 * ( 1977 ) 776 .
s. shapiro , phys .
rev .
lett .
* 11 * ( 1963 ) 80 .
r. l. kautz , j. appl .
phys . * 52 * ( 1981 ) 3528 .
see , _
e.g. _ , a. scott , active and nonlinear propagation in electronics ( wiley - interscience , new york , 1970 ) , chap .
iii .
p. f. byrd and m. d. friedman , handbook of elliptic integrals for engineers and scientists , second edition ( springer - verlag , berlin , 1971 ) .
y. braiman , e. ben - jacob , and y. imry , in : squid 80 , h. d. halhbohm and h. lbbig , eds .
( de gruyter , berlin , 1980 ) , pp .
783795 .
m. p. soerensen , a. davidson , n. f. pedersen , and s. pagano , phys .
rev .
a * 38 * ( 1988 ) 5384 .
see , _
e.g. _ , n. minorsky , nonlinear oscillations ( van nostrand , new york , 1962 ) , chap . 15 .
r. l. kautz and r. monaco , j. appl .
phys .
* 57 * ( 1985 ) 875 . |
in the attempt to extract values of physical parameters from stellar spectra one first tries to determine the value of radial velocity .
if the spectra have a wide wavelength coverage , like in the case of elodie spectra , it can be assumed that a fixed spectral mask gives radial velocities with sufficient accuracy ( katz et al .
analysis of gaia radial velocity spectrometer ( rvs ) data will profit from quite accurate knowledge of stellar parameters obtained from on - board photometric observations .
so all simulations of gaia radial velocity determination assumed that the choice of a proper template is given by complimentary photometric data ( katz et al .
2004 , munari et al .
2003 , zwitter 2002 ) .
alternatively it was assumed , while assessing the capabilities of gaia spectra to independently determine the values of stellar parameters , that the radial velocity is a - priori known ( esa-2000-sci-4 , thevenin et al .
2003 , katz et al .
note that these approaches are relevant at the end of the gaia mission , but at the start of the mission virtually nothing will be known about the values of stellar parameters , so that one would not know which kind of template to use for a radial velocity determination .
also , the wavelength coverage of gaia spectra is much smaller than that of a typical echelle ( elodie ) type spectrum .
so we attempt here to determine _ both _ the best radial velocity and the values of parameters of the stellar atmosphere simultaneously .
data from the rave experiment , which are very similar in both wavelength coverage and resolution to those of gaia s rvs , will be used to illustrate the point .
note that since virtually nothing is known about the rave targets it is obvious to use such an approach .
rave ( radial velocity experiment ) project ( steinmetz 2003 , munari et al .
2004 ) is an ambitious international collaboration aimed at conducting an all - sky spectroscopic survey of galactic stars .
the participating countries are australia , canada , france , germany , italy , japan , netherlands , slovenia , switzerland , uk , and usa . the spectra allow us to measure radial velocities as well as metallicites and other stellar parameters for a large number of stars using the 1.2-m uk schmidt telescope at the anglo - australian observatory .
data collection for this project started in april 2003 with more than 40,000 spectra observed to date .
spectral resolving power and wavelength range ( 84138746 ) are very similar to those of the gaia radial velocity spectrograph .
observed or synthetic spectra can be used for classification .
the advantage of the former is that they are `` real '' , so avoiding any simplifying assumptions used in synthetic spectra calculation ( munari et al .
the latter have the advantage of a more uniform coverage of the parameter space . at present
we are using a subset of a synthetic library of nearly 60.000 spectra with suitable resolving power ( zwitter , castelli & munari 2004 ) which were calculated from the latest generation of kurucz models .
the grid is characterized by the following ranges of stellar parameters : @xmath0 , @xmath1 , @xmath2 \le + 0.5 $ ] , @xmath3 km s@xmath4 , @xmath5 km s@xmath4 .
correlation routines , like the iraf s rvsao package ( kurtz & mink 1998 ) are a well established way to calculate radial velocity using a fixed stellar or galaxy spectrum template . their figure of merit is based on the value of correlation coefficient @xmath6 ( tonry & davis 1979 ) .
but one should not conclude that the template spectrum with the highest value of @xmath6 also gives the best fit to the observed spectrum .
1 shows results of analysis of a single observed spectrum using a set of template spectra .
the maximal value of the correlation coefficient @xmath6 occurs at the `` stem '' of area covering a caravel ship shape , though the minimum of @xmath7 occurs at its bottom .
the reason is that the correlation is defined using normalized quantities .
therefore it is not sensitive to any kind of constant shift or spread ( of the kind @xmath8 and @xmath9 where @xmath10 is a constant value or bias ) .
this explains why it is only sensitive to high variations in the line profile and is not suitable for minimization .
we can also say that in cross - correlation one tries to find the best alignment of the lines , in a way irrespective of their depth .
this is strictly valid for isolated single lines .
the effective wavelength of a blend of nearby lines can shift sideways and so worsens the cross - correlation only with a large change of the temperature and gravity .
figure 2 plots the observed spectrum which was used in figure 1 and one of the templates from the library .
the match is poor even though the template shown features the highest value of the correlation coefficient @xmath6 among all templates in the library ( the point is at the tip of the stem of the caravel shape in figure 1 ) .
cross - correlation alone is clearly not enough to find the template with the best match .
the situation can be improved by supplementing correlation analysis with a proper minimization scheme ( figure 3 ) .
the reason is that normalized squared distance is sensitive to line depth and shape as well as continuum level , and so to the values of stellar parameters . in our case
we first use a correlation routine to calculate the velocity shift between the observed spectrum and a template from the synthetic library .
but the goodness of fit is not based on the value of the correlation coefficient r. instead we calculate the standard deviation between the observed spectrum and the velocity - shifted template . the template which yields the smallest standard deviation
is assumed to give a fair representation of parameters of the stellar atmosphere .
values of several stellar parameters are primarily based on spectral analysis .
these include metallicity , abundances of individual elements and stellar rotation velocity .
the values of effective temperature and surface gravity can also be derived , or in the case of gaia checked , by spectral analysis .
both gaia and rave projects will provide too many spectra to be analyzed by hand .
automated procedures , such as the one proposed here , yield useful results .
any other information available , in the case of gaia these would be results of photometric and astrometric observations , can be seen as an additional constraint on the relevant range of stellar templates to be considered for a given star .
if an acceptable match could not be found despite a high s / n of the observed spectrum , this implies that any kind of peculiarity is present in the observed object , or that the observed star is a double lined spectroscopic binary .
cross correlation is sensitive to position of the lines and so radial velocity .
it is however not sensitive to line depth , so it is not to be used to determine the values of stellar atmosphere parameters unless blends of nearby lines are driving the correlation .
the situation gets worse with low s / n spectra and when sharp lines ( e.g. ca ii ir triplet ) are present . by adding a suitable minimum distance scheme which is sensitive to equivalent widths ( thevenin & foy 1983 ) the values of both radial velocity and stellar parameters like temperature , gravity , metallicity and rotation velocity can be determined reliably
tz acknowledges financial support from the slovenian ministry for education , science and sports .
katz , d. , soubiran , c. , cayrel , r. , adda , m. , cautain , r. 1998 , a&a 338 , 151 katz , d. , et al .
2004 , mnras , in press kurtz , m.j . , mink , d.j .
1998 , pasp 110 , 934 munari , u. , agnolin , p. , tomasella , l. 2001 , balt.a .
10 , 613 munari , u. , zwitter , t. , katz , d. , cropper , m. 2003 , in gaia spectroscopy : science and technology , asp conf .
298 , 275 munari , u. , zwitter , t. , siebert , a. 2004 , this volume steinmetz , m. , 2003 , in gaia spectroscopy : science and technology , asp conf .
298 , 381 thevenin , f. , foy , r. 1983 , a&a 122 , 261 thevenin , f. , bijaoui , a. , katz , d. 2003 , in gaia spectroscopy : science and technology , asp conf .
298 , 291 tonry , j. , davis , m. 1979 , aj 84 , 1511 zwitter , t. 2002 , a&a 386 , 748 zwitter , t. , castelli , f. , munari , u. 2004 , a&a , 417 , 1055 | one may consider cross - correlation routines applied to stellar spectra as a way to determine not only the radial velocities but also to assess the properties of stellar atmospheres .
we show that this is not the case . high value of the cross - correlation coefficient between the observed and a template spectrum does not mean that the template corresponds to correct values of stellar temperature , gravity or metallicity .
cross - correlation operates in normalized space , so it is not sensitive to scaling or shifting of stellar flux .
it is argued that cross - correlation is useful to efficiently determine the velocity shift between the observed and the template spectrum . but minimal distance methods need to be used to determine which template gives the best match to the observed spectrum , and so derive values of physical parameters . to illustrate the point we use data from the rave project which are being obtained at very similar spectral resolution and wavelength domain as will be the case for gaia s rvs .
[ 2004/06/22 1.2 ( kof ) ; 2001/04/25 1.1 ( pwd ) ] |
the development of experimental and theoretical methods of quantum information processing ( qip ) is an important direction of quantum informatics .
nmr methods are the simplest ones among different experimental approaches @xcite .
it is well known that the liquid state nmr methods @xcite are widely used for experimental realizations of quantum gates and algorithms on the basis of the pseudo - pure states @xcite
. however , the possibilities of qip based on the liquid state nmr are limited because the number of correlated qubits is very small ( about 10 ) @xcite and quantum correlations in such systems are not strong .
in particular , entanglement is almost absent @xcite . at the same time , the potential of the solid state nmr methods @xcite is not exhausted yet .
multiple quantum ( mq ) spectroscopy in solids @xcite is an example of such a method .
mq nmr not only creates multi - qubit coherent states but also allows the investigation of their relaxation under the action of the correlated spin reservoir .
mq nmr @xcite is an important method for the investigation of various problems of quantum information processing such as the transmission of quantum information @xcite and decoherence processes @xcite .
one - dimensional mq nmr methods are very suitable for solving problems of quantum informatics .
the reason is that a consistent quantum - mechanical theory of mq nmr dynamics has been developed only for one - dimensional systems @xcite .
that theory is based on the fact that the non - secular two - spin / two - quantum hamiltonian @xcite , describing mq nmr dynamics , is the xy hamiltonian @xcite , which can be diagonalized exactly for one - dimensional systems in the approximation of the nearest neighbor interactions @xcite . as a result , mq nmr dynamics in such systems can be studied analytically . in particular , only mq nmr coherences of the zeroth and plus / minus second orders arise in a one - dimensional chain initially prepared in a thermodynamic equilibrium state @xcite .
the developed theory @xcite is based on the model of an isolated spin chain with the nearest neighbor interactions .
such a model is realized in quasi - one - dimensional chains of nuclei in calcium fluorapatite with a hexagonal system of fluorine nuclei .
the distance between neighboring chains is about three times larger than the distance between the nearest fluorine nuclei in the same chain .
taking into account that the dipole - dipole interaction ( ddi ) of the next nearest spins in the chain is eight times weaker than the nearest neighbor interaction @xcite one can use the model of an isolated spin chain with the nearest neighbor interactions for the interpretation of the experimental data obtained from the mq nmr experiments @xcite .
the information resource of mq nmr exceeds the resource of conventional nmr @xcite .
however , that resource can be used only if the xy hamiltonian is created with sufficient accuracy @xcite . the xy hamiltonian is obtained as the averaged two - spin / two - quantum hamiltonian @xcite which is the average hamiltonian @xcite in the mq nmr experiments .
the corrections to the average hamiltonian @xcite spoil the xy hamiltonian .
these corrections are proportional to powers of the parameter @xmath0 ( @xmath1 is the period of the irradiating sequence of the preparation period of the mq nmr experiment and @xmath2 is of the order of the ddi ) .
we have designed a special probe @xcite for the generation of high - power ultra - short pulses and decreased the period @xmath1 and the parameter @xmath3 in mq nmr experiments .
the results @xcite show high accuracy of creating the xy hamiltonian .
it is very important that the xy hamiltonian ( the mq nmr hamiltonian ) is related to the flip - flop one by a simple unitary transformation @xcite for one - dimensional systems in the approximation of the nearest neighbor interactions .
that fact allows us to realize the quantum state transfer along a one - dimensional spin chain .
it is also significant that the relaxation of the mq nmr coherences can be considered as a model for studying the decoherence processes .
the paper is organized as follows .
an introduction to mq nmr dynamics is given in section 2 . in section 3
we show that mq nmr can be used for the quantum state transfer in one - dimensional spin chains .
relaxation of the mq nmr coherences in one - dimensional spin chains is discussed in section 4 .
we briefly summarize our results in section 5 .
[ cols="^ " , ]
we considered the methods of mq nmr spectroscopy of one - dimensional spin systems and their application for solving problems of quantum informatics . the quantum state transfer in linear spin chains
can be realized with high fidelity using mq nmr dynamics .
decoherence of many - qubit quantum state created on the preparation period of the mq nmr experiment @xcite can be studied on the evolution period of that experiment . the dipolar relaxation of the mq nmr coherences is considered as a model of the decoherence process .
the theory of the dipolar relaxation of the mq nmr coherences is developed .
the performed mq nmr experiments on the quasi - one - dimensional system of nuclei in calcium fluorapatite are in a good agreement with the theoretical predictions .
braunstein , s. l. , caves , c. m. , jozsa , r. , linden , n. , popescu , s. , and schack , r. , `` separability of very noisy mixed states and implications for nmr quantum computing , '' _ phys .
lett _ * 83 * , 1054 ( 1999 ) .
doronin , s. i. , vasilev , s. g. , samoilenko , a. a. , feldman , e. b. , and shumm , b. a. , `` dynamics and relaxation of multiple quantum nmr coherences in a quasi - one - dimensional chain of nuclear spins @xmath4f in calcium fluorapatite , '' _ jetp letters _
* 101 * , 613 ( 2015 ) .
bochkin , g. a. , feldman , e. b. , and vasilev , s. g. , `` relaxation of multiple quantum nmr coherences in quasi - one - dimensional spin systems , '' _ zeitschrift fr physikalische chemie international journal of research in physical chemistry chemical physics _
* 230 * ( 2016 ) . | multiple quantum ( mq ) nmr methods @xcite are applied to the analysis of various problems of quantum information processing .
it is shown that the two - spin / two - quantum hamiltonian @xcite describing mq nmr dynamics is related to the flip - flop hamiltonian of a one - dimensional spin system in the approximation of the nearest neighbor interactions . as a result , it is possible to organize quantum state transfer along a linear chain .
mq nmr experiments are performed on quasi - one - dimensional chains of nuclei in calcium fluorapatite .
relaxation of the mq nmr coherences is considered as the simplest model of decoherence processes .
a theory of the dipolar relaxation of the mq nmr coherences in one - dimensional systems is developed .
a good agreement of the theoretical predictions and the experimental data is obtained . |
_ gaia _ s radial velocity spectrometer @xcite data are processed on - ground by the data processing and analysis consortium ( dpac ) co - ordination unit ( cu ) 6 spectroscopic processing pipeline @xcite .
the pipeline formally runs at the cu6 data processing centre .
we present offline tests of the cu6 pipeline running at the mullard space science laboratory . as already presented in @xcite , fig .
[ fig1 ] ( left ) presents tentative evidence that the cu6 pipeline is able to achieve the end - of - mission rv precision predicted by simulations that include the straylight . the majority of the stars in fig .
[ fig1 ] ( left ) are g dwarfs so the measured @xmath4 km s@xmath0 at @xmath2 mag is consistent with simulations that predict a loss of 1.4 mag .
the fixed limiting magnitude of @xmath5 mag onboard rvs was changed to an adaptive one in september 2015 .
now the limiting magnitude ranges from @xmath6 mag as a function of time , corresponding to the straylight pattern to save telemetry on spectra that contain more noise than signal . selecting milky way halo stars from the gums simulation @xcite with @xmath7 mag
suggests that rvs is collecting spectra for @xmath31.8 million stars in the milky way s halo , the majority of which will be metal - poor giants .
having approximately verified the rv performance model in section [ sec1 ] with preliminary measurements , we apply this model to each gums star .
this predicts an _ upper _ limit ( due to the adaptive limiting magnitude ) on the number of halo stars in the final _ gaia _ catalogue with @xmath8 km s@xmath0 : @xmath3800,000 , @xmath342% of the observed halo stars ( red / dark grey dots in fig .
[ fig1 ] right ) .
[ fig1 ] ( left ) presents tentative evidence that @xmath9 can be measured up to 30 km s@xmath0 : @xmath31.2 million stars , 67% of the observed halo stars ( green / light grey dots in fig .
[ fig1 ] right ) . beyond this limit
, it has not been tested that the data follow poisson statistics and so whether the predictions are valid .
rvs spectra were obtained with a fixed across scan ( ac ) window width of 10 pixels .
the rvs s / n simulator suggests that adapting the ac width to the observing conditions could mitigate the impact of straylight , recovering @xmath30.14 mag .
this would increase the aforementioned predicted upper limit to @xmath3900,000 , a 13% increase ( all galactic components increase by several million ) .
_ gaia _ s onboard software was updated in april 2015 to observe with adaptive ac widths .
this new functionality has been successfully commissioned but depends very much on rvs calibrations and so is still being optimised .
mag looking face on : x and y are in the galactic plane with the sun at the origin ( square ) , where the cross is the galactic centre .
each star is colour - coded according to its predicted end - of - mission @xmath9 , assuming every star is a metal - poor k1 giant : @xmath8 km s@xmath0 ( red / dark grey ) , @xmath10 km s@xmath0 ( green / light grey ) , @xmath11 km s@xmath0 ( black).,title="fig:",scaledwidth=49.0% ] mag looking face on : x and y are in the galactic plane with the sun at the origin ( square ) , where the cross is the galactic centre .
each star is colour - coded according to its predicted end - of - mission @xmath9 , assuming every star is a metal - poor k1 giant : @xmath8 km s@xmath0 ( red / dark grey ) , @xmath10 km s@xmath0 ( green / light grey ) , @xmath11 km s@xmath0 ( black).,title="fig:",scaledwidth=41.0% ] _ gaia_-rvs is already the largest ever spectroscopic survey ( 5.4 billion spectra observed in its first year ) .
this means it will also be the largest ever survey of the milky way s halo .
it will provide @xmath31 km s@xmath0 precision radial velocities for @xmath12 mag , which is the planned cu6 contribution to the second _ gaia _ data release ( 2017 , to be confirmed ) . with _
astrometry , this will provide @xmath310,000 _ local field _ halo stars ( all galactic components @xmath32 million ) in 6d .
rvs spectra will also be used by dpac cu8 to derive abundances ( fe , ca , ti , si ) , @xmath13 , log @xmath14 , [ m / h ] and @xmath15 for @xmath12 mag , ready for later data releases .
cu6-measured @xmath16sin@xmath17 for these stars means that _ gaia _ will measure these @xmath310,000 local field halo stars and the @xmath32 million all - galactic - component stars in a total of 15 dimensions .
we present preliminary evidence that _ gaia_-rvs can provide @xmath315 km s@xmath0 precision end - of - mission radial velocities at @xmath2 mag . at this precision and with _ gaia _ astrometry , _ gaia _ will provide @xmath3800,000 - 900,000 halo stars ( all galactic components @xmath375 - 100 million ) in 6d in the final _ gaia _ catalogue ( 2022 , to be decided ) . when analysed with cu8-derived [ m / h ] from _ gaia
_ s bp / rp spectra of these stars , _ gaia _
s chemo-6d - kinematic mapping out to @xmath330 - 50 kpc from the sun will revolutionise our understanding of the milky way halo s structure , origin and evolution . | _ gaia _ s radial velocity spectrometer ( rvs ) has been operating in routine phase for over one year since initial commissioning
. rvs continues to work well but the higher than expected levels of straylight reduce the limiting magnitude .
the end - of - mission radial - velocity ( rv ) performance requirement for g2v stars was 15 km s@xmath0 at @xmath1 mag .
instead , 15 km s@xmath0 precision is achieved at @xmath2 mag , consistent with simulations that predict a loss of 1.4 mag
. simulations also suggest that changes to _ gaia _ s onboard software could recover @xmath30.14 mag of this loss . consequently _ gaia _ s onboard software was upgraded in april 2015 .
the status of this new commissioning period is presented , as well as the latest scientific performance of the on - ground processing of rvs spectra .
we illustrate the implications of the rvs limiting magnitude on _ gaia _ s view of the milky way s halo in 6d using the _ gaia _ universe model snapshot ( gums ) . |
spin peierls compounds such as cugeo have solitons in their incommensurate phase @xcite the magnetic profile of which can be measured by nmr techniques @xcite and which must be accounted for by any theoretical model . recently a systematic study of solitons in the heisenberg spin peierls model was done by quantum monte carlo methods@xcite , with results that differ essentially from those obtained in the xy model@xcite . however
, these authors did not determine the distribution of spins and the corresponding nmr signal in the incommensurate phase , which are the subject of the present paper .
here we calculate the magnetic structure of solitons in the heisenberg spin peierls model via the dmrg method of white @xcite and also within the hartree fock approximation @xcite .
our ( essentially exact ) dmrg results in the dimerised phase agree with those of ref@xcite and they are also surprisingly close to the results of a hartree fock calculation . the magnetic profiles in the incommensurate phase that we compute by hartree fock disagree with those reconstructed from nmr data @xcite .
however , if we eliminate the oscillations in these profiles by averaging over even and odd sites , we find spin distributions that agree qualitatively with those obtained by nmr in ref[@xcite ] . the spin gap peierls in cugeo and similar materials @xcite may be due to ( i ) magnetoelastic couplings @xcite and/or ( ii ) interactions among the chains @xcite .
we consider the simplest realisation of case ( i ) : @xmath0 @xmath1 are spin @xmath2 operators , all energies are measured in units of @xmath3 and @xmath4 is the only parameter of this model .
the @xmath5 are due to elastic deformations @xmath6 the fluctuations of which are thought to be stabilised by inter chain interactions and which are treated classically .
this approximation ignores the competing energy scales of phonons @xcite and magnons for cugeo ( an attempt to go beyond the static approximation was undertaken in , for example , @xcite ) .
we also ignored second nearest neighbour exchange couplings that might be needed in a realistic model of cugeo @xcite .
the stationary point of @xmath7 with respect to the deformations @xmath8 is given by @xmath9 and this inhomogenous classical background @xmath5 is the key difficulty in tackling the spin peierls hamiltonian of eq([spinpeierlsmodel ] ) .
we use the dmrg method of white in the original spin variables , while for hartree fock we use the jordan - wigner transform @xcite of eq([spinpeierlsmodel ] ) : @xmath10 as usual , the hartree fock ( hf ) approximation @xcite is given by an energy functional @xmath11 + \mu b\sum s_{n}^{z}\mbox { } \nonumber
\\ \mbox { } s_{n}^{z}\mbox { } & = & \rho _ { n , n}-\frac{1}{2 } \nonumber\end{aligned}\ ] ] plus a consistency condition @xmath12
to test our dmrg @xcite and hf approaches , we consider the ground state energy of eq([spinpeierlsmodel ] ) for prescribed alternating dimerisation @xmath13 at @xmath14 . in the hf calculation
there is an oscillating effective coupling @xmath15 that reflects oscillations in @xmath16 and that includes oscillations of the hartree fock variables .
we find ( details are given in an appendix ) @xmath17 where @xmath18 , @xmath19 are standard elliptic functions with modulus @xmath20 .
figure(1 ) displays , descending in energy , ( i ) the ground state energy of the renormalised xy model @xmath21 \(ii ) the hartree - fock energy and ( iii ) the dmrg result ( dmrg reproduces the bethe ansatz result @xmath22 at @xmath23 ) .
the dmrg and hartree fock results are close and at @xmath24 where the system decouples into independent dimers , the hartree fock approximation is exact .
less satisfactory is the incorrect gap of the hartree - fock result at @xmath25 that was avoided by bulaevski@xcite by assuming the hartree fock parameter to be uniform along the chain .
we conclude that the hartree fock approximation is distinct from the renormalised xy model .
both in dmrg and hf we iterate eq([elastic ] ) to converge towards the fixed point .
we test this procedure on the @xmath26 solitons of the xy spin peierls model of eq([xy ] ) or , equivalently the charge=@xmath2 solitons of the peierls model of polyacetylene @xcite .
we recall that in the xy spin peierls model @xmath27 for half the points @xmath28 $ ] on a chain of odd length @xmath29 with periodic boundary conditions @xcite .
this is due to the fact that the hamiltonian couples only even with odd points and is of the form @xmath30 with a spectrum that is symmetric under @xmath31@xmath32 by the symmetry @xmath33 there are @xmath34 eigenvalues of @xmath35 plus the eigenvalue @xmath36 of the form @xmath37 which alone contributes to @xmath38 and which is responsible for the vanishing of @xmath38 on half the lattice .
all this is borne out by figure 2 : + the magnetic profile of a soliton in the full heisenberg spin peierls model as obtained by dmrg and hf are given in fig.3 . clearly , this profile is quite different from that obtained in the xy spin peierls model .
+ the dmrg result gives the symmetric profile in fig.3 and it is hard to differentiate between the two profiles .
since dmrg and hf give comparable results for the spin density in the dimerised phase and since dmrg is difficult for long inhomogenous chains , we shall use hf to estimate the distribution of spins in the incommensurate phase@xcite .
+ we crudely fix the parameter @xmath39 by requiring that the period of the soliton structure be comparable to that observed in the nmr experiments .
consider the configuration of @xmath13 and @xmath40 , multiplied by an oscillating factor , in the incommensurate phase for @xmath41 , @xmath42 , @xmath43 in fig.4 .
+ the nmr data reflects the distribution of spins along the chain or the number of points that carry a prescribed value of spin .
the configuration of spins as displayed in fig.4 ( modulo an oscillating factor ) , gives rise to the distribution of fig.5 .
we see immediately that this distribution is incompatible with the nmr data of @xcite : it contains positive and negative spins and the value of @xmath44 disagrees by a factor of @xmath45 with the value quoted by @xcite .
so we are forced to conclude that the static heisenberg spin peierls model for cugeo is incompatible with the nmr data .
the most plausible resolution of this + discrepancy is that the motion of a nuclear spin in the nmr experiment averages over the dynamics of the spin plus lattice system . to mimic such an average that is , strictly speaking , outside of the domain of validity of our calculation
, we take averages @xmath46 between even and odd spins .
the distribution of these average spins that is given in fig.6 is qualitatively similar to the distribution of spins in the xy model , in that the averages have one sign only .
the value of @xmath44 for the distribution of averaged spins is of the same order as in the nmr data of @xcite , but the agreement with the data is only on a crude and qualitative level .
we have calculated the magnetic structure of solitons in a static heisenberg spin peierls model via dmrg and the hartree fock approximation .
thanks to the fact that the renormalised xy model is not the hf approximation of the heisenbergmmodel we found reasonable agreement between hf and dmrg results in the dimerised phase . within our static model
, we obtained a spin distribution in the incommensurate phase that is incompatible with the nmr data on cugeo .
we then assumed that the nmr data reflect averages in time over fluctuating spins and lattice deformations and mimicked such internal dynamics ( that is beyond the scope of our static approach ) by taking averages over even and odd spins .
the resulting spin distribution agrees qualitatively with the nmr data .
we conclude that the dynamics of the spin plus lattice system must be taken into account in a proper theoretical description of the spin peierls transition of the cugeo system .
* acknowledgements * : we are indebted to alexander buzdin for introducing us to the spin peierls problem and for showing us the nmr results .
we thank mladen horvatic and claude berthier for comments on their data and sergei brasovskii , lev bulaevski and kazumi maki for comments on the theory .
we also thank goetz uhrig for calling our attention to the qmc calculatios of ref@xcite that we had been unaware of .
to correct an error in the litterature , we give the details of the hartree fock calculation in the dimerised phase i.e. for prescribed and uniform @xmath13 with @xmath47 , see eq([hartreefock ] ) : @xmath48 we are interested in alternating couplings : @xmath49 fourier transforming the effective hamiltonian and diagonalising it @xmath50
\nonumber \\ \lambda & = & \sqrt{k^{2}\cos ^{2}p+\delta k^{2}\sin ^{2}p } \nonumber \\ \psi ( p ) & = & u(p)\alpha ( p)+v^{*}(p)\beta ( p ) \nonumber \\ \psi ( p+\pi ) & = & v(p)\alpha ( p)-u^{*}(p)\beta ( p ) \nonumber\end{aligned}\ ] ] we find two consistency conditions : @xmath51 = -\frac{% 1}{\pi } \left ( { \bf k}-{\bf d}\right ) \nonumber \\
\delta t & = & < \sum_{|p|<\pi /2}\left [ u^{*}(p)v(p)-v^{*}(p)u(p)\right ] e^{ip}=-\frac{\delta k}{\pi k}{\bf d } \nonumber \\ \kappa & = & \sqrt{1-\left ( \frac{\delta k}{k}\right ) ^{2 } } \nonumber\end{aligned}\ ] ] at @xmath52 both conditions can be combined into one fixed point equation for @xmath53 : | we compute the magnetic profile of spin peierls solitons in a simple heisenberg model with magneto elastic couplings , using independently the dmrg method of white and the hartree fock approximation .
the results obtained in such a static model are incompatible with existing nmr data on cugeo , but the distribution of averaged spins agrees qualitatively with the data .
we conclude that the dynamics in the spin plus lattice system must be included in a more detailed theory of the spin peierls transition in cugeo .
pacs numbers : 75.10.jm , 75.50.ee , 76.60.-k |
* synthesis of planar [ cu(pyz)@xmath12(pyo)@xmath12](pf@xmath14)@xmath12*. in the minimum amount of water , cucl@xmath582h@xmath2o ( 0.502 g , 2.95 mmol ) and agpf@xmath4 ( 1.489 g , 5.89 mmol ) were mixed together to yield a white precipitate of agcl and a pale blue solution containing the `` cu(pf@xmath4)@xmath2 '' product . to recover the blue solution , the agcl solid
was removed by careful vacuum filtration . in a separate solution , pyrazine and pyridine-@xmath5-oxide in a 3:1 ratio
were dissolved in a 1:1 mixture of h@xmath2o and ethanol to give a colourless solution . to this latter solution
was added the `` cu(pf@xmath4)@xmath2 '' solution . upon slow mixing of the chemical reagents , a small amount of pale blue powder formed , but was removed by vacuum filtration to afford a blue solution .
slow evaporation of this solution yielded a large mass of deep green square plates .
* synthesis of the chain - like compound [ cu(pyz)(pyo)@xmath12(h@xmath12o)@xmath12](pf@xmath14)@xmath12*. using a reaction scheme similar to that above , the ratio of of pyrazine to pyridine-@xmath5-oxide was decreased from 3:1 to 2:1 .
mixing of the chemical reagents immediately afforded a bright turquoise blue solution .
the solution was covered with a piece of perforated al - foil to allow slow solvent evaporation . upon standing at room temperature for several weeks
, small green blocks were deposited on the bottom of the beaker and subsequently isolated via vacuum filtration .
.room temperature lattice parameters determined from x - ray crystallography of [ cu(pyz)@xmath2(pyo)@xmath2](pf@xmath4)@xmath2 ( q2d ) and [ cu(pyz)(pyo)@xmath2(h@xmath2o)@xmath2](pf@xmath4)@xmath2 ( q1d ) . *
note that this value is the perpendicular distance between cu ions .
[ cols="<,^,>",options="header " , ] * quantum monte carlo simulations . *
the numerical results were obtained using the stochastic series expansion ( sse ) method to simulate the hamiltonian of equation 1 on finite - sized lattices .
sse is a finite temperature qmc method based on the evaluation of the diagonal matrix elements of the density matrix in a suitable basis .
the method is explained in detail in ref .
@xcite and references therein .
the simulations were performed on the nersc computing facility in berkeley , california
. * temperature - dependent susceptibility .
* measurements were performed using a quantum design physical properties measurement system equipped with a vibrating sample magnetometer option .
polycrystalline samples were placed into gelatin capsules and affixed to the end of a carbon fibre rod .
data were taken on warming from 2 k in a fixed magnetic field of 0.1 t. the datasets for the two compounds are quite distinct ( see fig .
[ chi ] ) , but both exhibit the broad hump in @xmath59 at @xmath60 expected for highly anisotropic antiferromagnets and caused by the onset of short - range correlations
. fits from 300 k down to temperatures just below the hump were made to theoretical models based on the low - dimensional heisenberg hamiltonian of equation 1 .
the layered compound is found to be in excellent agreement with the @xmath0 q2d model of woodward _ et al . _
@xcite with @xmath61 and @xmath62 k , while the best fit for the chain - like material is for the quasi - one - dimensional model of johnston _ et al . _
@xcite with @xmath63 and @xmath64 k. these values are in good agreement with those derived from the pulsed field magnetization .
we obtained similar results by also fitting to the earlier models of bonner & fisher @xcite ( q1d ) and lines @xcite ( q2d ) .
* electron - spin resonance .
* measurements of the @xmath31-factor anisotropy were performed in a superconducting magnet at the national high magnetic field laboratory in los alamos using a cavity perturbation technique @xcite .
the te102 mode of a rectangular resonator at 71.5 ghz , and a millimetre - wave vector network analyser manufactured by abmm were used .
the cavity was mounted on a goniometer and placed inside standard flow @xmath65he and single - shot @xmath66he cryostats . a temperature dependence ( down to 0.5 k ) of the spectrum along the principal axes
was performed to ensure the reported angular dependance of the resonance is not influenced by the long range order , but characteristic of the paramagnetic state .
for both compounds the data shown satisfy this condition . | gaining control of the building blocks of magnetic materials and thereby achieving particular characteristics will make possible the design and growth of bespoke magnetic devices .
while progress in the synthesis of molecular materials , and especially coordination polymers , represents a significant step towards this goal , the ability to tune the magnetic interactions within a particular framework remains in its infancy .
here we demonstrate a chemical method which achieves dimensionality selection via preferential inhibition of the magnetic exchange in an @xmath0 antiferromagnet along one crystal direction , switching the system from being quasi - two- to quasi - one - dimensional while effectively maintaining the nearest - neighbour coupling strength .
coordination polymers are self - organising materials consisting of arrays of metal ions linked via molecular ligands , with non - coordinated counterions supplying charge neutrality .
the choice of initial components permits a high level of control over the final product , enabling many different polymeric architectures to be obtained @xcite .
these materials provide a route to successful crystal engineering , and a number of functionalities are being actively studied , including gas storage @xcite , optoelectronic @xcite , ferroelectric @xcite and magnetic properties @xcite .
although it is now possible to generate an assortment of disparate magnetic lattices using this method @xcite , true control of magnetic exchange interactions implies an ability to adjust selected parameters while keeping others constant . to this end ,
a series of coordination polymers based on cu(ii ) ions bridged by pyrazine ( c@xmath1h@xmath1n@xmath2 ) molecules have proven to be highly versatile . in these systems
it has been shown that it is possible to alter significantly the primary exchange energies via adjustment of the ligands @xcite and the counterions @xcite , or fine - tune the exchange by a few percent via isotopic substitution @xcite , all the while maintaining the same basic metalpyrazine network . in this paper
we demonstrate the power of this strategy by chemically engineering a reduction in the dimensionality of a magnetic system .
after first designing a material based on coordinated planes of cu(ii ) , we adapt the recipe such that the ligand bridges are broken along a specific crystal direction , resulting in a chain - like compound . because the ligand mediating the magnetic interactions in both cases is unchanged , the nearest - neighbour exchange energies of the two materials are found to be equal to each other to within 5% .
the difference in numbers of nearest - neighbours , however , means that the strength of the combined exchange interactions acting on each magnetic ion in the quasi - two - dimensional material is twice that of its quasi - one - dimensional cousin
. figs .
[ fig1](a ) and ( b ) show the crystal structure of orthorhombic [ cu(pyz)@xmath2(pyo)@xmath2](pf@xmath4)@xmath2 ( where pyz = pyrazine and pyo = pyridine-@xmath5-oxide , c@xmath6h@xmath6no ) determined using single - crystal x - ray diffraction @xcite .
@xmath0 cu ions are linked by pyz molecules into nearly square planar arrays , with perpendicular non - bridging pyo ligands keeping the planes well - separated . because of the separation , as well as the staggered arrangement of adjacent planes shown in fig .
[ fig1](b ) , magnetic exchange energies are likely to be very small along the @xmath7-direction . in contrast , cupyzcu bridges are known to be good mediators of antiferromagnetic superexchange @xcite and so the magnetic properties of this material are expected to be quasi - two - dimensional .
this is confirmed by the magnetic measurements described below .
sample synthesis involves mixing together of the molecular components in a solution of water and ethanol .
intermolecular self - organisation means that only a small amount of intervention is subsequently required . to achieve the desired planar structure the pyz and pyo molecules
were added in a 3:1 ratio , previous experience suggesting that to account for the potential for pyo to substitute for pyz , the ligands must initially be in a proportion different to that found in the final product . in order to create a similar sample , but one based on cupyz chains rather than planes , we reduce the pyz : pyo ratio to 2:1 and proceed with the synthesis in a similar way .
the resulting material has the composition [ cu(pyz)(pyo)@xmath2(h@xmath2o)@xmath2](pf@xmath4)@xmath2 and the structure is shown in figs .
[ fig1](c ) and ( d ) . here
the pyz ligands link cu ions along the @xmath8-axis only , the other ligands being non - bridging pyo and water molecules .
the alteration in composition has the effect of changing the symmetry of the crystal from orthorhombic to monoclinic and reducing the number of formula units in the unit cell , but , most importantly for the magnetic exchange , the cupyzcu linkages along the @xmath9-axis are removed without altering the @xmath8-axis cu cu separation by more than a fraction of a percent ( @xmath10 for the planar material and @xmath11 for the chain compound ) .
sr ) spectra measured on planar [ cu(pyz)@xmath12(pyo)@xmath12](pf@xmath14)@xmath12 .
data at different temperatures are offset for clarity .
inset : evolution of the precession frequency @xmath15 with temperature .
long - range magnetic order is observed below 1.71 k. ( b ) @xmath16sr spectra measured on chain - like [ cu(pyz)(pyo)@xmath12(h@xmath12o)@xmath12](pf@xmath14)@xmath12 .
insets : the evolution of the amplitude @xmath17 ( left ) and relaxation rate @xmath18 ( right ) with temperature indicates the onset of long - range magnetic order below about 0.27 k. red lines are fits to functions described in the text and @xcite.,width=302 ] recent heat capacity measurements on the planar material in zero magnetic field see no evidence of a magnetic transition down to the lowest temperatures measured @xcite . however , thermodynamic probes are known to be less sensitive to transitions driven by interplanar couplings @xcite while local probes such as muon - spin relaxation ( @xmath16sr ) are much more effective at determining the antiferromagnetic transition temperature , @xmath19 @xcite . our @xmath20sr data on this compound , shown in fig .
[ muon](a ) , exhibits a clear precession signal which develops below @xmath21 k @xcite , demonstrating long - range magnetic order throughout the bulk of the sample .
in contrast , the @xmath16sr data for the chain - like compound exhibit no resolvable oscillations , see fig .
[ muon](b ) , probably due to a smaller ordered moment , but can be fitted to the expression @xmath22 , where @xmath17 represents the non - relaxing part of the signal .
both @xmath17 and @xmath18 rise markedly below @xmath23 k due to crossover from a regime in which the relaxation is dominated by dynamic magnetic fluctuations to one dominated by quasistatic magnetic order , see fig .
[ muon](b ) insets . from these fits
we estimate @xmath24 k for this material @xcite .
( pyo)@xmath12](pf@xmath14)@xmath12 at @xmath25 k , and chain - like [ cu(pyz)(pyo)@xmath12(h@xmath12o)@xmath12](pf@xmath14)@xmath12 at @xmath26 k. ( b ) the results of quantum monte carlo ( qmc ) simulations of the low temperature magnetization for 3d ( @xmath27 ) , 2d ( @xmath28 ) , and 1d ( @xmath29 ) antiferromagnets .
the lines are the pulsed - field data scaled by the saturation field ( @xmath30 ) .
( c ) the relation between the exchange anisotropy and the ratio of critical temperature and primary exchange energy in q1d and q2d antiferromagnets deduced from qmc simulations @xcite .
the circles indicate the materials reported here .
( d ) anisotropy of the @xmath31-factor in the planar and ( e ) chain - like compounds measured using esr at 10 k and 1.5k , respectively .
red lines are fits to @xmath32.,title="fig:",width=321 ] ( pyo)@xmath12](pf@xmath14)@xmath12 at @xmath25 k , and chain - like [ cu(pyz)(pyo)@xmath12(h@xmath12o)@xmath12](pf@xmath14)@xmath12 at @xmath26 k. ( b ) the results of quantum monte carlo ( qmc ) simulations of the low temperature magnetization for 3d ( @xmath27 ) , 2d ( @xmath28 ) , and 1d ( @xmath29 ) antiferromagnets .
the lines are the pulsed - field data scaled by the saturation field ( @xmath30 ) .
( c ) the relation between the exchange anisotropy and the ratio of critical temperature and primary exchange energy in q1d and q2d antiferromagnets deduced from qmc simulations @xcite .
the circles indicate the materials reported here . ( d ) anisotropy of the @xmath31-factor in the planar and ( e ) chain - like compounds measured using esr at 10 k and 1.5k , respectively .
red lines are fits to @xmath32.,title="fig:",width=321 ] the type of magnetic order displayed by the two compounds can be deduced from their low - temperature magnetization ( see fig . [ pulsed](a ) ) .
the form of our pulsed - field magnetization data up to saturation is in keeping with that expected for low - dimensional antiferromagnets .
the slightly concave curve exhibited by the planar material is typical of quasi - two - dimensional ( q2d ) antiferromagnetic interactions @xcite , while the more extreme curvature shown by data from the chain - like sample is indicative of a quasi - one - dimensional ( q1d ) magnetic lattice , where , for an ideal system , @xmath33 is known to diverge at the saturation field @xcite . to support these observations we compare the data with the results of low - temperature quantum monte carlo ( qmc ) simulations based on the hamiltonian @xmath34 here , for a q1d ( or q2d ) system , @xmath35 is the strength of the exchange coupling within the magnetic chains ( planes ) , @xmath36 is the coupling between chains ( planes ) , and the first and second summations refer to summing over unique pairs of nearest neighbours parallel and perpendicular to the chain ( plane ) , respectively .
comparisons of theory and data are shown in fig .
3(b ) .
theoretical magnetisation curves were calculated in finite steps of the @xmath37 parameter for both q1d and q2d magnetic lattices @xcite . for both materials curves corresponding to
the quoted values of @xmath37 gave the best matches with experimental data ; the q2d curve with @xmath38 for the planar sample , and the q1d curve with @xmath29 for the chain - like material .
the predicted curve for a three - dimensional antiferromagnet is also shown for contrast .
the deviation of the data from the simulations close to the saturation field is likely due to the finite temperatures at which the experiments were performed .
the saturation field ( @xmath30 ) can be extracted from the pulsed - field data and is found to be @xmath39 t for the planar material and @xmath40 t for the chain - like material . at saturation , the hamiltonian above implies that @xmath41 , where , for each spin , @xmath42 is the number of exchange bonds of interaction strength @xmath35 ( @xmath43 for q2d , 2 for q1d ) , and @xmath44 is the number of exchange bonds of interaction strength @xmath36 ( @xmath45 for q2d , 4 for q1d ) @xcite . from this , by assuming that @xmath46 and using the appropriate values for the @xmath31-factor determined from electron - spin resonance , we estimate the primary exchange couplings , @xmath35 , to be @xmath47 k for the planar compound and @xmath48 k for the chain - like compound .
another estimate of the magnetic dimensionality comes from the temperature dependence of the low - field magnetic susceptibility .
fits of such data for both materials results in estimates of @xmath35 that are in accord with those derived above from pulsed - field magnetization data @xcite .
the relative sizes of @xmath19 and @xmath35 are indicative of the anisotropy of the exchange interactions in a low - dimensional magnetic system . using quantum monte carlo ( qmc ) calculations yasuda _ et al . _
@xcite developed empirical relations between these values for @xmath49 heisenberg antiferromagnets , the results of which are shown in fig . [
pulsed](c ) . for compounds considered here the exchange anisotropies
are found to be @xmath50 in the planar material and @xmath51 in the chain - like material .
these values are in keeping with the comparison between data and simulation shown in fig .
[ pulsed](b ) .
the magnetic lattice in a low - dimensional system is not always obvious from an inspection of the crystal structure @xcite .
verification of the equivalence of the magnetic and structural planes and chains in our materials comes from the angle - dependence of the @xmath31-factor as determined by electron - spin resonance .
to first approximation , the cu(ii ) ions in the planar material have a local octahedral symmetry with a tetragonal distortion along the @xmath7-axis .
in such situations , the unpaired spin in a @xmath52 configuration is expected to occupy the @xmath53 orbital @xcite , and the @xmath31-factor parallel to the distorted @xmath54-axis takes a larger value than those in the @xmath55-plane ( see discussion in ref . ) .
accordingly , the data in fig . [ pulsed](d ) show that the @xmath31-factor is lowest when the excitation field is applied in the @xmath56-plane , implying that the direction of highest electronic orbital overlap is the cupyz directions , with the strong q2d exchange interactions being mediated via the molecular orbitals of the pyrazine . for the chain - like material ,
the distortion is more complicated due to the lower crystal symmetry . nevertheless , using two rotations , the smallest values of the @xmath31-factor
are found to be along the cupyz and cupyo bonds , as shown in fig .
[ pulsed](e ) , implying that again the magnetic orbital is @xmath53 .
this allows for the possibility of good exchange coupling along those bonds , but as the pyo molecules are non - bridging ligands , the q1d magnetism must be mediated along the cupyz chains .
taken together , these experimental observations paint a complete picture of the two closely - related magnetic systems . from the point of view of magnetic superexchange
, the chain direction in the q1d material looks very similar to the two cupyz directions in the q2d material and so , despite the compositional differences , the primary nearest - neighbour exchange energies remain largely unaltered . at the same time the critical field in the q2d material
is approximately double that for the q1d compound because it has twice the number of nearest neighbours .
the q2d compound is strongly anisotropic , comparable to the most 2d materials yet identified @xcite .
as suggested above , this is likely due to the disconnect and staggering that occurs between successive planes .
the extreme anisotropy explains why the zero - field heat capacity was not sensitive to the antiferromagnetic transition observed using @xmath16sr . in the q1d material
the anisotropy is less pronounced ( even though the @xmath57 ratio is smaller ) because the chains are not staggered , there are twice as many next - nearest neighbours , and the shortest distance between chains ( along the @xmath9-axis ) is approximately half the interlayer separation in the q2d material .
these materials showcase the ability to take deliberate control over the magnetic properties of polymeric systems .
the self - organisation of the coordination polymers enables them to spontaneously form crystalline lattices whose structure can be anticipated with a high level of predictability .
it is this predictive power , together with the ability to choose the starting ingredients and the knowledge of the exchange efficiency of various ligands accrued over the past few decades , that permits the preselection of exchange anisotropy . in the cupyz systems we have demonstrated the ability to make this preselection without significantly perturbing the magnitude of the primary interaction strengths , while previous studies of similar materials have highlighted the capacity to tune the exchange couplings without changing the overall dimensionality .
thus these compounds represent a promising approach to magnetic crystal engineering , and in particular raise the possibility of generating systems that exhibit higher ordering temperatures and other cooperative phenomena .
this project was supported by the epsrc ( uk ) , the nsf and doe ( us ) , and the european commission .
we thank peter baker for technical assistance .
pag would like to thank keola wierschem for useful discussions . 00
current address : department of physics , durham university , south road , durham , dh1 3le , uk .
s. r. batten , s. m. neville and d. r. turner , _ coordination polymers : design , analysis and application _ ( rsc , cambridge , 2009 ) .
o. k. farha _
et al . _ , nature chemistry * 2 * , 944 , ( 2010 ) .
s. bureekaew _
et al .
_ , nature materials * 8 * , 831 , ( 2009 ) .
n. l. rosi _
et al . _ ,
science * 300 * , 1127 ( 2003 ) .
a. m. kuchison , m. o. wolf and b. o. patrick , inorg . chem . * 49 * , 8802 ( 2010 )
. m. j. katz and d. b. leznoff , j. am .
chem .
soc . * 131 * , 18435 ( 2009 ) .
o. sengupta and p. s. mukherjee , inorg . chem . *
49 * , 8583 ( 2010 ) .
t. okubo , r. kawajiri , t. mitani and t. shimoda , j. am .
chem .
soc . , * 127 * , 1759 ( 2005 ) .
s. ohkoshi , k. imoto , y. tsunobuchi , s. takano and h. tokoro , nature chemistry * 3 * , 564 ( 2011 ) .
g. halder , k. w. chapman , j. a. schlueter and j. l. manson , angew .
chemie int
. ed . * 50 * , 419 ( 2011 ) .
j. h. her _
et al .
_ , inorg
. chem . * 49 * , 1524 ( 2010 ) . r. s. fishman , w. w. shum and j. s. miller , phys .
rev .
b * 81 * , 172407 ( 2010 ) . j. l. musfeldt _
et al . _ , phys .
rev .
lett . * 103 * , 157401 ( 2009 ) . j. l. manson _
et al . _ , j. am . chem . soc . * 131 * , 6733 ( 2009 ) . j. s. miller , chem .
soc . rev . *
40 * , 3266 , ( 2011 ) .
s. j. blundell , f. l. pratt , j. phys .
cond . mat .
* 16 * , r771 ( 2004 ) .
r. t. butcher , c. p. landee , m. m. turnbull and f. xiao , inorg .
chim .
acta * 361 * , 3654 ( 2008 ) .
p. a. goddard _
et al . _ , new j. phys . * 10 * , 083025 ( 2008 ) .
f. m. woodward _
et al . _ ,
inorg . chem . *
46 * , 4256 ( 2007 ) .
p. a. goddard _
et al . _ , phys .
rev .
b * 78 * , 052408 ( 2008 ) . see the supplemental material section at the end of the paper for detailed information on methods and crystal structures .
j. l. manson _
et al . _ ,
chem .
commun .
* 2006 * , 4894 ( 2006 ) .
j. darriet , m. s. haddad , e. n. duesler and d. n. hendrickson , inorg . chem . * 18 * , 2679 ( 1979 ) .
y. kohama _
et al . _ ,
phys .
rev .
b * 84 * , 184402 ( 2011 ) .
p. sengupta , a. w. sandvik and r. r. p. singh , phys .
rev .
b * 68 * , 094423 ( 2003 )
. a. j. steele _
et al . _ , phys .
rev .
b * 84 * , 064412 ( 2011 ) .
j. c. bonner , m. e. fisher , phys . rev . * 135 * a640 ( 1964 ) . c. yasuda
_ et al . _ ,
phys .
rev .
lett . * 94 * , 217201 ( 2005 ) .
j. l. manson _
et al . _ ,
chem .
mater . * 20 * , 7408 ( 2008 ) .
a. abragam and b. bleaney , _ electron paramagnetic resonance of transition ions . _ ( oup oxford , 1970 ) . |
we examine the out - of - equilibrium dynamical evolution of density profiles of ultrasoft particles under time - varying external confining potentials in three spatial dimensions .
the theoretical formalism employed is the dynamical density functional theory ( ddft ) of marini bettolo marconi and tarazona [ j. chem .
phys . * 110 * , 8032 ( 1999 ) ] , supplied by an equilibrium excess free energy functional that is essentially exact .
we complement our theoretical analysis by carrying out extensive brownian dynamics simulations .
we find excellent agreement between theory and simulations for the whole time evolution of density profiles , demonstrating thereby the validity of the ddft when an accurate equilibrium free energy functional is employed .
density functional theory ( dft ) is a very powerful tool for the quantitative description of the equilibrium states of many - body systems under arbitrary external fields .
it rests on the exact statement that the helmholtz free energy of the system , @xmath0 $ ] , is a unique functional of the inhomogeneous one - particle density @xmath1 .
moreover , the equilibrium profile @xmath2 minimises @xmath0 $ ] under the constraint of fixed particle number @xmath3 @xcite .
the task is then to approximate the unknown functional @xmath0 $ ] from which all equilibrium properties of the system follow .
much more challenging is the problem of studying _ out - of equilibrium dynamics _ of many - body systems , for which analogous uniqueness and minimisation principles are lacking . in this paper , we present results based on a recently - proposed dynamical density functional theory ( ddft ) formalism and we demonstrate that the latter is capable of describing out - of - equilibrium diffusive processes in colloidal systems at the brownian time scale .
we are concerned with the dynamics of typical soft - matter systems , such as suspensions of mesoscopic spheres and polymer chains in a microscopic solvent @xcite .
the enormous difference in the masses of the suspended particles and the solvent molecules implies a corresponding separation in the relaxational time scales of the two . at times of the order of the fokker - planck scale , @xmath4 , the solvent coordinates are long relaxed to thermal equilibrium . on the brownian diffusive time scale , @xmath5
, the momentum coordinates of the solute particles relax to equilibrium with the heat bath of the solvent molecules and thus a statistical description involving only the positions of the colloids is feasible @xcite . in this regime ,
the evolution of the coordinates @xmath6 of the @xmath3 colloidal particles is described by the set of stochastic langevin equations : @xmath7 + { \bf w}_i(t ) .
\label{bd : eq}\ ] ] in eq .
( [ bd : eq ] ) above , @xmath8 is the pair ( effective ) interaction potential between the mesoscopic particles @xcite , @xmath9 is the externally acting potential and @xmath10 $ ] is a stochastic term representing the random collisions with the solvent molecules and having the properties : @xmath11 where the averages @xmath12 are over the gaussian noise distribution and @xmath13 , the cartesian components . the constants @xmath14 and @xmath15 stand for the mobility and diffusion coefficients of the particles , respectively , and the einstein relation gives @xmath16 . applying the rules of the it stochastic calculus , marconi and tarazona
@xcite recasted the above equations into the form @xmath17 \\ & + & \nabla_{\bf r}\left[\int{\rm d}^3 r'\ , \langle \hat\rho({\bf r } , t ) \hat\rho({\bf r ' } , t)\rangle \nabla_{\bf r } v({\bf r } - { \bf r'})\right ] .
\label{exact.eq}\end{aligned}\ ] ] here , @xmath18 is the usual one - particle density operator and @xmath19 is the noise - average of this quantity . up to this point , all is exact .
now , the following _ physical assumption _ ( a ) is introduced : as the system follows its relaxative dynamics , the instantaneous two - particle correlations can be approximated with those of a system in thermodynamic equilibrium with the same , _ static _
one - particle density @xmath1 as the noise - averaged dynamical one - particle density @xmath20 .
then , eq . ( [ exact.eq ] ) can be cast into a form involving exclusively the _ equilibrium _ density functional @xmath0 $ ] as @xcite @xmath21}{\delta \rho({\bf r } , t)}\right ] , \label{ddft.eq}\ ] ] with the free energy functional @xmath22 = k_bt\int { \rm d}^3 r\rho({\bf r})\left\ { \ln\left[\rho({\bf r})\lambda^3\right ] - 1 \right\ } + f_{\rm ex}[\rho ] + \int{\rm d}^3 r v_{\rm ext}({\bf r } , t)\,\rho({\bf r } ) .
\label{f : eq}\ ] ] the dynamical equation of motion ( [ ddft.eq ] ) was in fact first derived in a phenomenological way by dieterich , frisch and majhofer @xcite . in carrying out concrete calculations with the theory put forward above and in comparing them with brownian dynamics ( bd ) simulation results based on the microscopic equations of motion , eq .
( [ bd : eq ] ) , two sources of possible discrepancies exist : first , the fundamental assumption ( a ) and second the approximate nature of the equilibrium density functional @xmath23 $ ] of eq .
( [ f : eq ] ) .
in this work we focus our attention to _ ultrasoft particles _ for which a very accurate and simple functional @xmath0 $ ] is known , namely the _ mean - field _ or _ random - phase approximation _ ( rpa ) functional given by eq .
( [ mfa : eq ] ) below .
this guarantees that one can explore the accuracy of the fundamental assumption ( a ) under well - defined external conditions .
consider a one - component system of ultrasoft particles .
it has been demonstrated that for such systems the following rpa - functional is quasi - exact @xcite : @xmath24 = \frac{1}{2}\int\int{\rm d}^3r\,{\rm d}^3r ' v(|{\bf r } - { \bf r'}|)\rho({\bf r})\rho({\bf r ' } ) .
\label{mfa : eq}\ ] ] eq .
( [ ddft.eq ] ) takes now with the help of eqs .
( [ f : eq ] ) and ( [ mfa : eq ] ) the form @xmath25 given an initial density field @xmath26 and a prescribed external potential @xmath27 , eq .
( [ explicit.eq ] ) can be numerically solved to yield @xmath28 . in this work
we apply an ultrasoft gaussian pair potential between the interacting particles that has been shown to describe the effective interaction between the centres of mass of polymer chains in athermal solvents @xcite @xmath29.\end{aligned}\ ] ] we set @xmath30 providing the energy unit for the problem , whereas @xmath31 , which corresponds to the gyration radius of the polymers , will be the unit of length henceforth .
accordingly , the natural time scale of the problem , providing the unit of time in this work , is the brownian time scale @xmath32 .
eq .
( [ explicit.eq ] ) is solved using standard numerical techniques , and for a variety of time - dependent confining external potentials @xmath33 to be specified below .
brownian dynamics simulations of eq .
( [ bd : eq ] ) are also straightforward to carry out .
the langevin equations of motion including the external field are numerically solved using a finite time - step @xmath34 in all simulations , and the technique of ermak @xcite . in order to obtain the time - dependent density @xmath28 we perform a large number @xmath35 of independent runs , typically @xmath36 , and average the density profile over all configurations for a fixed time @xmath37 .
we focus to external fields that correspond to a sudden change , i.e. , @xmath38 .
these force the system to relax from the equilibrium density @xmath39 , compatible to the external potential @xmath40 , to the new equilibrium density @xmath41 , corresponding to the external potential @xmath42 .
important questions related to such processes are what is the typical relaxation time @xmath43 for such a procedure and how does the system cross over from one equilibrium density to the other .
we consider two kinds of confinements : spherical ones , @xmath44 , where @xmath45 , and planar ones between two walls perpendicular to the @xmath46-cartesian direction , @xmath47 . in these cases
we obtain @xmath48 and @xmath49 , correspondingly , and the solution of eq .
( [ explicit.eq ] ) is greatly simplified since the integrals take the form of one - dimensional convolutions that can be evaluated very rapidly by use of fast fourier transform techniques .
three different external confinements have been specifically investigated .
two spherical ones @xmath50 ; \label{v1:eq } \\ v_{\rm ext}^{(2)}(r , t ) = \phi_0\left[(r / r_{1})^{10}\theta(-t ) + ( r / r_{2})^{10}\theta(t)\right ] ; \label{v2:eq } \label{spherical : eq}\end{aligned}\ ] ] and one slab confinement @xmath51 .
\label{v3:eq}\end{aligned}\ ] ] the energy scale @xmath52 sets the strength of the confining potential and is fixed to @xmath53 for all three confinements .
the only difference between the external potential for times @xmath54 and for @xmath55 lies in the different length scales @xmath56 for eqs .
( [ v1:eq ] ) and ( [ v2:eq ] ) , and @xmath57 for eq .
( [ v3:eq ] ) . for each confinement
we consider two cases that give rise to two different dynamical processes : @xmath58 ( @xmath59 ) , enforcing an _ expansion _ of the system and @xmath60 ( @xmath61 ) , bringing about a _
compression _ of the same . for the spherical confinements
an additional parameter is the particle number @xmath62 which is a conserved quantity , as is clear from eq .
( [ ddft.eq ] ) that has the form of a continuity equation .
@xmath3 enters the formalism through the normalisation of the density field at @xmath63 . for both spherical confinements
the particle number is @xmath64 . in the slab confinement ,
eq .
( [ v3:eq ] ) , the conserved quantity is the density per unit area @xmath65 .
we choose @xmath66 . in all cases
examined , the typical relaxation time was found to be of order @xmath67 ; after typically @xmath68 , the system fully relaxes into the new equilibrium profile . in the spherical confining potential @xmath69 with ( a ) @xmath70 and @xmath71 and ( b ) @xmath72 and @xmath73 .
the shown profiles are for the times @xmath74 , @xmath75 and @xmath76 , all in @xmath67-units .
the last time is practically equivalent to @xmath77 , since the system there has fully relaxed into equilibrium . in all figures ,
red curves denote the initial and blue ones the final static profile.,title="fig:",width=264 ] in the spherical confining potential @xmath69 with ( a ) @xmath70 and @xmath71 and ( b ) @xmath72 and @xmath73 .
the shown profiles are for the times @xmath74 , @xmath75 and @xmath76 , all in @xmath67-units .
the last time is practically equivalent to @xmath77 , since the system there has fully relaxed into equilibrium . in all figures ,
red curves denote the initial and blue ones the final static profile.,title="fig:",width=264 ] in fig . [
harmon : fig ] we show the results for the harmonic confining potential of eq .
( [ v1:eq ] ) .
it can be seen that the theory reproduces the time evolution of the density profile , both for the expansion [ fig .
[ harmon : fig](a ) ] and the compression [ fig .
[ harmon : fig](b ) ] processes .
an asymmetry in the two processes can be already discerned : the compression is not the ` time reversed ' of the expansion and this effect will be much stronger in the examples to follow .
though the profiles of the system are considerably different from those of an ideal gas , i.e. , effects of the interparticle interaction are present , the confining potential is smooth enough , so that the profiles are devoid of pronounced correlation peaks . in the spherical confining potential @xmath78 with ( a ) @xmath70 and @xmath79 and ( b ) @xmath80 and @xmath73 .
the shown profiles are for the times @xmath74 , @xmath81 and @xmath82 ( in units of @xmath67).,title="fig:",width=340 ] in the spherical confining potential @xmath78 with ( a ) @xmath70 and @xmath79 and ( b ) @xmath80 and @xmath73 .
the shown profiles are for the times @xmath74 , @xmath81 and @xmath82 ( in units of @xmath67).,title="fig:",width=340 ] the situation is different for the external potential of eq .
( [ v2:eq ] ) . here
, the power - law dependence is much more steep , so that the gaussian fluid develops correlation peaks close to the ` walls ' of the confining field .
the dynamical development of the profiles for the expansion and compression processes are shown in fig .
[ r10:fig ] . here , the asymmetry between the expansion and the compression processes is evident . in the former case , seen in fig .
[ r10:fig](a ) , the expansion of the confining potential leaves behind a density profile that has very strong density gradients close to the boundary of the initial confinement . since the latter ceases to act at @xmath83 , this leaves at @xmath84 instantaneously a region @xmath85 that is devoid of particles but in which the new external potential is essentially zero .
this leads to a collective diffusion of the particles towards the boundaries set by the new potential .
correspondingly , the high density peaks decrease rapidly and leak outward . in the inner region , @xmath86 of the profile ,
the dynamics is much slower and the relaxation to the final plateau there takes place at the end of the process , causing thereby the final development of the new , weaker correlation peaks close to the location of the boundary , @xmath87 . the compression process , depicted in fig .
[ r10:fig](b ) runs very differently .
there , the initial ` closing ' of the potential from @xmath88 to @xmath89 leaves at @xmath84 a region of high density at @xmath85 that now finds itself within a strongly repulsive external field .
there is an extremely rapid shrinking there , accompanied by the development of very high correlation peaks that actually ` overshoot ' in height with respect to the final equilibrium profile .
initially , the region in the centre of the sphere remains unaffected and only as the high peaks start diffusing does material flow toward the centre and at the latest stage of the dynamics the profile at @xmath90 reaches its new equilibrium value . , defined in eq .
( [ moment ] ) plotted against the time @xmath37 for the spherical confinement @xmath78 .
circles correspond to radii @xmath70 and @xmath79 ( expansion ) and squares show the resulting curve for the inverse process , @xmath80 and @xmath73 ( compression ) .
the lines are the analytical fits shown in the text .
solid line : eq .
( [ m2plus : eq ] ) ; long - dashed line : eq .
( [ m2minus : eq ] ) .
the arrows mark the characteristic time scales defined in these two equations.,width=302 ] in order to quantify better this asymmetry and also extract characteristic time scales for the two dynamical processes , we consider the second moment of the density , @xmath91 , defined through @xmath92 the quantity @xmath91 is a quantitative measure of the spread of @xmath93 around the centre of the external field and its time evolution is shown in fig .
[ m2:fig ] .
let the superscript ` @xmath94 ' denote the expansion and the superscript ` @xmath95 ' the compression process .
obviously , it holds @xmath96 .
we notice that for both processes @xmath91 is a monotonic function of @xmath37 but some interesting differences arise when one fits the two curves by analytic functions , shown as lines in fig .
[ m2:fig ] .
the expansion can be very accurately described by a single exponential : @xmath97 [ 1-\exp(-t/\tau^{+ } ) ] , \label{m2plus : eq}\ ] ] with the characteristic time scale @xmath98 . however , a double - exponential fit is necessary to parameterise the compression process , namely @xmath99\exp(-t/\tau_2^{- } ) , \label{m2minus : eq}\ ] ] with the fit parameter @xmath100 and the _ two _ characteristic time scales @xmath101 and @xmath102 . since @xmath103
, it follows that the compression process is at any rate faster than the expansion one .
the occurrence of the two distinct time scales @xmath104 in the compression requires some explanation .
the fast process that takes place at times @xmath105 corresponds to the abrupt shrinking of the profile at the wings of the distribution and is caused exclusively by the ` closing ' of the external field .
this is the same mechanism that brings about the overshooting of the density peaks .
once this is over , diffusion within the now already confined system takes place and the second characteristic time scale , @xmath106 , is solely determined by the interaction potential @xmath107 and the average particle density . in the expansion process , the first mechanism is absent thus a single time scale , @xmath108 , shows up , which is of intrinsic origin exclusively . since stronger density gradients occur during the compression than during the expansion process , even the larger of the two time scales of the compression , @xmath106 , is smaller than @xmath108
. the denser the system is , the faster the collective diffusion towards equilibrium . in a slab
confining potential @xmath109 with ( a ) @xmath110 and @xmath111 and ( b ) @xmath112 and @xmath113 .
the shown profiles are for the times @xmath114 and @xmath115 ( in units of @xmath67).,title="fig:",width=340 ] in a slab confining potential @xmath109 with ( a ) @xmath110 and @xmath111 and ( b ) @xmath112 and @xmath113 .
the shown profiles are for the times @xmath114 and @xmath115 ( in units of @xmath67).,title="fig:",width=340 ] finally , we turn our attention to the slab confinement .
the results from theory and simulation are shown in fig .
[ slab : fig ] .
once more it can be seen that the ddft offers an excellent description of the dynamics of the system .
the same asymmetry between expansion and compression that was seen in the spherical confinement also shows up for the case of the slab , including the overshooting of the peaks during the compression process .
in addition , the density profiles develop during their evolution secondary oscillations that are also very well reproduced by the theory . in summarising
, we have demonstrated that the dynamical density functional theory of marini bettolo marconi and tarazona @xcite , when supplemented by an accurate equilibrium density functional , can provide an excellent description of out - of - equilibrium dynamics of colloidal systems at the brownian time scale .
the accuracy of the ddft formalism has already been successfully tested for the system of one - dimensional hard rods @xcite , for which the exact density functional @xmath0 $ ] is known . to the best of our knowledge ,
this is the first study of the validity of ddft in three dimensions . as the phenomenology in 3d is much richer than in 1d , including the possibility of phase transitions , many intersecting ways for future applications open up .
discussions with andrew archer , bob evans , wolfgang dieterich and pedro tarazona are gratefully acknowledged .
this work has been supported by the deutsche forschungsgemeinschaft through the sfb tr6 . |
|
recently there has been renewed interest in studying the distribution of quark and gluon fields in the three - quark static - baryon potential .
while early studies were inconclusive @xcite , improved computing resources and analysis techniques now make it possible to study this system in a quantitative manner @xcite . in particular , it is possible to directly compute the gluon flux distribution @xcite using lattice qcd techniques similar to those pioneered in mesonic static - quark systems @xcite . like okiharu and woloshyn @xcite
our first interest is to test the static - quark source - shape dependence of the observed flux distribution , as represented by correlations between the quark positions and the action or topological charge density of the gauge fields . to this end , we choose three different ways of connecting the gauge link paths required to create gauge - invariant wilson loops . in the first case , quarks are connected along a t - shape path , while in the second case an l - shape is considered .
finally symmetric link paths approximating a y - shape such that the quarks approximate an equilateral triangle are considered .
the latter is particularly interesting as the probability of observing @xmath1-shape flux - tubes are maximized in this equidistant case . because the signal decreases in an exponential fashion with the size of the loop , it is essential to use a method to enhance the signal .
we use strict three - dimensional ape smearing @xcite to enhance the overlap of our spatial - link paths with the ground - state static - quark baryon potential .
time - oriented links remain untouched to preserve the correct static quark potential at all separations .
excellent signal to noise is achieved via a high - statistics approach based on translational symmetry of the four - dimensional lattice volume and rotational symmetries of the lattice as described in detail below .
this approach contrasts previous investigations using gauge fixing followed by projection to smooth the links and resolve a signal in the flux distribution @xcite .
to study the flux distribution in baryons on the lattice , one begins with the standard approach of connecting static quark propagators by spatial - link paths in a gauge invariant manner .
ape - smeared spatial - link paths propagate the quarks from a common origin to their spatial positions .
the smearing procedure replaces a spatial link , @xmath2 , with a sum of @xmath3 times the original link plus @xmath4 times its four spatially oriented staples , followed by projection back to @xmath5 .
we select the unitary matrix @xmath6 which maximizes @xmath7 , where @xmath8 is the smeared link , by iterating over the three diagonal @xmath9 subgroups of @xmath5 repeatedly .
we repeat the combined procedure of smearing and projection @xmath10 times , with @xmath11 .
untouched links in the time direction propagate the spatially separated quarks through euclidean time . for sufficient time evolution the ground state is isolated .
finally smeared - link spatial paths propagate the quarks back to the common spatial origin .
the three - quark wilson loop is defined as : @xmath12 where @xmath13 is a staple made of path - ordered link variables @xmath14 and @xmath15 is the path along a given staple . in this study , we consider two - dimensional spatial - link paths .
figures 1 and 2 give the projection of t and l shape paths in the @xmath16 plane .
figure 3 shows the idea behind the y - shape . in all cases
the three quarks are created at the origin , o ( white bubble ) , then are propagated to the positions q1 , q2 or q3 ( black circle ) before being propagated through time and finally back to a sink at the same spatial location as the source ( o ) .
-plane.,width=113,height=75 ] -plane.,width=113,height=75 ] -plane.,width=113,height=75 ] for the y - shape we create elementary diagonal `` links '' in the form of boxes as shown in fig .
4 . the @xmath17 and @xmath18 boxes are the average of the two path - ordered link variables going from one corner to the diagonally opposite one . taking both of these paths
better maintains the symmetry of the ground state potential and therefore provides improved overlap with the ground state .
we also consider @xmath19 boxes which are the averages of the possible paths connecting two opposite corners using 1x1 and 1x2 boxes .
we will create further link paths in the future for use in bigger loops as necessary .
hence a diagonal staple is , in fact , an average of several `` squared path '' staples connecting the same end points .
the quark co - ordinates considered for y - shape paths are summarized in table [ tab : coord ] .
we note that the origin @xmath20 is not at the centre of these coordinates .
rather the coordinates are selected to place the quarks at approximately equal distances from each other . .
@xmath21 coordinates for the three quarks considered for y - shape paths .
the separation of the two quarks along a cartesian ( cart . ) direction are compared to the separation of those from the third quark . [ cols="^,^,^,^,^ " , ]
in this investigation we characterize the gluon field by the action density @xmath22 observed at spatial coordinate @xmath23 at euclidean time @xmath24 measured relative to the origin of the three - quark wilson loop .
we calculate the action density using the highly - improved @xmath25 three - loop improved lattice field - strength tensor @xcite on four - sweep ape - smeared gauge links . defining the quark positions as @xmath26 , @xmath27 and @xmath28 relative to the origin of the three - quark wilson loop , and denoting the euclidean time extent of the loop by @xmath29 , we evaluate the following correlation function @xmath30 where @xmath31 denotes averaging over configurations and lattice symmetries as described below .
this formula correlates the quark positions via the three - quark wilson loop with the gauge - field action in a gauge invariant manner . for fixed quark positions and euclidean time
, @xmath32 is a scalar field in three dimensions . for values of @xmath23
well away from the quark positions @xmath33 , there are no correlations and @xmath34 .
this measure has the advantage of being positive definite , eliminating any sign ambiguity on whether vacuum field fluctuations are enhanced or suppressed in the presence of static quarks .
we find that @xmath32 is generally less than 1 , signaling the expulsion of vacuum fluctuations from the interior of heavy - quark hadrons .
for this work we consider 200 quenched qcd gauge - fields using the @xmath35-mean - field improved luscher - weisz plaquette plus rectangle gauge action @xcite on @xmath36 lattices at @xmath37 , providing a lattice spacing of @xmath38 fm as set by the string tension . to improve the statistics of the simulation we use various symmetries of the lattice .
first , we make use of translational invariance by computing the correlation on every node of the lattice , averaging the results over the four - volume . to further improve the statistics , we use reflection symmetries . through reflection on the plane @xmath39
we can double the number of t and y - shaped wilson loops . by using reflections on both the plane @xmath39 and @xmath40
we can quadruple the number of l - shaped loops .
we finally use @xmath41 rotational symmetry about the @xmath42-axis to double the number of wilson loops .
this means we are using both the @xmath16 and @xmath43 planes as the planes containing the quarks .
for this exploratory study we present images for @xmath44 and note that qualitatively similar results are observed for @xmath45 .
we plan to examine this and other similarly conservative alternatives on our anticipated larger lattice volumes providing further statistics improvement .
figure [ ortho ] plots the correlation function of eq .
( [ correl ] ) , @xmath46 , for an ortho - slice in the plane of the three - quark system .
the colours of the ortho - slice , denoting the scalar values of @xmath46 , are rendered as a surface plot below .
away from the quark positions @xmath47 , but within the three - quark system @xmath48 indicating the suppression of qcd vacuum field fluctuations from the region inside heavy - quark hadrons . here
the quarks are approximately 0.75 fm from the centre of the distribution and are about 1.25 fm from each other .
figure [ tubes ] renders the spatial points of @xmath46 where the gluon action density is largely suppressed .
tube - like structures are revealed in y - shape as opposed to @xmath1 shape in accord with expectations from precision static quark - potential analyses .
we note that the centre of the flux tube is equidistant from the quark positions and not centered over the origin of the wilson loop .
this gives us confidence that sensitivity to the source is minimal .
however it is important to examine this issue in greater detail and this will be the subject of a forthcoming publication .
h. ichie , v. bornyakov , t. streuer and g. schierholz , nucl .
* b * ( proc . suppl . )
* 119 * ( 2003 ) 751 , hep - lat/0212036 .
f. okiharu and r. m. woloshyn , nucl .
* b * ( proc . suppl . ) * 129 * ( 2004 ) 745 , hep - lat/0310007 . s. o. bilson - thompson , d. b. leinweber and a. g. williams , annals phys .
* 304 * , 1 ( 2003 ) [ hep - lat/0203008 ] .
m. luscher and p. weisz , commun .
phys . * 97 * , 59 ( 1985 ) [ erratum - ibid . *
98 * , 433 ( 1985 ) ] . | methods for revealing the distribution of gluon fields within the three - quark static - baryon potential are presented . in particular , we outline methods for studying the sensitivity of the source on the emerging vacuum response for the three - quark system . at the same time , we explore the possibility of revealing gluon - field distributions in three - quark systems in qcd without the use of gauge - dependent smoothing techniques .
renderings of flux tubes from a preliminary high - statistics study on a @xmath0 lattice are presented . |
fig . 1 . : : flow chart of the present procedure for gamow factor and/or coulomb wave function , which includes momentum resolution by generating the gaussian random numbers . fig . 2 . : : results of @xmath64 fit for 8 mkm target of @xmath66 reaction with @xmath31 mev / c by eq .
( [ eqn : a6 ] ) .
3 . : : results of the @xmath64 fit for ref .
@xcite of @xmath66 reaction with @xmath31 mev / c by eq .
( [ eqn : a9 ] ) .
4 . : : results of the @xmath64 fits for @xmath67 reactions with @xmath31 mev / c by eq .
( [ eqn : a9 ] ) : @xmath68 8 mkm target ; @xmath69 1.4 mkm target . fig . 5 .
: : physical picture of the obtained source size based on the assumed resonance effects . | we propose a new method for the coulomb wave function correction including the momentum resolution for charged hadron pairs and apply it to the precise data on @xmath0 correlations obtained in @xmath1 reaction at 70 gev / c .
it is found that interaction regions of this reaction ( assuming gaussian source function ) are @xmath2 and @xmath3 fm for the thicknesses of the target @xmath4 and @xmath5 microns , respectively .
the physical picture of the source size obtained in this way is discussed .
= -1 cm = 0 cm = 0 cm = 23.7 cm = 16 cm * 1 .
introduction.*recently we have obtained the new formulae for the coulomb wave function correction for charged hadron pairs @xcite . in particular
we have applied them ( in @xcite ) to data on @xmath0 correlation obtained in @xmath6 reaction at 70 gev / c @xcite ( which were originally corrected by usual gamow factor only ) . however , as it was pointed out to us by one of the author of @xcite , we did not take into account their published finite momentum resolution @xcite .
in fact , our formulae can not be applied directly to experimental data in which such momentum resolution is accounted for .
therefore in the present letter we would like to extend our method for the coulomb wave correction provided in @xcite to include also the momentum resolution case and to re - analyse data of @xcite and also to analyse the new , preliminary data of @xcite obtained with two kinds of thickness of ta target : 8 microns ( 8 mkm ) and 1.4 microns ( 1.4 mkm ) .
+ in the next paragraph we first reconstruct ( for the sake of completeness ) the analysis performed in ref .
@xcite and then , in the third paragraph , we propose our new method for the coulomb wave correction including this time also the momentum resolution .
the final part contains our concluding remarks .
+ * 2 . reconstruction of the analysis of @xmath0 correlation data performed by using the gamow factor with momentum resolution.*it has been stressed in @xcite that relative momenta of @xmath0 pairs observed by them have some finite resolutions .
the averaged correlation function , defined as @xmath7 depends therefore on this momentum resolution , where @xmath8 stands for non - coulomb correlation factor . to account for it
the following random number method has been proposed in ref .
@xcite in order to obtain the corresponding averaged quantities in analysis of the correlation data .
+ first of all , the relative momentum of the measured pair , @xmath9 , is decomposed into its longitudinal and transverse components : @xmath10 and @xmath11 , respectively , by making use of the uniform random number @xmath12 ( it is worthwhile to notice at this point that the transverse components @xmath11 in data of @xcite are smaller than @xmath13 mev / c ) .
one uses the following scheme here : @xmath14 at the next step , the gaussian random numbers for @xmath10 and @xmath11 are generated in the following way : @xmath15 in the above equations @xmath16 stands for the standard gaussian random number ] ] whereas @xmath17 and @xmath18 are longitudinal and transverse setup resolutions for the corresponding components , which are equal to ( values used in @xcite ) : @xmath19 mev / c ; @xmath20 mev / c ( for target of the thickness @xmath4 mkm ) and @xmath21 mev / c ( for the 1.4 mkm target ) . + finally , using the randomized number @xmath22 one calculates the corresponding randomized gamow factor correction : @xmath23 where @xmath24 . the full flow chart for this procedure is shown in fig .
1 . calculating now the average value of @xmath25 in 100 k events one can estimate the gamow factor with this finite momentum resolution , @xmath26 where @xmath27 is a free parameter .
it is understood ( or , rather , implicitly assumed ) that essentially all unlike sign pions one deals with here originate from decays of long lived particles like @xmath28 , @xmath29 , @xmath30 , and so on .
figure 2 shows the results of analysis of new data ( for 8 mkm target ) @xcite for region @xmath31 mev / c using this method .
+ * 3 .
proposal of the new method.*we would like to propose now a new method of coulomb wave function correction with a source function @xmath32 instead of the gamow factor , in order to analyse the same data . as usual
we decompose the wave function of unlike charged bosons with momenta @xmath33 and @xmath34 into the wave function of the center - of - mass system ( c.m . ) with total momentum @xmath35 and the inner wave function with relative momentum @xmath36 .
this allows us to express coulomb wave function @xmath37 in terms of the confluent hypergeometric function @xmath38 @xcite : @xmath39 where @xmath40 and the parameter @xmath41 .
assuming factorization in the source functions , @xmath42 ( here @xmath43 ) , we obtain the expression for coulomb correction for the system of @xmath0 pairs identical ( modulo the sign ) as in @xcite : @xmath44\ : , \label{eqn : a8}\end{aligned}\ ] ] where @xmath45 for the specific choice of gaussian source distribution , @xmath46 , we have @xmath47 whereas exponential source function , @xmath48 , leads to @xmath49 using now the same method of gaussian random numbers as in the previous paragraph , we can analyse the old and the new data on @xmath0 pairs @xcite using the following formula : @xmath50 figs .
3 and 4 show results of our analysis of the old and the new data , respectively .
table [ tbl : a1 ] show our results obtained using eq .
( [ eqn : a8 ] ) applied to old and new data with @xmath51mev / c . + * 4 . concluding remarks.*we have proposed the new method for the coulomb wave function correction with momentum resolution and applied it to the analysis of the precise data provided by @xcite .
authors of ref .
@xcite have analysed their @xmath0 correlation data using gamow factor for coulomb corrections together with the random numbers method to account for final momentum resolution .
we have repeated this analysis replacing gamow factor by the coulomb wave function but following the same method for correction for the momentum resolution effect ( cf .
eq .
( [ eqn : a8 ] ) ) . as a result
we have obtained the following ranges of interaction for the gaussian source function : @xmath52 to get a correct physical picture of the source size , we should calculate the root mean squared size , which is equal to : @xmath53 the present study of @xmath0 pair correlations has shown therefore that one can estimate the interaction region even from the @xmath0 correlation data .
it can be compared with the size of the ta nucleus , which is given by : @xmath54 as one can see , @xmath55 is significantly bigger than @xmath56 .
we attribute this difference to a physical picture shown in fig . 5 , i.e. , to the fact that unlike - sign pions are mostly ( if not totally ) emerging from the long - lived resonances shown there .
( in a future one should consider also a possibility of more direct estimation of the parameter @xmath27 and its role in determining the source size parameter correlation data , a similar function @xmath57 is introduced : @xmath58\:,\ ] ] where @xmath59 and @xmath60 are the degree of coherence and an exchange function due to the bose - einstein effect .
@xmath57 is attributed the resonances effect ; @xmath61 depends on the monte carlo programs @xcite . ] ) . + for completeness we have also tried to analyse the same data using exponential source function instead of gaussian .
as is shown in table [ tbl : a2 ] this leads to errors on @xmath62 of the order of @xmath63% , i.e. , with this type of source function we can not estimate the source size ( therefore it has to be discarded ) . +
* acknowledgements:*authors are grateful to dr .
l. g. afanasev for his kind correspondences and for providing us with the new data on @xmath0 correlation prior to publication .
this work is partially supported by the grant - in - aid for scientific research from the ministry of education , science and culture of japan ( # 06640383 ) , and the japan society of promotion of science ( jsps ) .
one of authors ( i. a. ) is also partially supported by russian fund of fundamental research ( grant 96 - 02 - 16347a ) . 99 m. biyajima , t. mizoguchi , t. osada and g. wilk , _ phys .
lett . _
* b353 * ( 1995 ) 340 .
m. biyajima , t. mizoguchi , t. osada and g. wilk , _ phys .
lett . _ * b366 * ( 1996 ) 394 .
l. g. afanasev et al .
, _ sov .
j. nucl .
phys . _ * 52 * ( 1990 ) 666 ( russian ed . : _ jad .
fiz . _
* 52 * ( 1990 ) 1046 ) .
l. g. afanasev , private communications ( oct . , 1995 ) .
l. g. afanasev , private communications ( dec . , 1995 ) ; l. g. afanasev et al .
, in preparation .
m. g. bowler , _ phys .
lett . _
* b270 * ( 1991 ) 69 .
l. i. schiff , _ quantum mechanics _ , 2nd ed .
( mcgraw - hill , new york , 1955 ) , p. 117 .
e. a. de wolf , proceeding of xxivth int .
sym . on multiparticle dynamics ( vietri sul mare , sept .
1994 ) .
[ tbl : a1 ] .results of the @xmath64 fits of @xmath65 for gaussian source by eqs .
( [ eqn : a6 ] ) and ( [ eqn : a9 ] ) . [ cols="^,^,^,^,^",options="header " , ] |
type ia supernovae ( sne ia ) are thought to be the thermonuclear explosion of a white dwarf .
the light curves of sne ia are powered by deposition in the sn ejecta of the @xmath1-ray and positron products of the @xmath2 decay @xcite . the extreme brightness and seemingly uniform light curves of sne
ia make them good candidates for use as standard candle distance indicators . in more recent years , it has been shown that type ia supernovae do not have uniform light curve magnitudes , shape or spectra .
the light curves can , however , be normalized to account for this inhomogeneity , thus allowing these objects to be used at standard candle distance indicators ( e.g. * ? ? ?
* ; * ? ? ?
* ) . between 100 - 200 days
after the explosion the ejecta become transparent to the @xmath1-rays and the light curve is powered by the deposition of the positron kinetic energy into the ejecta .
the escape of a fraction of these positrons from the ejecta has been suggested as a possible source of the galactic 511 kev annihilation radiation @xcite .
there are currently two methods of modeling the late emission of sne ia .
one is radiation transport with complete and instantaneous trapping of the positrons .
@xcite showed , by comparing a model to the late time spectra of sn 1972e , that the ejecta will cool leading to an increased fraction of the emission coming out in the infrared , the so named infrared catastrophe " ( irc ) .
other studies of radiation transport , have reproduced the irc , but they also predict the abrupt fall off of the optical light curves as the emission shifts into the nir and ultimately into the ir , which is not seen in observed light curves .
the other method consists of positron energy deposition modeling without radiation transport . in this type of modeling ,
optical band light curves are used as tracers of the bolometric luminosity and fit to model energy deposition curves .
the results show model curves with varying degrees of positron escape fitting the light curves .
one weakness in this model fitting technique is in using the optical bands as tracers of bolometric .
@xcite constructed bolometric curves using bvri bands and showed those curves roughly fitting the positron escape energy deposition curves .
we preformed aperture photometry on six normal " sne ia at late epochs , sn 2000e , sn 2000ce , sn 2000cx , sn 2001c , sn 2001bg , sn 2001dp .
some of these sne were located in very complicated regions in their host galaxies .
for this reason , we chose to do template image subtraction , on all but sn 2000cx , before preforming the aperture photometry . all data reduction , image subtraction and aperture photometry was performed using the image reduction and analysis facility ( iraf ) software .
the combined light curves can be seen in figures [ radmodel ] & [ posmodel ] , where they are normalized to be zero magnitude at 200days past explosion assuming an 18d rise time to peak light .
the data set for sn 2000e includes photometry from @xcite , and the data set for sn 2000cx includes data from @xcite , @xcite , @xcite , and , where the data from our observations are plotted as the filled symbols .
the decline rates , the slope of the light curve , between 200 - 500 days were calculated for these light curves and the averages are shown in figure [ slopes ] , where the solid line is average for the six sne .
the calculated averages for b , v , r , & i bands were 1.43 ( 0.07 ) , 1.46 ( 0.04 ) , 1.36(0.04 ) , 0.95 ( 0.06 ) , respectively , in magnitudes per day . the shaded bar represents the average decline rate for 16 normal / super - luminous sne ia from @xcite with a @xmath3 error bar . in the r - band , there is a second average , represented by the dot - dashed line , which is the average decline rate leaving out sn 2000ce and sn 2001c .
this was done only to show the agreement with the milne et al
. averages . as shown in figure [ slopes ] ,
the b , v , & r bands have decline rates of @xmath4 mag / day but the i - band has a much shallower slope of 0.95 mag / day .
this is in agreement with the decline rates of sn 2000cx as shown by .
these results suggest that a slower i - band decline rate is a general feature of the late light curves of normal / super - luminous sne ia , and is possibly suggesting a shift in the late emission to longer wavelengths .
a major result of was the constant late time emission seen in the nir curves of sn 2000cx , which supports the idea that the emission is moving into the nir and eventually into the ir resulting in an irc .
our results from the analysis of these sne reinforce the need for more observations of sne ia in the nir in an attempt to reproduce what was seen in sn 2000cx and also in sn 1998bu ]
figure [ radmodel ] shows the combined light curves of the six sne plotted on the radiation transport models of .
the v - band model light curve has been normalized to be zero magnitude at 200d along with the data .
the b , r , & i band model light curves have been adjusted so that the colors of the model are preserved .
the dotted curve is the model including photoionization and the dot - dashed curve is the model without photoionization .
figure [ posmodel ] shows the combined light curves of the six sne plotted on the positron energy deposition curves of @xcite .
the model curves have been normalized to be zero magnitude at 200d .
the solid curve is the energy deposition with the positron kinetic energy trapped and deposited into the ejecta and the dashed curve is the energy deposition curve with a radially combed magnetic field allowing a fraction of the positrons to escape the ejecta without depositing their kinetic energy .
as can be seen in these figures , the shape of the b , v , & r band light curves could be explained by either the color evolution in the radiation transport model or the escape of positrons from the ejecta , while the i - band has a slower decline rate than both models .
this suggests that a model combining radiation transport with positron transport would be preferred to attempt to explain the late light curves of sne ia .
one thing is clear from the light curves ; these sne show very little deviation from each other in a given band , implying that within this class of normally - luminous sne ia there is only one answer for the question of positron escape from sne ia ejecta . , p. , krisciunas , k. , suntzeff , n. b. , gonz ' alez , d. , espinoza , j. , leiton , r. , rest , a. , smith , r. c. , cuadra , j. , tavenner , t. , logan , c. , snider , k. , thomas , m. , west , a. a. , gonz ' alez , g. , gonz ' alez , s. , phillips , m. m. , hastings , n. c. , mcmillan , r. , mar .
optical and infrared photometry of the unusual type ia supernova 2000cx .
pasp 115 , 277294 . , w. , filippenko , a. v. , gates , e. , chornock , r. , gal - yam , a. , ofek , e. o. , leonard , d. c. , modjaz , m. , rich , r. m. , riess , a. g. , treffers , r. r. , oct
the unique type ia supernova 2000cx in ngc 524 .
pasp 113 , 11781204 . , j. , lindahl , j. , kozma , c. , challis , p. , filippenko , a. v. , fransson , c. , garnavich , p. m. , leibundgut , b. , li , w. , lundqvist , p. , milne , p. , spyromilio , j. , kirshner , r. p. , dec .
the late - time light curve of the type ia supernova 2000cx .
a & a 428 , 555568 . , g. , di carlo , e. , massi , f. , dolci , m. , arkharov , a. a. , larionov , v. m. , pastorello , a. , di paola , a. , benetti , s. , cappellaro , e. , turatto , m. , pedichini , f. , dalessio , f. , caratti o garatti , a. , li causi , g. , speziali , r. , danziger , i. j. , tornamb , a. , oct .
optical and near - infrared photometry of the type ia supernova 2000e in ngc 6951 .
apj 595 , 779793 . | the use of type ia supernovae as cosmological tools has reinforced the need to better understand these objects and their light curves .
the light curves of type ia supernovae are powered by the nuclear decay of @xmath0 . the late time light curves can provide insight into the behavior of the decay products and their effect of the shape of the curves . we present the optical light curves of six normal " type ia supernovae , obtained at late times with template image subtraction , and the fits of these light curves to supernova energy deposition models . |
the magnetic properties of small transition metal clusters have been of growing interest in the past few years .
however , there has not been any study about the dependence on temperature so far . as shown in a large variety of papers ( e.g. refs . ) small clusters exhibit , unlike the bulk , smooth structural transformations , which one might call _ isomer hopping _ , and which occur between pure solid and fluid phases over a relatively wide temperature range , in a so - called coexistence phase . in the following
we will be concerned with the effect of those properties on the magnetic behaviour of clusters .
the basic idea is that a cluster of a specific size might have two or more structures with different magnetic moments and that these structures or _ isomer states _
occur with their statistical probability .
as shown below , this simple assumption causes a strong deviation of the paramagnetic behaviour of the magnetic susceptibility from the curie law . as an interesting feature , a dependence on the strength of an external magnetic field might occur , even at relatively small fields .
transition metal clusters seem to be natural candidates for the occurrence of such effects because of their different possible electron configurations with very similar energies , which in turn yield quite different average magnetic moments .
we consider to have @xmath0 isomers with magnetic moments @xmath1 and ground state energies e@xmath2 , calculated using an appropriate spin - density functional hamiltonian . in the presence of an external magnetic field the energy changes .
first order quantum mechanical perturbation theory yields @xmath3 where g is the land factor and the magnetic field is pointing in the @xmath4-direction ( see refs . ) .
the first term describes a paramagnet , which will be considered exclusively in what follows and can be described with a purely classical description @xcite , as @xmath5 now we are able to write down the partition function as @xmath6 indeed this is an extremely simple partition function , which can be improved to any complexity by adding all degrees of freedom of the clusters , e.g. by substituting the summation over the isomers by integration over the whole configuration space over the atomic positions or by adding a summation over different spin multiplicities of the clusters . from eq .
( [ part ] ) the average magnetic moment @xmath7 and the magnetic susceptibility @xmath8 can be calculated from eq .
( [ part ] ) easily @xcite , using @xmath9 @xmath10 if @xmath11 is taken as the number of particles per unit volume . by the dissipation - fluctuation theorem is @xmath12 . ] in the case of small magnetic fields @xmath13 h @xmath14 we get @xmath15 and @xmath16 here , @xmath17 is the partition function defined in eq .
( [ part ] ) for zero magnetic field .
( [ avchi ] ) reveals simply that @xmath8 is a linear superposition of the susceptibilities of the individual isomers weighted by their thermal probability .
the general behaviour of the paramagnetic susceptibility according to eq .
( [ avchi ] ) is plotted in fig . 1 for a hypothetical system with only two major isomer states with magnetic moments @xmath18 and @xmath19 and their energy difference @xmath20 . unlike a purely paramagnetic behaviour according to the curie law , the plots reveal local minima and maxima .
a similar behaviour has recently been experimentally found by cowen _
@xcite for fe@xmath21 clusters in supercages of nay zeolite .
the locations of the extrema only depend on the ratio between the magnetic moments @xmath22 and @xmath23e . for a given ratio @xmath22 ,
the position of the minimum depends in an almost linear fashion on @xmath23e , as can be seen in fig . 2 .
the extraordinary sensitivity of these results on @xmath23e is illustrated by the fact that a change of @xmath23e by only a few mev moves the minimum by hundreds of degrees kelvin . in fig .
3 the average magnetic moments of the canonical ensemble are plotted for various magnetic fields .
these plots reveal the fact , that in the presence of a magnetic field the occupation probability of the isomers changes dramatically due to the additional magnetic energy . if one views h to be small in the sense of eq .
( 5 ) , the magnetic susceptibility can be easily calculated .
for varying magnetic fields this calculation yields a behavior which is very similar to that of a varying ground state energy difference ( see fig . 4 ) . at first sight ,
configurations of different symmetry such as bcc versus fcc structures of fe clusters seem to be the best candidates to show the effects discussed above .
even if the energy difference between two isomers might be very small , the transition from one isomer to the other may involve a complex concerted motion of atoms and may be associated with a nonzero activation energy .
thus a thermal relaxation might take quite a long time , and a hysteresis might be observable .
lee and callaway @xcite have found interesting results for cr@xmath24 and v@xmath24 bcc clusters , which are given in table i. with varying lattice spacing the average magnetic moment changes by a factor of up to five , whereas the ground state energy changes are only @xmath25 ry / atom .
this is especially interesting since even a simple spatial expansion of the transition metal clusters intuitively is more probable than a structural transformation . from our results
we infer that it is extremely hard to obtain phenomenological results for the magnetic behaviour of clusters from spin - density functional methods , since the results depend very sensitively on ground state energy differences , which are often very small and comparable in magnitude to the precision of these _ ab initio _ methods .
in addition , for larger clusters , the number of relevant isomers increases dramatically .
nevertheless , we have shown that in the model case of two cluster isomers , the rich behaviour of the magnetic susceptibility as a function of temperature and the external magnetic field is a sensitive tool to probe structural properties of clusters . on the other hand , once the general magnetic response due to the above discussed effects is understood , one might use the susceptibility of the clusters as a very sensitive thermometer .
moreover , by applying a sufficiently strong magnetic field , one might be able to suppress one of the transition metal cluster isomers , provided the clusters have ample time for structural rearrangement .
an extended study of these effects , including specific examples , will be published elsewhere .
we thank professors cowen and dye for making their experimental data available to us prior to publication .
one of us ( dt ) acknowledges financial support by the national science foundation under grant number phy-92 - 24745 and the office of naval research under grant number n00014 - 90-j-1396 . | we investigate the magnetic properties of small transition metal clusters using a simple statistical model , which requires some input data from _ ab initio _ spin - density functional calculations . in our study , we consider a thermodynamically equilibrated ensemble of clusters with different structures , spin multiplicities , and ground state energies .
we calculate the physical properties of this system by weighting the individual configurations according to the boltzmann statistics .
we find that presence of isomers with very similar ground state energies , yet very different magnetic properties , gives rise to a rich magnetic behaviour of the system which differs significantly from what would be expected for single configurations .
we apply the present model to determine the magnetic susceptibility of a cluster ensemble of langevin paramagnets .
our results show that some of the anomalies in the magnetic behaviour of transition metal clusters might be understood in the framework of our model which is , of course , limited by the extremely high computational effort needed to obtain the input data . |
positron emission tomography ( pet ) is a nuclear imaging technique used to monitor metabolic activity of the body .
the pet system detects gamma rays generated when electrons collide with positrons emitted by radiolabelled biologically active molecules , such as fluorodeoxyglucose . in oncology , pet is widely used in diagnostics of cancer metastases , in monitoring of progress in course of the cancer treatment , and also in planning radioterapheutic interventions . in the last case , pet scans , often in combination with computer tomography ( ct ) scans ,
are used to delineate biologically active parts of tumors , which are then treated with ionizing radiation .
accurate delineation of the tumor is crucial for delivering appropriate radiation dose and minimizing adverse side - effects of the therapy .
however , the problem is not trivial as evidenced by substantial intra- and interobserver variations when delineation is performed manually by experts@xcite
. therefore it is not surprising that automated methods for accurate and reproducible delineation are sought .
in this piece of research we evaluated 3d implementations of spatial distance weighted fuzzy c - means ( sdwfcm ) of guo et al .
@xcite , dictionary - based model ( dict ) of dahl and larser @xcite and convolutional neural network ( cnn ) @xcite , and compared them to classical approaches clustering approaches : k - means ( km ) @xcite and gaussian mixture models ( gmm ) @xcite . in order to assure consistency of the input data ,
images detected to be sharper than an arbitrary threshold ( after convolution with the 3d laplacian kernel ) were slightly blurred using the gaussian filter .
the step was omitted in the gmm and cnn case . in order to clean resulting labels from small artifacts ,
the labels were subject to subsequent morphological opening and closing , except the cnn method .
we used @xmath0 implementations of km and gmm methods .
the method is a spatial information - aware extension of the fuzzy c - means clustering algorithm ( fcm ) @xcite .
both methods assign to each point a coefficient of belonging to one of @xmath1 clusters .
similarly to fcm , sdwfcm starts by calculating cluster centers and euclidean distances based on regular features ( such as image intensity ) .
however , in the next step the distance matrix is modified with weight based on spatial distance of each pixel to the cluster center .
then , coefficients of belonging are calculated based on the modified distance matrix .
the procedure repeats until convergence or maximum runtime .
finally the tumor label is assigned to @xmath2 most intense clusters .
parameters for the sdwfcm algorithm ( as well as for km and gmm ) were optimized for the training set ( see tabl .
[ results ] and ref .
@xcite ) .
the general idea of the method is to assign each patch of the test image , the label which corresponds to the most similar patch in the dictionary .
the dictionary , which consists of a set of patch - label pairs is built in two steps .
first , a sample of training patches is used to seed the dictionary .
based on the label similarity threshold , similar patches are clustered and averaged . then , a version of the vector quantization technique is used to adjust the dictionary patches such that real labels of its matches are as close to binarized dictionary labels ( also adjusted in the training ) .
finally , the labeling algorithm assigns binary labels of the most similar dictionary patch . in our implementation
, the labeling window walks pixel by pixel and each pixel gets the label of the best fitting patch or an average label , which is then binarized using the final labeling threshold @xmath3 .
dict was set up with the following parameters : 3x3x3 patches were utilized , 10% of the training patches were used to seed the dictionary using similarity threshold 0.5 ; all training patches were used for adjusting the dictionary in 10 iterations with the step coefficient @xmath4 0.05 ( see ref .
@xcite ) .
deep convolutional neural networks have proved to be one of the most efficient tools in image processing . for the tumor delineation problem we tested many cnn architectures consisting of up to dozen layers , including three or four convolutional layers .
the input of the network was a batch of 2d or 3d patches from the pet tumor images .
the network was trained using the adagrad stochastic gradient descent algorithm @xcite , which aimed at minimizing the euclidean distance between the output of the final layer of the network and the ground truth . to account for a relatively small number of training samples , the set of available data
was artificially augmented with rotationally transformed samples .
the best architecture , selected in the 5-fold cross - validation process , was the 3d convolutional neural network with 3 convolutional layers followed by relu activations with ascending number of filters ( fig . 1 ) .
[ figcnn ] , activ @xmath5 - activation layer with function @xmath5.,width=432 ]
the training dataset provided by organizers of the petseg challenge consisted of 4 scans from 3 clinical samples , 9 scans from 3 phantoms and 6 simulated scans in 2 sets .
we assessed efficiency of the methods on the training set in terms of the dice coefficient . as the scores were calculated on the training set , they are rather upper estimates of the real performance of the methods .
.*dice coefficients for training data . *
notations : km - k - means , gmm - gaussian mixture model , sdwfcm - spatial distance weighted fuzzy c - means , dict - dictionary - based model , cnn - convolutional neural network ; @xmath6/@xmath7/@xmath1 - number of clusters , @xmath2 - number of selected most intense clusters , @xmath8 - degree of fuzzy classification , @xmath9 - weight of spatial features , @xmath10 - number of neighbours . [
cols="<,<,>,>,>,>,>,>",options="header " , ] the best results were obtained using cnn ( dice score mean : 0.86 , median : 0.89 ) .
the remaining methods performed slightly worse than cnn and similarly to each other ( dice score mean : 0.82 - 0.83 , median : 0.81 - 0.83 ) . in general , simulated data proved to be the easiest ( mean dice score 0.88 - 0.91 ) , while clinical data were the hardest ( mean dice score 0.76 - 0.78 ) , regardless the method . a single most difficult case was _
clinical_1 _ for which none of the algorithms exceeded dice score of 0.69 .
it is of note , that the gaussian blurring had a positive impact on segmentation of this case .
clinical_1 , clinical_3 _ and _ phantom_2.1 _ were the only cases where cnn did not reach dice score of 0.80 .
interestingly , cnn was always better than other methods for phantom data , with average margin over the second best result of almost 7% .
looking more into details , cnn and dict achieved the highest sensitivity ( 0.89 and 0.85 , respectively ) , while sdwfcm achieved the highest precision ( 0.85 ) . in accordance with these results ,
cnn and dict were more prone to overestimate the total volume of the tumor ( on average by 10% ) , while sdwfcm lined towards underestimated volumes ( on average by 3% ) .
all methods overestimated the volume of _
( by 30 - 49% ) , _ phantom_2 _ ( 9 - 58% ) and _ phantom_3 _ ( 8 - 47% ) , while the volume of _
clinical_3 _ was generally underestimated ( 12 - 26% ) .
interestingly , while cnn was the method which overestimated the volume of clinical samples the most ( 22% ) , its volume predictions were closest to the ground truth for the phantoms ( + 9% ) .
accordingly , the contour mean distance of cnn predictions was the worst for clinical samples ( 2.28 in comparison to 1.81 by dict ) , and the best for phantom samples ( 0.72 in comparison to 1.30 by dict ) .
overally , our early results suggest that deep convolutional neural networks can enable a step forward also in the pet image segmentation .
this claim should be further validated with more testing , especially on clinical samples , for which performance gain using cnn was less impressive than for phantom data .
this research has been conducted under the support programme of the partnership between higher education and science and business activity sector financed by city of wroclaw .
the authors thank jakub szewczyk for his help with preparing the manuscript , and piotr krajewski for continuous support of the project . | in oncology , positron emission tomography imaging is widely used in diagnostics of cancer metastases , in monitoring of progress in course of the cancer treatment , and in planning radiotherapeutic interventions .
accurate and reproducible delineation of the tumor in the positron emission tomography scans remains a difficult task , despite being crucial for delivering appropriate radiation dose , minimizing adverse side - effects of the therapy , and reliable evaluation of treatment . in this piece of research we attempt to solve the problem of automated delineation of the tumor using 3d implementations of the spatial distance weighted fuzzy c - means , the deep convolutional neural network and a dictionary model .
the methods , in diverse ways , combine intensity and spatial information . |
the authors are grateful to the useful discussion with hsien - chung kao and shoichi kawamoto in the early stage of this work .
wyw would like to thank the warm hospitality received in the ustc , china when part of this work was presented in the east asia joint workshop on fields and strings and insightful discussion with sang - jin sin .
this work is supported in parts by the chung yuan christian university , the taiwan s ministry of science and technology ( grant no .
102 - 2112-m-033 - 003-my4 ) and the national center for theoretical science .
in this appendix , we will derive the relation among parameters @xmath74 in the warping factors : one can freely absorb the combination @xmath80 into redefinition of @xmath14 , that is to set @xmath81 .
furthermore one can eliminate @xmath82 by a choice of regularization scheme , such that all the divergent terms to be _
@xmath14-independent _ in the onshell action of gravity sector . in the other words
, one would use the same counterterm in both confinement and deconfinement phases . to be specific
, the onshell action reads j. m. maldacena , int .
j. theor .
phys . * 38 * , 1113 ( 1999 ) [ adv .
* 2 * , 231 ( 1998 ) ] doi:10.1023/a:1026654312961 [ hep - th/9711200 ] .
s. s. gubser , i. r. klebanov and a. m. polyakov , phys .
b * 428 * , 105 ( 1998 ) doi:10.1016/s0370 - 2693(98)00377 - 3 [ hep - th/9802109 ] .
e. witten , adv .
theor . math .
* 2 * , 253 ( 1998 ) [ hep - th/9802150 ] .
s. s. gubser , class .
. grav . * 22 * , 5121 ( 2005 ) doi:10.1088/0264 - 9381/22/23/013 [ hep - th/0505189 ] .
s. s. gubser , phys .
d * 78 * , 065034 ( 2008 ) doi:10.1103/physrevd.78.065034 [ arxiv:0801.2977 [ hep - th ] ]
. s. a. hartnoll , c. p. herzog and g. t. horowitz , phys .
* 101 * , 031601 ( 2008 ) doi:10.1103/physrevlett.101.031601 [ arxiv:0803.3295 [ hep - th ] ] .
s. s. gubser , phys .
* 101 * , 191601 ( 2008 ) doi:10.1103/physrevlett.101.191601 [ arxiv:0803.3483 [ hep - th ] ] .
e. nakano and w. y. wen , phys .
d * 78 * , 046004 ( 2008 ) doi:10.1103/physrevd.78.046004 [ arxiv:0804.3180 [ hep - th ] ] . t. albash and c. v. johnson , jhep * 0809 * , 121 ( 2008 ) doi:10.1088/1126 - 6708/2008/09/121 [ arxiv:0804.3466 [ hep - th ] ] . s. a. hartnoll , c. p. herzog and g. t. horowitz , jhep * 0812 * , 015 ( 2008 ) doi:10.1088/1126 - 6708/2008/12/015 [ arxiv:0810.1563 [ hep - th ] ] . m. kruczenski , d. mateos , r. c. myers and d. j. winters , jhep * 0405 * , 041 ( 2004 ) doi:10.1088/1126 - 6708/2004/05/041 [ hep - th/0311270 ] .
t. sakai and s. sugimoto , prog .
phys . * 113 * , 843 ( 2005 ) doi:10.1143/ptp.113.843 [ hep - th/0412141 ] .
j. erlich , e. katz , d. t. son and m. a. stephanov , phys .
* 95 * , 261602 ( 2005 ) doi:10.1103/physrevlett.95.261602 [ hep - ph/0501128 ] .
l. da rold and a. pomarol , nucl .
b * 721 * , 79 ( 2005 ) doi:10.1016/j.nuclphysb.2005.05.009 [ hep - ph/0501218 ] .
o. aharony , j. sonnenschein and s. yankielowicz , annals phys . * 322 * , 1420 ( 2007 ) doi:10.1016/j.aop.2006.11.002 [ hep - th/0604161 ] .
c. p. herzog , phys .
lett . * 98 * , 091601 ( 2007 ) doi:10.1103/physrevlett.98.091601 [ hep - th/0608151 ] . s. w. hawking and d. n. page , commun .
* 87 * , 577 ( 1983 ) .
doi:10.1007/bf01208266 y. nambu , phys . rev . * d10 * , ( 1974 ) 4262 j. w. chen , y. j. kao and w. y. wen , phys . rev .
d * 82 * , 026007 ( 2010 ) doi:10.1103/physrevd.82.026007 [ arxiv:0911.2821 [ hep - th ] ] .
t. faulkner , g. t. horowitz , j. mcgreevy , m. m. roberts and d. vegh , jhep * 1003 * , 121 ( 2010 ) doi:10.1007/jhep03(2010)121 [ arxiv:0911.3402 [ hep - th ] ] .
s. s. gubser , f. d. rocha and p. talavera , jhep * 1010 * , 087 ( 2010 ) doi:10.1007/jhep10(2010)087 [ arxiv:0911.3632 [ hep - th ] ] .
g. t. horowitz and m. m. roberts , phys .
d * 78 * , 126008 ( 2008 ) doi:10.1103/physrevd.78.126008 [ arxiv:0810.1077 [ hep - th ] ] .
r. hofmann , int .
j. mod .
a * 20 * , 4123 ( 2005 ) doi:10.1142/s0217751x06035129 , 10.1142/s0217751x05023931 [ hep - th/0504064 ]
. t. faulkner , h. liu , j. mcgreevy and d. vegh , phys .
d * 83 * , 125002 ( 2011 ) doi:10.1103/physrevd.83.125002 [ arxiv:0907.2694 [ hep - th ] ] .
d. b. kaplan , j. w. lee , d. t. son and m. a. stephanov , phys .
d * 80 * , 125005 ( 2009 ) doi:10.1103/physrevd.80.125005 [ arxiv:0905.4752 [ hep - th ] ] .
w. y. wen , phys .
b * 707 * , 398 ( 2012 ) doi:10.1016/j.physletb.2011.12.053 [ arxiv:1009.3952 [ hep - th ] ] .
m. unsal , phys .
d * 80 * , 065001 ( 2009 ) doi:10.1103/physrevd.80.065001 [ arxiv:0709.3269 [ hep - th ] ] . | we show that a hairy black hole solution can provide a holographically _ dual _ description of quark confinement .
there exists a one - parameter sensible metric which receives the backreaction of matter contents in the holographic action , where the scalar and gauge field are responsible for the condensation of chromomagnetic monopoles .
this model features a preconfining phase triggered by second - order monopole condensation and a first - order confinement / deconfinement phase transition . to confirm the confinement ,
the quark - antiquark potential is calculated by probing a qcd string in both phases . at last ,
contribution from kaluza - klein monopoles in the confining phase is discussed .
the holographic correspondence between a gravitational theory in the bulk and a quantum field theory on the boundary , first emerged under the anti - de sitter / conformal field theory ( ads / cft ) correspondence @xcite , has been proved useful to study condensed matter phenomena . in particular , the authors in @xcite proposed a gravity model in which abelian symmetry of higgs is spontaneously broken by the existence of black hole , also known as hairy black hole .
this mechanism was incorporated in the model of superconductivity and critical temperature was observed @xcite .
this model was later studied in the presence of magnetic field @xcite and with full backreaction @xcite .
on the other hand , the ads / cft analogy has also explained many qualitative and quantitative features of confining gauge theories like qcd , either by engineering branes and strings in the ten dimensional string theory @xcite , or by bottom - up construction of a randall - sundrum like background @xcite .
in particular , holographic models of deconfinement were first discussed in the sakai - sugimoto model at finite temperature@xcite and the hard / soft wall model@xcite . in all cases , the confinement / deconfinement transition is identified as the first - order hawking - page phase transition , where the thermal ads is energetically favored at low temperature , while a black hole solution at high temperature @xcite . in this paper
we propose the first holographic confinement model without using the hawking - page phase transition .
we recall an old but appealing proposal of dual superconductor @xcite , stating that the confining phase can be regarded as a dual type ii superconducting state due to the condensation of chromomagentic charges ( monopoles ) , such that the chromoelectric lines between a quark - antiquark pair are squeezed by dual meissner effect into flux tubes , as known as the qcd strings .
one may wonder if the hairy black hole scenario in the holographic model of dual superconductor@xcite works just fine by trivially replacing cooper pairs by monopole condensate , and the backreacted metric in the @xcite might be the confinement geometry in desire .
however , a second thought and straightfoward computation will show this is not the case .
the backreaction of condensate may have resulted to a gapped excitation as shown in the single electron spectral function @xcite , but the attractive force mediated by phonons is coulomb - like , rather than a linear potential for flux tube in the dual picture .
then the challenging task is to find out the appropiate ansatze which can produce the linear potential while condensation occurs . in this letter
, we consider a @xmath0-dimensional dual supercondcutor model which has a holographic description of eisntein - maxwell - dilaton gravity theory in the ads@xmath1 .
the action is composed of a gravity sector @xmath2 , a matter sector @xmath3 for massive scalars and a dual @xmath4 gauge field sector @xmath5 as follows : @xmath6 we will study a class of metric of following general form : @xmath7 with @xmath8\nonumber\\ & g_{1}(z)=\frac{exp(\beta ( p z / z_{h})^2)}{z^2}\frac{1}{1-(\frac{z}{z_{h}})^3}\nonumber\\ & g_{2}(z)=\frac{exp(\gamma ( p z / z_{h})^2)}{z^2}\end{aligned}\ ] ] the metric corresponds to a hairy black hole with a flat horizon at @xmath9 and approaches asymptotically to ads as @xmath10
. one can show by explicit calculation that the oversimplified ansatz @xmath11 , which was adopted in the backreacted holographic superconductor such as one in @xcite , is unable to produce the linear potential in the confining phase .
as shown in the appendix , the warping factors can be further pinned down to @xmath12 and @xmath13 after imposing the condition that the onshell action of gravity sector is independent of the choice of @xmath14 after regularization .
the total free energy is given by summing up onshell action of all sectors and the value of @xmath14 is determined by minimizing the total free energy at a given temperature .
the variable @xmath15 , on the other hand , is a free parameter , which can be fine tuned to match the tension of flux tube . in practice ,
the desirable onshell action of gravity sector @xmath2 should have local minimum only at @xmath16 , which happens as @xmath15 is within some range as shown in the figure [ alpha_value ] . for different @xmath15 .
the blue , green , purple , yellow curves correspond to @xmath17 - 0.6 , 0 , 0.2 and 1 , respectively .
it is obvious that the blue ( @xmath18 ) and yellow ( @xmath19 ) curves are undesirable since that they have additional local minimum at some @xmath14 other than @xmath20.,width=302 ] in the deconfining phase , the solution ( [ ansatz ] ) reduces to the ads schwarzschild black hole , while confining parameter @xmath14 is zero and the oneshell actions of scalar and gauge sectors are trivially zero .
as temperature decreases , one expects a transition to the confining phase as the the black hole develops hairs after receiving backreaction from condensate . the scalar field , which represents the order parameter of chromomagnetic charge condensate , poccesses the asymptotical form : and confining parameter @xmath14 at different temperatures .
those curves associated to temperature above @xmath21 usually exhibit a cusp at @xmath22 and a cutoff at @xmath23 , in between the monopole condensation occurs .
the blue , purple , yellow and green curves correspond to the scaled temperatures @xmath24 at 1.0 , 1.1 , 1.2 , 1.3 , respectively .
one observes competition between local minima @xmath25 ( confining phase ) and @xmath16 ( deconfining phase ) at the temperature @xmath26 , which is between @xmath27 and @xmath28 , signaling a preconfining phase .
there is only a confining phase when temperature is below @xmath21 .
here we set @xmath29 , @xmath30 and @xmath31 for simulation .
, width=302 ] @xmath32 with @xmath33 , where @xmath34 and @xmath35 are interpreted as source and condensate , respectively .
we remark that one can also switch the role of source and condensate for a scalar field in asymptotical ads@xmath1 .
that would correspond to the condensate of operators with scaling dimension @xmath36 .
the chemical potential @xmath37 and charge density @xmath38 can be read out from the asymptotic form of gauge field : @xmath39 in our simulation , the same boundary conditions adopted in the @xcite are imposed , that is , @xmath40 and @xmath38 is fixed at the asymptotic boundary and @xmath41 at the horizon .
the condensate @xmath42 and chemical potential @xmath37 are obtained numerically by the shooting methods .
the phase transition is justified by evaluation of the total onshell action against confining parameter @xmath14 at different temperatures . in the figure [ onshell_action ]
, we see that the confining phase ( local minimum at @xmath25 ) is energetically favored at and below the critical temperture @xmath21 .
the preconfining phase appears when two local minima @xmath16 and @xmath25 competes with each other during @xmath43 .
the confinement / deconfinement phase transition occurs around @xmath26 when the local minimum @xmath16 starts to dominate .
each onshell curve with temperature above @xmath21 exhibits a cusp at @xmath44 and a cutoff .
the cusp is generated by nontrivial condensate @xmath42 , which occurs when @xmath45 .
there is no ground state solution for the scalar @xmath46 above the cutoff . since confinement appears only when monopoles condensate
, one can conclude that the former phase transition is directly triggered by the latter in the dual superconductor model .
our model shows that @xmath47 and predicts the existence of preconfining phase with a fraction window @xmath48 .
we remark that the preconfing phase did not appear in the previous model@xcite and our result agrees with observation in some nonperturbative approach to thermal @xmath49 yang - mills theory @xcite .
although the dual superconductor model is the an effective ginzburg - landau theory which describes a second - order phase transition for the monopole condensate , we argue that the confinement / deconfinement phase transition in our hairy black hole model is of first order .
this is because temperature in our model is not only determined by the horizon but also the hair , that is @xmath50 the sudden shift of parameter @xmath14 at the transition causes a discontinuous jump of horizon position @xmath51 and therefore a first - order phase transition .
is plotted against the seperation between string end points on the boundary . in the static configuration
, the action can be regarded as the potential between a heavy quark - antiquark pair . in the deconfinement phase ,
the coulomb potential ( red , lower branch ) is terminated as the string is _ sucked _ into the black hole ( red , upper branch ) . in the confinement phase , the linear potential ( blue ) dominates as seperation distance increases .
, title="fig:",width=302 ] is plotted against the seperation between string end points on the boundary . in the static configuration
, the action can be regarded as the potential between a heavy quark - antiquark pair . in the deconfinement phase ,
the coulomb potential ( red , lower branch ) is terminated as the string is _ sucked _ into the black hole ( red , upper branch ) . in the confinement phase
, the linear potential ( blue ) dominates as seperation distance increases . , title="fig:",width=302 ] in the imhomogenous background where monopole condensate occurs locally , one may expect both confinement and deconfinement coexist in different regions and the color force lines are squeezed thanks to the dual meissner effect .
one can further confirm both the confinement and deconfinement background by probing a string of profile @xmath52 , given by the nambu - goto action @xmath53 and @xmath38 ( black curve ) in the @xmath54-@xmath46 plane . by calculating the wavefunction @xmath55 at each intersecting point , we find they correspond to the ground state ( @xmath56 , blue curve ) , first excited state ( @xmath57 , pruple curve ) , and second excited state ( @xmath58 , brown curve ) , respectively . from viewpoint of boundary theory ,
those excited modes are the kaluza - klein ( kk ) monopoles with heavier mass .
we use contour curves @xmath59 and @xmath30 , parameters @xmath31 , and @xmath60 for this simulation.,width=377 ] the string profile in the gravity bulk is plotted against the seperating distance in the left figure [ string ] . with increasing seperation , the u - shaped string eventually touches the horizon and breaks in the presence of hairless black hole , indicating the deconfinement phase . in the confining phase
, the string can not enter the infared core of bulk in the presence of hairy black hole and stay near @xmath61 .
the horizontal segment of string is responsible to the linear potential .
we remark that string in the confining phase can not break without introducing additional dynamic degrees of freedom .
the onshell string action can be regarded as the free energy or potential of static heavy quark - antiquark pair , which is plotted against the seperation distance @xmath62 in the right figure [ string ] . in the deconfining phase , though it exhibits a coulomb potential for small seperation , no force exists for seperation @xmath63 in the unit @xmath64 because the string is eventually pulled into the black hole . in the confining phase , on the other hand
, a linear potential has already manifested for seperation @xmath65 .
-excited state can be approaximated by the relation @xmath66 .
( right ) the plot on the right shows the condensate ratio @xmath67 for each kk monopole , title="fig:",width=302 ] -excited state can be approaximated by the relation @xmath66 .
( right ) the plot on the right shows the condensate ratio @xmath67 for each kk monopole , title="fig:",width=302 ] at last , we would like to address a possible role played by excited modes of scalar hair in the confining phase . as demonstrated in the figure [ excitemode ] ,
multiple solutions exist as temperature well below the critical temperature of condensation .
those solutions correspond to those wavefunctions @xmath55 with @xmath68 nodes , or excited states . from the point of view of ads
bulk , the tower of excited modes might be related to the efimov states due to loss of conformality @xcite . from viewpoint of dual theory on the boundary ,
those excited states are the kaluza - klein ( kk ) monopoles with effective mass which grows with mode number @xmath68 . in the figure [ monopole ]
, we plot the critical temperature @xmath69 and condensate @xmath70 for the first five kk modes .
we observe that the a @xmath68-order kk monopole can only be excited at temperature lower than @xmath69 .
the measured monopoles mass @xmath71 would be proportional to the expectation value of condensate @xmath70 from all avaliable kk modes up to @xmath72 at some temperature , that is @xmath73 . as a result , an increase in monopole mass @xmath71 is expected as temperature moves away from the critical point in the confining phase thanks to the growing @xmath72 .
we remark that the kk monopole was condisered as part of a magnetic bion condensation in some qcd - like theory@xcite . in conclusion , we are among the first to construct a holographic model of quark confinement by chromomagnetic monopole condensation .
this toy model features a second - order monopole condensation as well as first - order confinement / deconfinement phase transition , and it predicts a preconfining phase , which is mostly unseen in the previous holographic construction but observed in other nonperturbative approach .
finally we hypothesize that excited modes of condensate might contribute to the increasing monopole mass in the confining phase .
our noval result has provided supportive evidence for the application of holographic method and serves as a toy model toward the quark confinement in realistic qcd . |
recent surveys have found a significant population of low - mass stars , brown dwarfs and planetary - mass objects in young open clusters . since low - mass objects evolve little over the lifetime of the universe , the present day mass function of these objects is a good representation of the initial mass function ( imf ) .
the mass function in this low - mass regime is however poorly known due to faintness of these objects and also due to uncertainty in the mass - luminosity relations .
low - mass objects at or below the hydrogen burning mass limit ( hbml ) of 0.08 m@xmath2 are known to be warmer and hence more luminous when young although they cool rapidly and fade with age ( baraffe et al . 1998 ) .
the combination of youth and proximity in some open clusters make them ideal targets for searches of low - mass objects below the hbml particularly at infrared wavelengths . in the present study
we have adopted a statistical approach to determine the mass function ( dn / dm @xmath4 m@xmath5 ) of objects in the mass range @xmath6 to 0.0250.05 m@xmath2 using data of three open clusters namely ic 348 , @xmath0 orionis and pleiades .
we have used the data from two extended sky surveys 2mass second incremental release and the latest version of gsc on the three open clusters .
the limiting magnitudes of 16.5 , 15.5 , 15 and 21 in the @xmath7 , @xmath8 , @xmath9 and @xmath10 ( poss ii iiia - f ) passbands , respectively , enable us to probe down to 0.025 m@xmath2 in ic 348 and @xmath0 orionis and 0.04m@xmath2 in pleiades . unlike most other previous studies which rely on confirming candidate low - mass objects through spectroscopy we use a statistical approach to estimate the number of low - mass objects . in this approach
it is important to use several control fields close to each cluster to subtract the contribution of foreground and background objects .
the nature of these two extended surveys permitted us to use several control fields and variable field sizes .
table 1 lists the positions and radii of the fields chosen for the three clusters .
lllcl + fields&ra ( j2000)&dec ( j2000)&radius + & ( h m s ) & ( @xmath11 @xmath12 @xmath13)&(arcmin ) + ic 348&03 44 30&+32 17 00&20 + control 1&03 49 08&+31 19 08&20 + control 2&03 44 10&+33 19 26&20 + & + @xmath0 orionis&05 38 45&02 36 00&30 + control 1&05 58 29&04 29 48&30 + control 2&0.5 11 00&00 20 00&30 + & + pleiades&03 47 00&+24 07 00&90 + control 1&03 18 00&+26 41 00&90 + control 2&03 05 00&+24 42 00&90 + in the first stage of analysis we merged the 2mass and the gsc sources by taking 2mass coordinates and cross correlating them with the gsc catalogue .
a search radius of 2was found to be the optimum value for the cross correlation being small enough to reject spurious and multiple detections and large enough to include any minor positional uncertainties in the two catalogues . selection criteria to pick out cluster members were derived by inspecting various colour magnitude diagrams ( cmds ) .
the use of the f versus ( f r ) cmd overcomes the degeneracies between the mass and distance found in the k@xmath14 versus ( j k@xmath14 ) cmd , and minimizes the overlap between reddened background stars and low - mass members of the cluster .
this leads to a more efficient rejection criteria for non members which is accomplished using the empirical data from leggett ( 1992 ) and the theoretical isochrones of baraffe et al .
the selection criteria for low - mass members , derived using the suitably distance - scaled and extinction corrected model isochrones of baraffe et al .
( 1998 ) , are listed in table 2 .
the sources satisfying the criteria are further statistically filtered for possible contaminants using the control fields .
details of the procedure are discussed in tej et al .
finally , the masses of the selected candidates are determined by comparing observed magnitudes with those derived from evolutionary models ( baraffe et al .
1998 and chabrier et al .
2000 ) .
llll + ic 348&@xmath0 orionis&pleiades + @xmath15&@xmath16&@xmath17 + + 10.14 ] & + 10.26]&@xmath18 + & & @xmath19 $ ] + @xmath20&@xmath21&@xmath22 + @xmath23 & @xmath24 & @xmath25 + @xmath26 0.90&@xmath26 0.94&@xmath26 0.83 + @xmath27 0.20&@xmath27 0.20&@xmath27 0.22 + = 10truecm
we first carried out a detailed study for ic 348 . for this cluster , we derived the mass function using the solar metallicity models of baraffe et al ( 1998 ) and dusty models of chabrier et al .
( 2000 ) both of which gave similar results .
the location of low - mass members isolated by us and the spectroscopically confirmed low - mass members of luhman ( 1999 ) are in good agreement which builds the confidence in our selection criteria .
we then used the same methodology for @xmath0 orionis and pleiades .
the resulting exponents of the mass functions for ic 348 , @xmath0 orionis and pleiades are respectively 0.7 , 1.2 and 0.5 with an estimated error of @xmath28 0.2 . for the younger clusters ic 348 and @xmath0 orionis , there is some hint of a possible dip in the mass function at the position of the hbml . the results of this statistical approach ( table 3 )
imply that though the mass function continues to rise above the hbml it is appreciably flatter compared to the salpeter mass function . in figure 1 we have plotted the derived mass function for the three clusters . taking the canonical salpeter exponent of 2.35 in the mass range 110 m@xmath2 , the chabrier exponent of 1.55 in the mass range 0.51.0 m@xmath2 and the values obtained by us below 0.5 m@xmath2 we estimate the mass contribution to be about 40% for objects below 0.5 m@xmath2 and 4% for objects below the hbml of 0.08 m@xmath2 .
our results are consistent with previous studies ( e.g. bjar et al . , 2001 ) and suggest that although low - mass objects are at least as numerous as their stellar counterparts their contribution to the total mass of the cluster is small .
we would like to thank brian mclean and mario lattanzi ( gsc - ii project scientists ) for access to the development version of gsc - ii in advance of publication .
we are grateful to i. baraffe and f. allard for making electronic versions of the latest models available and generating model isochrones for the nonstandard f passbands .
baraffe , i. , chabrier , g. , allard , f . , & hauschildt , p.h .
1998 , a&a , 337 , 403 bjar , v.j.s . ,
martin , e.l . ,
zapatero osorio , m.r .
, et al . 2001 , apj , 556 , 830 chabrier , g. , baraffee , i. , allard , f. , & hauschildt , p.h .
2000 , apj , 542 , 464 leggett , s.k .
1992 , apjs , 82 , 351 luhman , k. l. 1999 , apj , 525 , 466 tej a. , sahu , k.c .
, chandrasekhar , t. and ashok , n.m .
2002 apj ( in press ) ( astro - ph/0206325 ) | we present a statistical method to derive the mass functions of open clusters using sky survey data such as the 2 micron all sky survey ( 2mass ) and the guide star catalogue ( gsc ) .
we have used this method to derive the mass functions in the stellar / substellar regime of three young , nearby open clusters , namely ic 348 , @xmath0 orionis and pleiades .
the mass function in the low mass range ( m@xmath1 ) is appreciably flatter than the stellar salpeter function for all three open clusters .
the contribution of objects below 0.5 m@xmath2 to the total mass of the cluster is @xmath340% and the contribution of objects below 0.08 m@xmath2 to the total is @xmath34% .
# 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in |
heavy meson hadronic matrix elements play an essential role in determining many of the parameters of the standard model , such as the ckm matrix elements .
theoretically , lattice gauge theory provides a means of computing these hadronic matrix elements with better control of systematic errors @xcite .
the heavy quark methods that have been successfully used on the lattice are : sheikholeslami - wohlert ( sw ) action , nonrelativistic qcd , heavy quark effective theory ( hqet ) and fermilab action . here
we focus on the fermilab action because it may best control the systematic errors associated with the large quark mass .
renormalization of lattice operators is necessary in order to obtain physical results from numerical simulations .
non - perturbative renormalization ( npr ) methods are attractive since they avoid possibly large errors associated with lattice perturbation theory .
this is especially important when domain wall fermions are used for the light quarks . among various npr methods ,
we decide to focus on ri / mom scheme npr @xcite , because of the promising results @xcite reported by the rbc collaboration .
we will use npr to represent the ri / mom scheme npr method in the rest of this paper .
our goal is to adopt the ri / mom scheme and to extend its application to heavy quarks .
in particular we will show how to generalize the usual npr `` window restriction '' : @xmath0 to the kinematic region required by the fermilab approach to heavy quarks .
we need to find a new renormalization region , which meets three requirements : i ) it permits evaluation in continuum perturbation theory .
thus , it should involve non - exception external momenta , giving no infrared singularities as light quark and gluon masses are set to zero .
ii ) the fermilab method remains valid , i.e. the region is not too far from the heavy quark mass pole .
iii ) it can be studied using a euclidean , lattice green s function .
let s take a look at a typical feynman diagram with a one loop qcd correction integral , for example , that shown in figure [ fig : feynman ] , with the integral @xmath1 here q is the internal gluon momentum and @xmath2 is the net external quark momentum flowing into @xmath3 internal quark line within the loop .
-0.2 in -7 mm the denominator of the @xmath3 quark line , with minkowski external momenta but euclidean loop momentum is @xmath4 .
since @xmath5 may be small , it does nt guarantee that we can avoid the pole on the @xmath6 axis during integration .
therefore , additional conditions have to be set to avoid singularities and permit the use of continuum perturbation theory .
specifically , we require that the absolute value of each denominator be much larger than @xmath7 .
let s first check our formalism with a massless quark .
we find that @xmath8 , which is consistent with the the original npr method for light quarks .
how about heavy quarks ?
we propose : @xmath9 . in order to keep fermilab discretization errors under control
, we have to constrain the above quantity to be much smaller than @xmath10 as well so that the heavy quark lines remain nearly on - shell .
therefore , our `` window '' of renormalization is @xmath11 .
-7 mm figure [ fig : q_sq_plane ] is a plot in complex @xmath12 plane .
our choice of renormalization points are located within the small region circled .
the distance from this circled region to the mass pole has to be much smaller than @xmath13 and much larger @xmath7 for perturbation theory to be valid .
this is what i mean by `` slightly off - shell condition '' in the rest of the paper .
note that the region we choose is time - like , while the usual npr s choice is space - like . why do we pick a time - like point , instead of a space - like point ?
the constraint comes from the fermilab action , which is an on - shell o(a ) improvement .
if we choose a deep , space - like point , the well - behaved properties of fermilab action would no longer be valid .
recall `` heavy quark '' means the product of @xmath14 and lattice spacing @xmath15 may be larger than or equal to 1 . under this circumstance , it s natural to expect an improved action to break the time - space symmetry .
here is the original fermilab action @xcite : @xmath16 \nonumber\\ & -&\hskip -0.15 in \kappa_s \sum_{n , i } [ \bar{\psi}_n ( r_s-\gamma_i ) \textsl{u}_{n , i } + \bar{\psi}_{n+\hat{i } } ( r_s+\gamma_i ) \textsl{u}_{n , i}^\dag \psi_n ] \nonumber \\ & + & \hskip -0.15 in \frac{i}{2 } c_{b } \kappa_{s } \sum_{n;i , j , k } \varepsilon_{ijk } \bar{\psi}_{n } \sigma_{ij } b_{n;k } \psi_{n } \nonumber \\ & + & \hskip -0.15 in ic_{e } \kappa_{s } \sum_{n;i } \bar{\psi}_{n } \sigma_{0i } e_{n;i } \psi_{n } % \end{equation}\end{aligned}\ ] ] note that those coefficients are the functions of @xmath17 , and are expected to remain finite for both small and large @xmath17 .
what happens when we go slightly off - shell ?
if the external quark masses differ from the physical ones by a small amount @xmath18 , with @xmath19 then the resulting errors will be no larger than the other discretization errors in the fermilab approach .
however , when we go off - shell , we have to include more terms to make the o(a ) improvement complete .
because contact terms and new non - gauge - invariant operators can appear . ) first , we have to add o(a ) off - shell improvement terms in the action .
fortunately , those terms which need to be added in the action can be compensated by improving the quark fields @xcite .
therefore , the action itself remains the same , including the well - behaved coefficients .
the improved quark fields will look similar to those in ref @xcite , but with broken space - time symmetry .
likewise for the composite operators .
the broken symmetry gives us at least double the number coefficients to be determined non - perturbatively , compared with the light quark cases .
we are still exploring how these coefficients may be determined in a more efficient way .
to respect the `` slightly off - shell condition '' , we need to change the time - component fourier transformation to laplace transformation .
take the operator @xmath20 as an example , for a general dirac matrix @xmath21 . the non - amputated green s function in momentum space
is : @xmath22 where @xmath23 .
we calculate the amputated green s function and apply the projector onto @xmath24 to define : @xmath25,\end{aligned}\ ] ] where the s(pa ) is the gauge - averaged propagator . following the usual npr procedure ,
we apply the renormalization condition : @xmath26 where @xmath27 represents tree - level value .
thus , imposing @xmath28 will determine the renormalization factor @xmath29 .
our lattice npr calculations are done in the ri renormalization scheme .
we need continuum ri renormalization calculations to match to physical values given in the continuum @xmath30 scheme .
the previous matching calculations done at @xmath31 , while taking @xmath32 must be extended to our new scheme .
let s take a look at the simplest example : the calculation of @xmath33 and @xmath34 .
our new renormalization conditions become : @xmath35_{m^2-p^2 = \mu^2 } = 1\end{aligned}\ ] ] @xmath36_{m^2-p^2= \mu^2 } = 1\end{aligned}\ ] ] where @xmath37 $ ] .
the calculations are done in the dimensional regularization scheme , where d is 4 - 2@xmath38 . here
are the matching factors for @xmath34 and @xmath33 in the ri and @xmath30 schemes : @xmath39ln \frac{m^2}{\mu^2}\nonumber \\ & + & \hskip -0.15 in ln\frac{\mu'\;^2}{\mu^2 } ( 3 + 2\xi ) \ } + o(\alpha_s^2)\end{aligned}\ ] ] @xmath40 where @xmath41 is defined as @xmath42 .
in this paper , we present a first npr renormalization proposal for relativistic heavy quarks . we propose a new renormalization point : @xmath11 , in a slightly off - shell region .
we must add off - shell improvement terms and determine the corresponding coefficients as well as evaluating laplace transformations in the time . | we discuss the application of the regularization independent ( ri ) scheme of rome / southampton to determine the normalization of heavy quark operators non - perturbatively using the fermilab action . |
the international linear collider ( ilc ) @xcite is an electron - positron collider with a centre - of - mass energy up to 1 tev and a luminosity goal of @xmath0 .
the achievement of this goal is challenging , and requires nanometre - sized colliding beams at the interaction point , achieved through emittance reductions in dedicated damping rings and strong focusing before the interaction point .
this , combined with the high bunch charge leads to intense electromagnetic interactions when the beams collide , causing particles of each bunch to be deflected by the space charge of the other .
such deflections strongly enhance the angular divergence of the outgoing beams and significantly dilute their energy distributions , through radiation of so - called beamstrahlung photons .
re - interactions involving these photons also produce additional secondary charged particles .
the production of beamstrahlung , whilst exploitable as a diagnostic , is generally troublesome to the design of the interaction region and subsequent extraction line .
the photons are produced in the direction of the outgoing beam , with considerable power ( in the order of mws ) , in a cone of some opening angle in the forward direction ( typically up to a mrad ) , and must be dumped in a controlled way .
they may irradiate parts of the machine , potentially quench superconducting magnets and produce backgrounds in the interaction region detectors , through backscattering .
hence a detailed knowledge and characterisation of the beamstrahlung production is critical to successful linear collider design .
a further contribution to the photon spectrum arises from the so - called compton photons .
these correspond to quantum interactions between electrons and positrons of the colliding beams , where the accompanying photon radiation has high energy .
the dominant contribution is from the radiative bhabha process , in the particular kinematic domain involving the exchange of a virtual photon only slightly off mass - shell .
the hard part of this process can be described as compton scattering of a beam particle on this quasi - real photon , and mostly factorises from the part corresponding to its emission off the electron or positron on the other side .
the total power corresponding to these additional photons is however only a few tens of watts and they are radiated with angles comparable to those of the beamstrahlung photons . in this report ,
comprehensive calculations of the beamstrahlung and compton photon production for the newest ilc beam parameter sets are presented .
the resulting photon angular distributions are obtained and a set of cone half - opening angles to represent successive total beamstrahlung powers are presented for each ilc parameter set . in section [ seccalcs ] the computational methods and the ilc parameter sets under consideration are discussed . in section [ sectheory ]
approximate analytical expectations of the photon cones are calculated .
they are compared to computational results in section [ secresults ] .
conclusions are presented in section [ secconc ] , including the practical beam stay - clear requirements in terms of cone half - opening angles .
in this section , the current ilc beam parameter sets , the key parameters relevant to beamstrahlung production and the method used to simulate the beamstrahlung and compton photons are described .
the latest ilc beam parameter sets @xcite are similar to the previous working space for the 500 gev machine whilst reducing the magnitude of the beam - beam interaction for the 1 tev case , resulting in smaller mean particle energy losses to beamstrahlung photons , @xmath1 , at that energy .
the parameters for the new working space relevant to this work are shown in table [ tabparasets ] , where e , n@xmath2 , n , @xmath3 , p and @xmath4 are the centre - of - mass energy , the number of bunches per train , the number of particles per bunch , the luminosity , the total power contained in the beamstrahlung photons and the r.m.s bunch sizes in the horizontal , vertical and longitudinal dimensions , respectively
. ._key parameters of the new beam parameter sets used in this work , at 500 gev and 1 tev in the centre - of - mass . _ [ cols="<,^,^,^,^,^,^,^ " , ] [ tabprimanglesextra ] since they use the rigid beam model , these calculations are only valid in the horizontal plane and for cases with small disruption .
comparing tables [ tab500beamcone ] and [ tabtevbeamcone ] indicates that the calculations predict the maximum horizontal angle of photon emissions reasonably well only for some of the parameter sets .
for example , the 500 gev nominal theoretical maximum angle is 0.376 mrad , which agrees well with the 0.35 - 0.39 mrad range computed from the beam - beam simulation for the 100 - 1 w criteria .
this is however not the case for the large y and high luminosity sets , where some differences are seen .
such differences are attributed to extreme colliding particle trajectories in guinea - pig .
these may originate from the input angular distribution of the beams and may also result from some disruption occuring for these parameter sets . in all cases ,
the guinea - pig calculation gives larger values and should be used for conservative results .
similar distributions for the compton photons are presented in figures [ fig500compt ] and [ figtevcompt ] , in the horizontal and vertical planes and for the five parameter sets . while extending to similar angles as for beamstrahlung photons , the corresponding power is orders of magnitude less .
the maximum cone half - opening angles previously computed from beamstrahlung are hence not modified .
in this paper , the angles of photons emitted through the beam - beam interaction at the international linear collider have been computed using both the rigid beam model and the beam - beam simulator guinea - pig .
these calculations , and the subsequent understanding of the beamstrahlung , are crucial to the effective design of the interaction region and extraction line .
the rigid beam theoretical predictions tend to underestimate the photon cone opening angles for some of the beam parameter sets , particularly for cases with large disruption .
guinea - pig is hence used for conservative results .
cones of excluded photon power are defined corresponding to tolerances relevant to different aspects of beam - line design : 100 w for general activation and 10 - 1 w for super - conductive magnet quenching .
two contributions were studied , from beamstrahlung emission and from a compton process involving the exchange of a slightly virtual photon between the incident electrons and positrons . by
far the first contribution dominates for most of the angles .
the results are summarised in table [ tabprimangles ] . for the general design of the extraction line , the 100 w definition is applicable .
in this case , half - opening angles of 0.75 and 0.85 mrad can be used as conservative definitions of the required beam - stay - clear in the horizontal and vertical planes , respectively .
[ secconc ]
we would like to thank daniel schulte , olivier napoly , olivier dadoun , mark briscombe , daniel smallqy and ccile rimbault for helpful advice and assistance , and special thanks to deepa angal - kalinin for checking the manuscript and useful advice .
this work was supported by the commission of the european communities under the 6th framework programme `` structuring the european research area '' , contract number rids-011899 , and by the alliance programme of the british council and ministre des affaires trangres .
99 the ilc bcd , http://www.linearcollider.org/wiki/doku.php?id=bcd:bcd_home the ilc reference design report rdr , http://media.linearcollider.org/report-apr03-part1.pdf and new beam parameters circulated by t.raubenheimer to the rdr leaders http://flc.web.lal.in2p3.fr/mdi/bbsim/bbsim.html http://flc-mdi.lal.in2p3.fr/spip.php?rubrique17 r. appleby and p. bambade , care / elan document 2004 - 21 ( 2004 ) e. keil , cern sl/94 - 78 ( ap ) r. appleby and p. bambade , jinst.1:o10004 ( 2006 ) | the intense beam - beam effect at the interaction point of the international linear collider ( ilc ) causes large disruption of the beams and the production of photons .
these photons , arising dominantly through beamstrahlung emission , are problematic for the machine design as they need to be transported and dumped in a controlled way . in this work ,
we perform simulations of the beam - beam interaction to predict photon production rates and distributions for the different beam parameters considered at ilc .
the results are expressed in terms of a set of cones of excluded power , allowing to define the beam - stay - clear requirements relevant for different cases and contexts .
a comparison is also made with theoretical expectations .
the suggested photon cone half - opening angles are 0.75 and 0.85 mrad in the horizontal and vertical planes , respectively .
these cones cover all machine energies and parameter sets , and include the low power compton photons . |
the strangeness meson photoproduction off the nucleon target is one of the most well - studied experimental and theoretical subjects to reveal the hadron production mechanisms and its internal structures , in terms of the strange degrees of freedom , breaking the flavor su(3 ) symmetry explicitly .
together with the recent high - energy photon beam developments in the experimental facilities , such as lpes2 at spring-8 and clas12 at jefferson laboratory @xcite , higher - mass strange meson - baryon photoproducitons must be an important subject to be addressed theoretically for future studies on those reaction processes . in the previous works @xcite ,
the @xmath0 photoproduction was investigated , the born approximation being used with the regge contributions . in comparison with the preliminary experimental data
@xcite , the theory reproduced the data qualitatively well , but the theoretical cross - section strength was underestimated in the vicinity of the @xmath4 . in the present talk ,
we want to report our recent study to explain this discrepancy observed in the previous work .
based on the theoretical framework as employed in ref .
@xcite , we include the nucleon resonances in the @xmath7-channel baryon - pole contribution . as for the nucleon resonances
@xmath8 , we take into account nine of them , i.e. @xmath9 , @xmath10 , @xmath11 , @xmath12 , @xmath13 , @xmath14 , @xmath15 , @xmath9 , @xmath16 , and @xmath17 , in a full relativistic manner .
we start with explaining the theoretical framework briefly and represent the important numerical results in our study .
we note that the nucleon resonances are carefully taken into account in a full - relativistic manner , in addition to the born diagrams , @xmath18 and @xmath19 meson - exchanges in the @xmath20 channel , and @xmath21 and @xmath22 hyperon exchanges in the @xmath23 channel , which were already employed in ref .
all the effective interaction vertices for the nucleon resonances are taken from ref .
for instance , the invariant amplitudes for the spin-@xmath24 and spin-@xmath25 resonance contributions in the @xmath7 channel can be written as follows : @xmath26 \cr & & \frac{ie_q\mu_{n^*}}{2m_n}\gamma^{\mp}(\not{k_1}+\not{p_1}+m_{n^ * } ) \gamma^{\mp}\sigma^{\mu{i}}k_{1i}u_n(p_1){\varepsilon}_{\mu}(k_1 ) , \cr \mathcal { m}_{n^*}\left(\frac{3}{2}^\pm \right)&= & \frac{g_{{k^*}n^*\lambda}}{s - m_{n^*}^2 } { \varepsilon}_{\nu}^*(k_2){\bar u}_{\lambda}(p_2)({k_2^\beta}g^{{\nu}i}-k_2^ig^{\nu\beta } ) \frac{e_q}{2m_{k^*}}\gamma_i^{\pm}\delta_{\beta\alpha } \cr & & \left[\frac{\mu_{n^*}}{2m_n}\gamma_j\,\mp\,\frac{\bar \mu_{n^ * } } { 4m_n^2}p_{1j } \right]\gamma^{\pm}({k_1^\alpha}g^{{\mu}j}-{k_1^j } g^{\mu\alpha})u_n(p_1){\varepsilon}_{\mu}(k_1),\end{aligned}\ ] ] where @xmath27 stand for the @xmath28 momenta and @xmath29 for the helicity amplitude .
the @xmath30 and @xmath31 denote the strong vector and tensor coupling strengths , respectively .
the polarization vectors for the photon and @xmath32 are assigned as @xmath33 and @xmath34 .
the @xmath35 controls the parity of the relevant resonances in the following way : @xmath36 relevant parameters for the resonances are estimated using the experimental and theoretical information @xcite . in figure
[ fig1 ] , we show the total cross section for the present reaction process , i.e. @xmath37 . the numerical results are drawn separately for the cases including the @xmath2 ( left ) and @xmath3 ( right ) , varying the coupling constants @xmath30 . as shown in the figure , the cross - section enhancement is observed in the vicinity of the threshold region , if we choose the strong coupling strengths as @xmath38 .
we verified that other nucleon resonances are not so effective to interpret the discrepancy . [ cols="^,^ " , ]
in the present work , we have studied the @xmath39 photoproduction theoretically , employing the tree - level born approximation and nucleon - resonance contributions below the @xmath4 . among the nucleon resonances , the @xmath2 and @xmath3 play a dominant role to reproduce the experimental data .
it also turns out that other @xmath8 contributions are not so effective to improve the theoretical results .
we note that the nucleon resonances beyond the @xmath4 may contribute to the threshold enhancement , especially due to the @xmath40 , since the @xmath4 for the present reaction process is about @xmath41 mev .
related works are under progress and appear elsewhere .
the authors are grateful to a. hosaka for fruitful discussions .
the present work is supported by basic science research program through the national research foundation of korea ( nrf ) funded by the ministry of education , science and technology ( grant number : 2009 - 0089525 ) .
the work of s.i.n . was supported by the grant nrf-2010 - 0013279 from national research foundation ( nrf ) of korea .
99 leps2 ( http://www.hadron.jp ) and clas12 ( http://www.jlab.org/hall-b/clas12 ) y. oh and h. kim , phys .
c * 74 * , 015208 ( 2006 ) .
y. oh and h. kim , phys . rev .
c * 73 * , 065202 ( 2006 ) .
l. guo and d. p. weygand [ clas collaboration ] , arxiv : hep - ex/0601010 .
y. oh , c. m. ko and k. nakayama , phys . rev .
c * 77 * , 045204 ( 2008 ) .
k. nakamura [ particle data group ] , j. phys .
g * 37 * , 075021 ( 2010 ) .
s. capstick and w. roberts , phys
. rev .
d * 58 * , 074011 ( 1998 ) .
s. capstick and w. roberts , prog .
* 45 * , s241 ( 2000 ) . | in this presentation , we report our recent studies on the @xmath0 photoproduction off the proton target , using the tree - level born approximation , via the effective lagrangian approach . in addition , we include the nine ( three- or four - star confirmed ) nucleon resonances below the threshold @xmath1 mev , to interpret the discrepancy between the experiment and previous theoretical studies , in the vicinity of the threshold region . from the numerical studies , we observe that the @xmath2 and @xmath3 play an important role for the cross - section enhancement near the @xmath4
. it also turns out that , in order to reproduce the data , we have the vector coupling constants @xmath5 and @xmath6 . |
the decay @xmath16 ( @xmath17 ) provides unique information about the dynamics of the strong interactions .
it has been a testing ground for such theories as current algebra , pcac , chiral perturbation theory(chpt ) .
the study of this decay has a particular interest in view of new two - loop order ( @xmath18 ) calculations for k@xmath19 decays in chpt @xcite .
the high - order chpt calculations make a definite prediction for the quadratic term in the vector @xmath20 form - factor and link the scalar @xmath21 form - factor linear and quadratic slopes to the @xmath22 corrections . in turn
, @xmath22 is known to be crucial for the @xmath23 measurements .
in fact , the latest measurements do not report any visible non - linearity in the form - factors @xcite .
in this paper we present a high - statistics measurement ( @xmath24 919k events ) of the dalitz plot density in this decay . the description of the experimental setup , trigger and reconstruction procedure can be found in our previous paper @xcite .
the current analysis is based on the high - statistics data collected during run in winter 2001 . in total ,
332 m events were logged on tapes .
this statistics is complemented by about 160 m mc events generated with geant3 @xcite monte carlo program .
the mc generation includes a realistic description of the setup with decay volume entrance windows , tracking chambers windows , chambers gas mixtures , sense wires and cathode structures , erenkov counters mirrors and gas , the shower generation in em calorimeters , etc .
the events with one charged track identified as electron and two or three additional showers in the electromagnetic calorimeter are selected for further processing .
it was observed , that the main background contribution ( about 95% of the background events ) is related to the decay @xmath25 , when the hadronic interaction of the charged pion simulates the electromagnetic shower in the calorimeter . following the method of angular selection used in our analysis of the @xmath26 decay @xcite
, we choose the angle between the beam particle direction and the vector sum of momenta of the final state track and photons as the variable to perform signal - background separation . the expected distribution over this angle is shown in fig.1 together with the real data .
one can observe a clear background peak at small values and a good agreement of the data and monte - carlo .
the cut value was selected in the region where the maximum of the function @xmath27 is reached .
after that , the momenta of the final state particles were refined with 2c @xmath28 kinematic fit . only the convergence of the fit
was required .
the missing energy @xmath29 after 2c fit is shown in fig.2 .
this variable should exhibit a strong peak at @xmath30 in the presence of noticeable background contributions .
the complete absence of any enhancement at small values of the missing energy proofs the quality of the selection procedure .
figure 1 : angle between the beam track and the vector sum of final state particles momenta .
the points with errors are data and the solid histogram is mc .
the shaded area shows the background contribution .
figure 2 : energy of the neutrino compared with mc .
the shaded area shows the surviving background contribution .
the signal monte - carlo events for figures 1 and 2 are weighted with the @xmath31 matrix element where we use @xmath32 ( fixed from our preliminary measurements @xcite ) . finally , 919k events were selected .
we estimate the surviving background contribution to be around 2.1% .
the most general lorentz - invariant form of the matrix element for the @xmath33 decay is @xcite : @xmath34\gamma^{\alpha } + i \frac{2f_{t}}{m_{k } } \sigma_{\alpha \beta}p^{\alpha}_{k}p^{\beta}_{\pi}]v(p_{l})\ ] ] it consists of scalar , vector , and tensor terms .
the @xmath35 form - factors are the functions of @xmath36 . in the standard model ( sm )
, the w - boson exchange leads to the pure vector term .
the scalar and/or tensor terms which are `` induced '' by ew radiative corrections are negligibly small , i.e nonzero scalar or tensor form - factors would indicate the physics beyond the sm .
the term in the vector part , proportional to @xmath37 , is reduced ( using the dirac equation ) to the scalar form - factor . in the same way
, the tensor term is reduced to a mixture of the scalar and vector form - factors .
the redefined vector ( v ) and scalar ( s ) terms , and the corresponding dalitz plot density in the kaon rest frame ( @xmath38 ) are @xcite : @xmath39 with the selected number of events we can not neglect the @xmath40 interference term proportional to the electron mass .
the term proportional to @xmath41 is neglected in our analysis .
for further analysis we assume a general quadratic dependence of @xmath42 on t : @xmath43 the procedure of the extraction of the form - factor parameters starts with the subdivision of the dalitz plot region @xmath44 @xmath45 into @xmath46 bins .
the signal mc was generated with the constant matrix element and the amplitude - induced weights should be calculated during the fit procedure .
one can observe that the dalitz - plot density function @xmath47 in ( 2 ) can be presented in the factorisable form : @xmath48 where @xmath49 are simple bilinear functions of the form - factor parameters and @xmath50 are the kinematic functions which are calculated from the mc - truth information . for each @xmath51 ,
the sums of @xmath50 over events are accumulated in the dalitz plot bins ( i , j ) to which the mc events fall after the reconstruction .
finally , every bin in the dalitz plot gets weights @xmath52 and the density function @xmath53 which enters into the fitting procedure is constructed : @xmath54 this method allows one to avoid the systematic errors due to the `` migration '' of the events over the dalitz plot due to the finite experimental resolution and automatically takes into account the efficiency of the reconstruction and selection procedures . to take into account the finite number of mc events in the particular bin and strong variation of the real data events over the dalitz plot , we minimize a @xmath55 function defined as @xcite : @xmath56 + 2\sum_j ( n_j+m_j+1)\ln\left ( \frac{1+\frac{r_j}{m_j}}{1+\frac{n_j}{m_j+1}}\right),\ ] ] where the sum runs over all populated bins , and @xmath57 , @xmath58 and @xmath59 are the number of data events , expected events and generated monte carlo events respectively . for large @xmath59 eq .
( 8) reduces to the more familiar expression @xmath60\ ] ] the radiative corrections were taken into account by re - weighting every monte - carlo event , using mc - truth information , according to the recent calculations in @xcite .
the minimization is performed by means of the `` minuit '' program @xcite .
the errors are calculated by `` minos '' procedure of `` minuit '' at the level @xmath61 , corresponding to 68% coverage probability for 1 parameter .
a fit of the @xmath17 data with @xmath62 gives @xmath63 .
the total number of bins is 6991 and @xmath64 .
the quality of the fit is illustrated in figures 3 and 4 where the projected variables @xmath65 and @xmath66 are presented .
figure 3 : y distribution .
+ the points with errors are the real data + and the shaded area signal mc .
figure 4 : z distribution .
+ the points with errors are the real data + and the shaded area
signal mc .
the table 1 represents fits with possible nonlinear term in @xmath67 ( eq .
3 ) as well as the fits with tensor and scalar contributions ( eq .
every row of the table 1 represents a particular fit where the parameters shown without errors are fixed . to qualify the statistical significance of the particular fit
, we also show the change in the @xmath68 value obtained with respect to the fit without non - linear or anomalous contributions .
the second row shows a fit where the nonlinearity is allowed in @xmath2
. one can observe @xmath69 ( fig.5 ) correlation that results in a significant @xmath1 errors enhancement and visible shift of @xmath1 parameter . [
cols="^,^,^,^,^",options="header " , ] table 2 . the systematic error contributions .
the @xmath70 decay has been studied using in - flight decays of 25 gev @xmath71 detected by the `` istra+ '' magnetic spectrometer .
the leptoquark - induced amplitudes for @xmath17 decay were considered in @xcite . in this model the relation between tensor and scalar terms is fixed : @xmath77 .
the fit of our data with this constraint gives the following scalar contribution : @xmath78 .
this result can be converted in the upper limit @xmath79 ( 90% c.l . ) . using the expression in @xcite : @xmath80 where @xmath81 is the ratio of leptoquark mass to the square of the yukawa - like coupling , we get @xmath82 99 p.post and k.schilcher , eur . phys .
j. * 25*(2002 ) , 427 .
j.bijnens and p.talavera , nucl.phys . *
b669*(2003 ) , 341 .
s. shimizu et al .
( e246 kek - ps collaboration ) , phys .
lett . * b495*(2000 ) , 33 .
levchenko et al .
( e246 kek - ps collaboration ) , yad.fiz * v65*(2002 ) , 2294 , i.v.ajinenko et al .
( istra+ collaboration ) , phys.lett . *
b574*(2003 ) , 14 .
o.p.yushchenko et al .
( istra+ collaboration ) , phys.lett . *
b581*(2004 ) , 31 .
r brun et al . ,
cern - dd / ee/84 - 1 .
h. steiner et al . , phys.lett . *
b36*(1971 ) , 521 .
chizhov , phys.lett . *
b381*(1996 ) , 359 .
l. rosselet et al . , phys.rev . *
d15*(1977 ) , 574 .
v. cirigliano , m. knecht , h. neufeld , h. rupertsberger , p. talavera , eur .
j. * c23*(2002 ) , 121 .
f. james , m.roos , cern d506,1989 .
kiselev , a.k .
likhoded and v.f .
obraztsov , hep - ph/0204066 ( 2002 ) . | the decay @xmath0 is studied using in - flight decays detected with the `` istra+ '' spectrometer .
about 920k events are collected for the analysis .
the @xmath1 slope parameter of the decay form - factor @xmath2 in the linear approximation ( average slope ) is measured : @xmath3(stat ) @xmath4(syst ) . the quadratic contribution to the form - factor
was estimated to be @xmath5(stat ) @xmath6(syst ) .
the linear slope , which has a meaning of @xmath7 for this fit , is @xmath8(stat ) @xmath4(syst ) .
the limits on possible tensor and scalar couplings are derived : @xmath9(stat ) @xmath10(syst ) , @xmath11(stat ) @xmath12(syst ) . by -by -21.9
cm -10pt 0.5 in 17.0 cm * high statistic measurement of the @xmath13 decay form - factors * + * o.p .
yushchenko , s.a .
akimenko , g.i .
britvich , k.v.datsko , a.p .
filin , a.v .
inyakin , a.s .
konstantinov , v.f .
konstantinov , i.y .
korolkov , v.a .
khmelnikov , v.m .
leontiev , v.p .
novikov , v.f .
obraztsov , v.a .
polyakov , v.i .
romanovsky , v.m .
ronjin , v.i .
shelikhov , n.e .
smirnov , o.g .
tchikilev , v.a.uvarov .
* 0.15 cm * @xmath14 * 0.35 cm * v.n .
bolotov , s.v .
laptev , a.yu . polyarush . * 0.15 cm * @xmath15 * |
the time evolution of the intrinsic continuum v - band polarization ( v - pol ) of @xmath0 aqr is shown in figure 1 .
we find evidence of clockwise loop - like structures ( figure 2 ) when comparing the evolution of the polarization across the balmer jump ( bj ) vs v - pol , particularly during polarimetric outburst events ( red in figure 1 ) .
60 cyg also displays this behavior .
we use the non - lte 3d monte carlo code developed by @xcite , hdust , to investigate the origin of the loop - like behavior of the bj vs v - pol during polarimetric outbursts .
interestingly , we find that the clockwise loop structures can be reproduced when the mass - loss from the central star which feeds the disk is turned on ( 6 to 12 o@xmath1clock , figure 3 ) then off ( 12 to 6 o@xmath1clock , figure 3 ) .
we therefore suggest that this diagnostic can provide insight into the time dependence of the density of the innermost disk region .
counter - clockwise loops are also observed in @xmath0 aqr and 60 cyg and will require further modeling to ascertain thier origin .
we note that @xcite found similar loop structures in cmd diagrams of be stars .
in ( * ? ? ? * paper i ) , we detected variations in the pa of disks during polarimetric outbursts , and speculated that these variations could be indicative of warps , non - equatorial blob injections , or spiral density waves in the inner disk .
figure 4 depicts deviations in the mean pa during polarimetric outbursts of @xmath0 aqr .
as shown in figure 5 , we model a density enhancement on one side ( orange ) of the disk and a decrement on the opposing side ( black ) using hdust .
the result of computing the polarization from different viewing angles in a counter - clockwise motion are shown in figure 6 .
this model suggests that asymeteric material being ejected from the star can potentially match observed deviations in the pa . | in @xcite , paper i , we analyzed 15 years of spectroscopic and spectropolarimetric data from the ritter and pine bluff observatories of 2 be stars , 60 cygni and @xmath0 aquarii , when a transition from be to b star occurred .
here we anaylize the intrinsic polarization , where we observe loop - like structures caused by the rise and fall of the polarization balmer jump and continuum v - band polarization being mismatched temporaly with polarimetric outbursts .
we also see polarization angle deviations from the mean , reported in paper i , which may be indicative of warps in the disk , blobs injected at an inclined orbit , or spiral density waves .
we show our ongoing efforts to model time dependent behavior of the disk to constrain the phenomena , using 3d monte carlo radiative transfer codes . |
dense nano - particle systems have been shown to exhibit collective behavior , as evidenced by aging , and non - equilibrium effects similar to spin glasses.@xcite whether that collective behavior is associated with a `` true '' spin glass phase transition is still controversial . in this paper , we show a dynamic scaling analysis to a spin glass transition for a highly concentrated fe - c nano - particle sample with a narrow particle size distribution .
we also discuss why the scaling analysis may not indicate a phase transition for samples with less interactions or wider size distributions . the sample consisted of ferromagnetic nanoparticles of amorphous @xmath5 ( x@xmath60.22 ) , with an average particle size of @xmath7 nm , prepared by the method described by van wonterghem et al . in ref .
the sample was studied in the frozen state and contained 17 vol% of particles .
the ac - susceptibility measurements were performed in a non - commercial squid magnetometer for frequencies in the range @xmath8 17 mhz - 170 hz . fig . 1 shows @xmath9 and @xmath10 at different frequencies . a sample that exhibit a spin glass transition will show critical slowing down , and hence the characteristic relaxation time @xmath11 diverges at the transition temperature according to @xmath12 where @xmath13 is the transition temperature , @xmath14 is related to the relaxation time of the individual particle magnetic moments , and @xmath15 is a critical exponent .
we extracted the freezing temperature @xmath16 , associated with a relaxation time ( @xmath17 ) , from the out - of - phase component of the ac - susceptibility as @xmath18 with @xmath19 .
we also tried other criteria to make sure that the choice of criterion is not significantly influencing the results of the critical slowing down analysis .
the critical slowing down analysis gives @xmath1 , @xmath20 s , and @xmath21 k ( see fig .
we also performed a full scaling of @xmath3 according to , @xmath22 and found data collapse to a single function @xmath23 , for different frequencies , using @xmath2 ( see fig .
3 ) . the value of @xmath15 compares quite well with values found for spin glasses with long range interactions ( rkky ) , while the value of @xmath24 is slightly larger than typical spin glass values , but is consistent with the value of @xmath25 found by jonsson et al .
@xcite for an interacting nanoparticle sample by a static scaling analysis .
the dynamic scaling analysis will only reveal a phase transition if the single particle contribution to @xmath3 is vanishingly small for @xmath4 , i.e. all slow dynamics is due to collective behavior .
two criteria have to be fulfilled for this to be possible ; i ) the interparticle interactions need to be strong and ii ) the particle size distribution needs to be narrow . if we compare the sample used for the scaling analysis with the same sample but much more dilute ( 0.05 vol.% ) we can see that the out - of - phase component is almost zero for @xmath4 ( see inset of fig .
we conclude that the concentrated sample is appropriate to use for scaling analysis .
9 j. l. dormann , et al . , j. magn .
magn . mater . *
187 * , l139 ( 1998 ) .
h. mamiya , i. nakatani , and t. furubayashi , phys .
lett . * 82 * , 4332 ( 1999 ) .
p. jnsson , m. f. hansen , and p. nordblad , phys .
b * 61 * , 1261 ( 2000 ) j. van wonterghem , s , mrup , s.w .
charles , and s wells , j. colloid interface sci . *
121 * , 558 ( 1988 ) . | a highly concentrated ( 17 vol.% ) fe - c nano - particle system , with a narrow size distribution @xmath0 nm , has been investigated using magnetic ac susceptibility measurements covering a wide range of frequencies ( 17 mhz - 170 hz ) .
a dynamic scaling analysis gives evidence for a phase transition to a low temperature spin - glass - like phase .
the critical exponents associated with the transition are @xmath1 and @xmath2 .
the reason why the scaling analysis works for this sample , while it may not work for other samples exhibiting collective behavior as evidenced by aging phenomena , is that the single particle contribution to @xmath3 is vanishingly small for @xmath4 and hence all slow dynamics is due to collective behavior .
this criterion can only be fulfilled for a highly concentrated nano - particle sample with a narrow size distribution . |
the study of ultra - relativistic heavy - ion collisions provides insight into properties of very high density nuclear matter .
since the observed particle distributions to first order only reflect the conditions in the final state of the system , signatures originating from the early stage are needed to conclude whether the system passes through a partonic phase .
this is one necessary step to identify the predicted state of matter called the quark - gluon plasma ; the other one being the proof that the system is thermalized .
one observable which is sensitive to the early stage of the collision is the second harmonic coefficient , @xmath0 , of the fourier expansion of the azimuthal momentum distribution , called elliptic flow @xcite . in non - central collisions
the initial spatial anisotropy is transformed into an anisotropy in momentum - space if sufficient interactions occur among the constituents within the system .
once the system has expanded enough to quench the spatial anisotropy , further development of momentum anisotropy ceases . in the following
we will discuss results on @xmath0 for identified hadrons measured in @xmath1 minimum bias au+au collisions from the star experiment at rhic .
with the high statistics available from rhic s run iv the coverage for identified hadron @xmath0 was extended up to @xmath11 by disentangling the different contributions to the overall @xmath12 , as shown in fig.[fig:1 ] . to suppress non - flow effects
, particles were correlated to the reaction plane determined in the opposite @xmath13-subevent .
the difference of this @xmath0-measurement from the results of the method where the event plane is measured over the full acceptance , is an estimate of one of the contributions to the systematic error ; another factor in the systematic error is based on the estimated level of contamination of protons by kaons .
the systematic errors are shown as bands in fig.[fig:1 ] , while the error bars include statistical uncertainties only . at low
@xmath5 the systematic errors were estimated to be less than 10% @xcite . for identified hadrons ( upper panel ) and ratio ( lower panel ) between the measurements and a polynomial fit through all data points except pions for 200 gev minimum bias au+au collisions . for both figures
the open symbols for @xmath3 and @xmath4 were taken from @xcite.[fig:2 ] ] while the proton @xmath0 saturates at @xmath14 the measurements for @xmath3 show a decline starting from their maximum at about @xmath15 .
the flow of these non - strange hadrons is strikingly similar to that of the strange particles @xmath16 and @xmath17 . the mesons and baryons fall into separate groups and this behavior seems to extend out to rather high transverse momentum .
most surprisingly , even at the highest @xmath5 measured a large @xmath0 is still observed .
this appears to be in contradiction to parton energy loss models @xcite and multi - component calculations @xcite , which both predict a smaller @xmath0 at and above @xmath18 . at these high momenta
the remaining @xmath0 value should be essentially driven by the path - length dependence of jet quenching only @xcite .
to further study the observed grouping into mesons vs. baryons , the top of fig.[fig:2 ] shows the scaled @xmath19 for identified hadrons over a broad range of scaled transverse momentum @xmath20 . here
@xmath21 is the number of constituent quarks ( ncq ) of a given hadron .
figure [ fig:2 ] , bottom displays the ratio between the measurements and a polynomial fit to all data . at low @xmath20
@xmath22 the observed deviations from the fit follow a mass - ordering which is expected from hydrodynamic flow . at higher @xmath5 ,
all @xmath19 measurements are very close to the common ` mean value ' .
while the shown errors include statistical uncertainties only , it is still striking to see that the similarity of the scaled @xmath0 extends out to @xmath20 as high as @xmath23 .
it seems that all mesons fall above the fit while all baryons fall below .
the observation that the @xmath24 is similar for all the different particle species , strongly supports quark coalescence ( see for example @xcite ) as the dominant process of hadronization in the intermediate @xmath5 region . with the available statistics small deviations from exact ncq - scaling are now detectable , which were expected even for simple recombination models @xcite .
compared to @xmath3 , @xmath25 , and @xmath26 @xcite , measurements of particle spectra at rhic have shown that the multi - strange hadrons @xmath6 and @xmath27 are less affected by the hadronic phase @xcite than by the partonic phase . it has been demonstrated @xcite that the @xmath28 and @xmath29 baryons possess a significant amount of @xmath0 , which suggests that this azimuthal anisotropy is generated at an early and partonic stage of the system s evolution . for the @xmath6 meson , earlier measurements disfavored kaon coalescence as the dominant channel for @xmath6 production at rhic energies @xcite . also its lifetime is long compared to the lifetime of the fireball .
hence the @xmath6 is a useful probe of the early stage of the system as well .
the @xmath0 of the @xmath6 is particularly interesting , since the @xmath6-mass of @xmath30 is similar to the mass of the proton @xmath31 . for strange hadrons ( left ) and multi - strange hadrons ( right ) in 200 gev minimum bias au+au collisions .
the dashed lines show a common fit @xcite to the @xmath16 and @xmath32 data .
hydrodynamic model calculations @xcite are shown as shaded areas .
[ fig:3 ] ] the new high statistics measurements of azimuthal anisotropy @xmath0 of multi - strange hadrons show strong elliptic flow for all studied particles : @xmath7 , @xmath8 , and @xmath6 ( see fig.[fig:3 ] , right ) .
the error bars contain statistical uncertainties only .
for the @xmath6-measurement systematic errors obtained by the comparison of two different methods are also shown .
a common fit to the results obtained for @xmath16 and @xmath17 , as depicted in fig.[fig:3 ] , left and motivated by number - of - constituent - quark scaling @xcite , was used to compare the @xmath0-data of multi - strange hadrons to those of the other particles .
a detailed comparison , carried out by calculating @xmath33 for the difference between the measurements and the fit function ( see tab.[table:1 ] ) , suggests that @xmath7 and @xmath29 indeed flow as strongly as the other baryons , while the @xmath6 favors the similarity to other mesons .
note that the fit function does not reproduce the data perfectly due to small deviations from the exact number - of - constituent - quark scaling , as discussed in sec.[ncqoldi ] .
.comparison of @xmath34 measurements for multi - strange hadrons to a common fit @xcite to @xmath34 of @xmath16 and @xmath35 .
[ table:1 ] [ cols="^,^,^ " , ] + since the @xmath6 flows like a meson and not as strongly as baryons , e.g. the proton with its similar mass , it is found that the observed scaling is a meson - baryon effect and not a mass effect .
the observed strong flow of multi - strange hadrons substantiates the development of collectivity among partons at rhic .
we have presented the azimuthal anisotropy parameter @xmath0 for identified particles in 200gev minimum bias au+au collisions .
elliptic flow of @xmath36 and @xmath3 was measured up to @xmath37 , where these particles still show a strong @xmath0 signal .
the observed meson - baryon grouping at intermediate @xmath5 suggests parton coalescence to be the dominant process of hadronization in that region , even though small deviations from ideal number - of - constituent - quark scaling are observed .
this scaling is a meson - baryon effect and not a mass effect . finally , the multi - strange hadrons @xmath6 , @xmath7 , and @xmath38 flow as strongly as the other mesons and baryons , which confirms partonic collectivity at rhic .
the remaining item to address for the discovery of a quark - gluon plasma is the thermalization of the system .
99 a.m. poskanzer and s.a .
voloshin , phys.rev .
* c58 * ( 1998 ) 1671 .
s. adler _ etal .
_ ( phenix collaboration ) , phys.rev.lett .
* 91 * ( 2003 ) 182301 .
j. adams _ etal . _
( star collaboration ) , phys.rev .
* c72 * ( 2005 ) 014904 .
wang , m. gyulassy , phys.rev.lett .
* 68 * ( 1992 ) 1480 .
d. molnr , nucl - th/0503051 .
a. dainese , c. loizides , g. pai , eur.phys.j .
* c38 * ( 2005 ) 461 .
d. molnr and s.a .
voloshin , phys.rev.lett .
* 91 * ( 2003 ) 092301 .
j. adams _ etal . _
( star collaboration ) , phys.rev.lett .
* 92 * ( 2004 ) 112301 .
j. adams _ etal . _
( star collaboration ) , phys.rev.lett .
* 92 * ( 2004 ) 182301 .
j. adams _ etal . _
( star collaboration ) , phys.rev.lett .
* 95 * ( 2005 ) 122301 .
j. adams _ etal . _
( star collaboration ) , phys.lett .
* b612 * ( 2005 ) 181 .
x. dong , s. esumi , p. sorensen , n. xu and z. xu , phys.lett .
* b597 * ( 2004 ) 328 .
p. huovinen , private communication ( 2004 ) . | the azimuthal anisotropy parameter @xmath0 has been measured with high statistics for identified hadrons in @xmath1au+au collisions with the star experiment . at
high transverse momentum @xmath2 a strong @xmath0 for @xmath3 and @xmath4 is observed . in the intermediate @xmath5 region ,
number - of - constituent - quark scaling was tested to high precision .
a detailed comparison of @xmath0 for the multi - strange hadrons @xmath6 , @xmath7 , and @xmath8 with other particle species substantiates the development of collectivity among partons in the early phase of the collisions at rhic . |
[ cols="<,^ , < " , ] trim conditions for the aircraft at 20 m/s are : @xmath0 , @xmath1 and @xmath2 and have been used as initial conditions for the controller . again a prediction window of 5 seconds along with 50 coincidence points were used . the upper limit on the thrust constraint continually changes based on the true airspeed of the aircraft according to the equations given in . the minimum thrust level set always to @xmath3 . if however an engine failure
is detected the upper limit on thrust is set to the filter estimate plus @xmath4 uncertainty . +
a ukf filter was designed to perform fdi with the following process noise and noise covariance matrices : @xmath5 where @xmath6 is the filter update rate 0.01 secs .
the initial state vector and covariance matrix are : @xmath7^\intercal , \quad \mathbf{p}(0 ) = \begin{bmatrix } ( 0.5)^2 & 0 & 0 & 0\\ 0 & ( 0.5)^2 & 0 & 0\\ 0 & 0 & ( 0.0850)^2 & 0\\ 0 & 0 & 0 & ( 6)^2 \end{bmatrix}.\ ] ] finally the fault detection logic is based on that given in @xcite . the following scenarios were set up to test the active ftc system on the uav model : 1 .
no fault case 2 .
engine failure - @xmath8 power loss 20 seconds into flight , 3 .
engine failure - @xmath9 power loss 30 seconds into flight .
the aircraft was required to follow the flight trajectory given in figure [ fig : chap6_activeftc_reftraj ] ( note : wind effects have been taken into account using the dryden wind model in matlab ) .
figure [ fig : chap6_activeftc_faultflag ] presents the fault detection logic for each scenario .
there was no fault present in scenario 1 and this is reflected in the results of the fault detection logic as the value of the fault flag remained zero throughout the duration of the flight .
the results for scenarios 2 and 3 show that the fault flag is triggered ( ie .
the value of the flag switches to 1 ) within seconds of the fault occurring .
the control inputs produced by the controller for each scenario are given in figures [ fig : chap6_activeftc_controls_nf ] , [ fig : chap6_activeftc_controls_50 t ] and [ fig : chap6_activeftc_controls_30 t ] .
the results clearly indicate that the controller is able to successfully reconfigure based on fdi data and as the loss of power increases the demand on the elevator increases .
loss of power - controls ] loss of power - controls ] the true airspeed response of the aircraft is given in figure [ fig : chap6_activeftc_controls_vt ] .
the demanded speed was @xmath10 and the results show that for a @xmath8 loss in power the true airspeed demand is unachievable during climb to altitude .
however during straight and level flight the velocity demand is gradually achieved and is finally reached once the aircraft begins the descent phase . during the descent
the true airspeed demand is similar to the no fault case . in the case of @xmath9 power loss
the aircraft is unable to meet the true airspeed demand during straight and level flight , however halfway through the descent phase the aircraft picks up speed and is able to maintain the reference . in any given scenario stall speed is never reached . .
stall speed did not occur in any scenario . ]
the climb rate ( or vertical speed ) response is shown in figures [ fig : chap6_activeftc_controls_vd ] and [ fig : chap6_activeftc_controls_vd_subs ] and shows that during power loss the vertical speed oscillates between the upper and lower constraints values .
this is to be expected as the elevator is working harder to regulate the speed , and hence bounces between the two limits . ] ] finally the trajectories flown by the aircraft in each scenario are shown in figure [ fig : chap6_activeftc_controls_height ] .
the interesting points to note here are that in the highest loss of power case ( scenario 3 ) the aircraft did not have enough power to reach the highest flight altitude so instead cruised at an altitude it was capable of flying . once the straight and level phase of the flight was over the controller was able to fly the aircraft back onto the demanded trajectory .
the @xmath8 loss of power case shows that aircraft still had enough power to fly back onto the demanded path halfway through the straight and level at altitude flight phase .
in this paper we demonstrated the successful application of an nmpc based active ftc design on an actual uav which is currently in operation .
the controller was implemented using actual aircraft data and shows great promise for active fault tolerant flight control .
an appendix , if needed , appears before the acknowledgements .
an acknowledgements section , if used , immediately precedes the references .
sponsorship and financial support acknowledgements should be included here .
9 kale , m. m. , chipperfield , a.j . , `` robust and stabilized mpc formulations for fault tolerant and reconfigurable flight control , '' _ proceedings of the 2004 ieee international symposium on intelligent control _ , 2004 , pp . 222227 ,
doi : 10.1109/isic.2004.1387686 vos , david w. , motazed , b. , `` application of fault - tolerant controls to uavs , '' _ aerospace / defense sensing and controls _ , 1996 , pp .
khan , r. , williams , p. , riseborough p. , rao , a. and hill , r. , _ designing a nonlinear model predictive controller for fault tolerant flight control_. arxiv e - prints 2016 ; https://arxiv.org/abs/1609.01529 , [ last accessed : 02 - 10 - 2016 ] .
khan , r. , williams , p. , riseborough p. , rao , a. and hill , r. , _ fault detection and identification - a filter investigation_. arxiv e - prints 2016 ; https://arxiv.org/abs/1609.02407 , [ last accessed : 02 - 10 - 2016 ] .
boskovic , j.d .
, sai - ming l. and mehra , r.k .
, `` on - line failure detection and identification ( fdi ) and adaptive reconfigurable control ( arc ) , '' _ proceedings of the 2001 american control conference _ , vol . 4 , 2001 , pp . 26252626 ,
doi : 10.1109/acc.2001.946269 gopinathan , m. , boskovic , j.d .
, mehra , r.k . and rago , c. , `` a multiple model predictive scheme for fault - tolerant flight control design , '' _ proceedings of the 37th ieee conference on decision and control _ , vol . 2 , 1998 , pp . 13761381 ,
doi : 10.1109/cdc.1998.758477 maciejowski , j.m .
, `` fault - tolerant aspects of mpc , '' _ iee two - day workshop on model predictive control : techniques and applications - day 2 ( ref
1999/096 ) _ , 1999 , pp . 1/11/4 .
bateman , f. , noura , h. , and ouladsine , m. , `` actuators fault diagnosis and tolerant control for an unmanned aerial vehicle , '' _ ieee international conference on control applications .
cca 2007 _ , 2007 , pp .
bateman , f. , noura , h. , and ouladsine , m. , `` a fault tolerant control strategy for an unmanned aerial vehicle based on a sequential quadratic programming algorithm , '' _
47th ieee conference on decision and control .
cdc 2008 _ , 2008 , pp .
copeland , r.p . and rattan , k.s .
, `` a fuzzy logic supervisor for reconfigurable flight control systems , '' _ proceedings of the 1994 ieee national aerospace and electronics conference ( naecon ) _
, 1994 , pp .
579586 . chen , j. , patton , r.j . and
chen , z. , `` an lmi approach to fault - tolerant control of uncertain systems , '' _ proceedings of the 1998 intelligent systems and semiotics ( isas ) and intelligent control ( isic ) . held jointly with ieee international symposium on computational intelligence in robotics and automation ( cira ) _ , 1998 , pp .
wu , s. , grimble , m.j . , wei , w. , `` qft based robust / fault tolerant flight control design for a remote pilotless vehicle , '' _ proceedings of the 1999 ieee international conference on control applications _ , vol . 1 , 1999 ,
beainy , f. , mai , a. and commuri , s. , `` unmanned aerial vehicles operational requirements and fault - tolerant robust control in level flight , '' _ 17th mediterranean conference on control and automation .
med09 _ , 2009 , pp .
krger , t. , schnetter , p. , placzek , r. and vrsmann , p. , `` fault - tolerant nonlinear adaptive flight control using sliding mode online learning , '' _ neural networks _ , vol .
32 , 2012 , pp .
khan , r. , williams , p. , riseborough p. , rao , a. and hill , r. , _ active fault tolerant flight control system design_. arxiv e - prints 2016 ; https://arxiv.org/abs/1610.02139 , [ last accessed : 11 - 10 - 2016 ] .
williams , p. , `` uav model , ''
_ private communication _ , full details of the uav model can not be disclosed due to a confidentiality condition , 2015 mccormick , b.w .
, `` aerodynamics , aeronautics and flight mechanics , '' _ john wiley & sons inc , usa , ny _ , 1995 . | fault tolerance is achieved through multiply redundant hardware systems in large civil aircraft .
this means of achieving fault tolerance is infeasible for small compact unmanned aerial vehicles . in this paper
we apply a fault tolerant control system which exploits analytical redundancy rather than hardware redundancy to an actual uav model currently in operation via model - in - the - loop simulation .
the fault tolerant control system comprises a nonlinear model predictive controller integrated with an unscented kalman filter for fault detection and identification .
the results show that our fault tolerant control system design is able to identify engine failure within seconds of fault occurrence and distribute control authority to the healthy actuators to maintain safe flight . |
the new family of the charmonium or charmonium - like states include @xmath5 , @xmath6 , @xmath7 , @xmath8 , @xmath9 , @xmath10 , @xmath11 , @xmath12 , @xmath13 , @xmath14 and @xmath15 etc @xcite .
many states sit on the the threshold of two charmed mesons , which inspired some of them ( especially those charged ones ) to be candidates of heavy moleculues @xcite . in the heavy quark limit
, the s - wave and p - wave heavy mesons can be categorized into three doublets : @xmath16 , @xmath17 , @xmath18 .
we collect their masses from pdg in table [ hs ] .
the bottom mesons in the @xmath19 doublet are still missing experimentally .
thus , we will adopt the theoretical predictions of the bottom meson masses in the @xmath19 doublet when we study the heavy flavor molecular system composed of the bottom and anti - bottom mesons . in the framework of the meson exchange model
, we have investigated the possible loosely bound molecular states composed of a pair of heavy mesons in refs .
@xcite . in this work
, we will investigate the possible heavy molecular system constructed by the charmed and anti - charmed mesons , where one meson is in the @xmath20 doublet and the other one is in the @xmath19 doublet . in the following ,
we denote the heavy flavor molecular system as the @xmath21 system for the convenience .
the @xmath22 system can be categorized into four subsystems : @xmath23 $ ] , @xmath24 $ ] , @xmath25 $ ] and @xmath26 $ ] .
they correspond to different quantum number combinations @xmath27 , @xmath28 , @xmath29 and @xmath30 , respectively . since charmed mesons belong to the fundamental representation of flavor @xmath31 , the system constructed by the charmed meson and anti - charmed meson forms an octet and a singlet : @xmath32 as illustrated in table [ wavefunction ] .
the parameter @xmath33 in the flavor wave functions corresponds to the charge parity @xmath34 respectively for the neutral systems as pointed out in refs .
@xcite .
this paper is organized as follows .
we review the formalism in section [ sec2 ] and present the results in section [ sec3 ] .
the last section is a short summary .
the potential model is an effective approach to study the two - body bound state problem . for the @xmath22 system
, the scattering between the charmed and anti - charmed meson occurs via exchanging the light pseudoscalar , scalar and vector mesons , which play the role of providing long - distant , intermediate - distance and short - distance forces . at the hadron level , there exist two types of diagrams in the scattering of the charmed and anti - charmed mesons , i.e. , the cross and direct diagrams as shown in table [ diagrams ] .
the exchanged light mesons relevant to the four subsystems @xmath23 $ ] , @xmath24 $ ] , @xmath35 $ ] and @xmath36 $ ] are also presented in table [ diagrams ] .
when writing out the scattering amplitude , the monopole form factor is introduced at every interaction vertex to compensate the off - shell effect of the exchanged light meson @xmath37 where the phenomenological cutoff parameter @xmath38 is about 1 gev . @xmath39 and
@xmath40 denote the four - momentum and the mass of the exchanged meson .
.the flavor wave functions of the @xmath23 $ ] , @xmath24 $ ] , @xmath35 $ ] and @xmath36 $ ] systems .
we use @xmath69^{a}_{b}$ ] to name the different states , where the superscript @xmath70 denotes the charge of the state and subscript @xmath71 is introduced to distinguish the different states in a subsystem .
[ wavefunction ] [ cols="^,^",options="header " , ] | we study the possible heavy molecular states composed of a pair of charm mesons in the h and s doublets . since the p - wave charm - strange mesons @xmath0 and
@xmath1 are extremely narrow , the future experimental observation of the possible heavy molecular states composed of @xmath2 and @xmath3 may be feasible if they really exist .
especially the possible @xmath4 states may be searched for via the initial state radiation technique . |
a gapped state of quantum condensed matter is called topological phase when it supports stable gapless boundary modes , such as an edge or a surface state . the integer quantum hall effect
( qhe ) , which exists in @xmath3 spatial dimensions and under a strong magnetic field , is the best known example of such a phase .
the recent discovery of the quantum spin hall effect ( qshe ) in @xmath3 and the @xmath0 topological insulator in @xmath4 @xcite shows topological phases can exist even in @xmath5 spatial dimensions , and can be protected by some discrete symmetries such as time - reversal symmetry ( trs , t ) , particle - hole symmetry ( phs , c ) , and chiral ( or sublattice ) symmetry ( sls , s ) . for non - interacting fermions , an exhaustive classification of topological insulators ( tis ) and superconductors ( tscs )
is proposed in refs .
@xcite : tis / tscs are classified in terms of spatial dimensions @xmath6 and the @xmath7 symmetry classes ( two `` complex '' and eight `` real '' classes ) ( table [ charge ] ) .
the ten symmetry classes are in one - to - one correspondence to the riemannian symmetric spaces ( without exceptional series ) and , as pointed out in @xcite , they are equivalent to k - theory classifying spaces @xcite . for example , the iqhe , qshe , and @xmath0 ti are a topologically non - trivial state belonging to class a ( @xmath3 ) , aii ( @xmath3 ) , and aii ( @xmath4 ) , respectively .
the complete classification of non - interacting tis and tscs opens up a number of further questions , most interesting among which are interaction effects : do non - interacting topological phases continue to exist in the presence of interactions ?
can interactions give rise to novel topological phases other than non - interacting tis / tscs ? what is a topological field theory underlying tis / tscs , which can potentially describe tis / tscs beyond non - interacting examples ?
on the other hand , the ten - fold classification of tis / tscs reminds us of d - branes , which are fundamental objects in string theory , and are also classified by k - theory @xcite ( table [ dbrane ] ) via the open string tachyon condensation @xcite .
it is then natural to speculate a possible connection between tis / tscs and of d - branes . in this paper , we propose a systematic construction of tis / tscs in terms of two d - branes ( d@xmath8- and d@xmath9-branes ) , possibly with an orientifold plane ( o - plane ) . besides the appealing mathematical similarity between tis / tscs and d - branes , realizing tis / tscs in string theory has a number of merits , since string theory and d - branes are believed to be rich enough to reproduce many types of field theories and interactions in a fully consistent and uv complete way . indeed
, our string theory realizations of tis / tscs give rise to massive fermion spectra , which are in one - to - one correspondence with the ten - fold classification of tis / tscs , and come quite naturally with gauge interactions .
these systems , while interacting , are all topologically stable , as protected by the k - theory charge of d - branes .
we thus make a first step toward understanding interacting tis / tscs @xcite .
we are also separately preparing a regular paper with more details and expanded results in @xcite . in d@xmath8-d@xmath9-systems ,
massive fermions arise as an open string excitation between the two d - branes .
the distance between the branes corresponds to the mass of fermions .
open strings ending on the same d - branes give rise to a gauge field , which we call @xmath10 ( d@xmath8 ) and @xmath11 ( d@xmath9 ) with gauge group @xmath12 and @xmath13 , respectively , and couple to the fermions .
these two gauge fields play different roles in our construction : the gauge field @xmath10 `` measures '' k - theory charge of the d@xmath9-brane , and in that sense it can be interpreted as an `` external '' gauge field . in this picture , the d@xmath9-brane charge is identified with the topological ( k - theory ) charge of tis / tscs . on the other hand , @xmath11 is an internal degree of freedom on the d@xmath9-brane . for example , in the integer / fractional qhe , the external gauge field is the electromagnetic u(1 ) gauge field , which measures the hall conductivity , while the internal gauge field is the chern - simons ( cs ) gauge field describing the dynamics of the droplet itself .
the massive fermions can be integrated out , yielding the description of the topological phase in terms of the gauge fields .
the resulting effective field theory comes with terms of topological nature , such as the cs or the @xmath14-terms . in our string theory setup
, they can be read off from the wess - zumino ( wz ) action of the d - branes , by taking one of the d - branes as a background for the other .
one can view these gauge - interacting tis / tscs from d@xmath8-d@xmath9-systems as an analogue of the projective ( parton ) construction of the ( fractional ) qhe @xcite .
our string theory realization of tis / tscs sheds light on extending the projective construction of the qhe to more generic tis / tscs ; it tells us what type of gauge field is `` natural '' to couple with fermions in topological phases , and guarantees the topological stability of the system . .
[ charge ] classification of topological insulators and superconductors @xcite ; @xmath6 is the space dimension ; the left - most column ( a , aiii , @xmath15 , ci ) denotes the ten symmetry classes of fermionic hamiltonians , which are characterized by the presence / absence of time - reversal ( t ) , particle - hole ( c ) , and chiral ( or sublattice ) ( s ) symmetries of different types denoted by @xmath16 in the right most three columns .
the entries `` @xmath17 '' , `` @xmath0 '' , `` @xmath18 '' , and `` @xmath19 '' represent the presence / absence of topological insulators and superconductors , and when they exist , types of these states ( see ref .
@xcite for detailed descriptions ) .
[ cols="^,^,^,^,^,^,^,^,^,^,^,^",options="header " , ]
the main conclusion of this paper is that there is a one - to - one correspondence between the tachyon - free d@xmath8-d@xmath9 systems and the ten classes of topological insulators in @xmath20 dimensions .
indeed , we explicitly constructed the corresponding ten classes of d@xmath8-d@xmath9 brane configurations in superstring theory .
two out of ten are realized in type ii string theory without orientifolds , while the other eight require orientifolds .
the k - theory charges of the d@xmath9-branes agree with that of the topological insulators .
one may wonder if there are other tachyon - free d@xmath8-d@xmath9 systems which have not been considered in this paper .
however , it turns out that their low - energy theories just correspond to multiple copies of the ten classes of topological insulators ( for details refer to @xcite ) .
since a topological insulator has a mass gap in the bulk , the distance between the d@xmath8 and d@xmath9 is taken to be non - vanishing in its corresponding d - brane system .
when we discuss the boundary of a ti / tsc , however , the d@xmath8-brane is bent toward the d@xmath9-brane and thus d@xmath8 and d@xmath9 are intersecting with each other .
therefore massless fermions appear at the intersection and they are identified with the boundary modes ( or edge modes ) .
we can also consider holographic descriptions of these systems by extending the constructions in @xcite in principle , though it is not possible to take the large-@xmath21 limit of @xmath0 charged d - branes .
we acknowledge `` quantum criticality and the ads / cft correspondence '' miniprogram at kitp , `` quantum theory and symmetries '' conference at university of kentucky .
we would like to thank k. hori , p. kraus , a. ludwig , j. moore , m. oshikawa , and s. sugimoto for useful discussion , and a. furusaki for his clear lecture at `` development of quantum field theory and string theory '' ( yitp - w-09 - 04 ) at kyoto university .
sr thanks center for condensed matter theory at university of california , berkeley for its support .
tt is supported in part by jsps grant - in - aid for scientific research no . 20740132 , and by jsps grant - in - aid for creative scientific research no . | realization of topological insulators ( tis ) and superconductors ( tscs ) , such as the quantum spin hall effect and the @xmath0 topological insulator , in terms of d - branes in string theory is proposed .
we establish a one - to - one correspondence between the k - theory classification of tis / tscs and d - brane charges .
the string theory realization of tis and tscs comes naturally with gauge interactions , and the wess - zumino term of the d - branes gives rise to a gauge field theory of topological nature .
this sheds light on tis and tscs beyond non - interacting systems , and the underlying topological field theory description thereof .
topological insulators and superconductors from d - brane + shinsei ryu@xmath1 and tadashi takayanagi@xmath2 |
there are geological evidence that earth had to face multiple episodes of global ( or quasi - global ) glaciation , at the end of the archean 2.45 - 2.22 gyrs ago and during the neoproterozoic era 710 and 650 myears ago @xcite .
it is widely believed that the carbonate@xmath0silicate cycle @xcite was the main agent to trigger deglaciations on past earth .
in particular , on a completely frozen planet , also called hard snowball , the weathering of co@xmath1 is stopped ; continuous volcanic outgassing builds up atmospheric co@xmath1 , which warms up the climate until liquid water is produced in the equatorial regions . by extension
, this mechanism may be crucial to stabilize the climate of earth - like exoplanets .
it is even central for the definition of the classical habitable zone @xcite , which assumes that planets can build up co@xmath1 atmospheres ( as massive as wanted ) suitable for the stability of surface liquid water .
planets near the outer edge of the habitable zone may suffer , as earth did , episodes of total glaciation .
recent work by @xcite has even shown that , in case of planets lacking land vascular plants , temperate climates may not be stable , because at high co@xmath1 partial pressure , the increased weathering rate does not allow temperate stable solutions .
this effect , enhanced for planets weakly irradiated by their star , may drive systematically earth - like exoplanets toward episodes of glaciation . can earth - like planets in the habitable zone of their star always escape from episodes of glaciation ? in this work ,
we use 3d - global climate model simulations of snowball planets to study the ability of the increased co@xmath1 greenhouse effect resulting from the carbonate - silicate cycle to drive them out of glaciation . as
the co@xmath1 outgassed by volcanoes accumulate in the atmosphere , the temperature of condensation of co@xmath1 can exceed the surface temperature of the poles .
this lead to the trapping of extra outgassed co@xmath1 , forming permanent co@xmath1 polar ice caps , and therefore seriously limits the efficiency of the carbonate@xmath0silicate cycle .
this possibility has already been suggested by @xcite and @xcite , but has never been explored yet .
we propose in this paper a detailed study of this scenario .
we use in this paper the 3-dimensions lmd generic global climate model to study the deglaciation of earth - like planets orbiting circularly around a sun - like star ( sun spectrum and luminosity ) in response to increasing amount of atmospheric co@xmath1 ( from 0.01 to 3 bars ) , and for orbital distances ranging from 1.10 to 1.45 astronomical units ( au ) .
detailed information on the model can be found in appendix [ appen_lmd_model ] .
our simulations were designed to represent completely frozen earth - like planet characteristics .
these include the radius ( 6370 km ) , the gravity field ( 9.81 m s@xmath4 ) , the obliquity ( 23.5@xmath8 ) and the rotation speed ( 7.28@xmath1310@xmath14 rad s@xmath15 ) .
the roles of obliquity , planetary mass and rotation rate on the ability of planets to escape glaciation episodes are discussed in sections [ null_obliquity_section ] and [ sensitivity ] .
eventually , most of the simulations were performed for a uniformly flat topography .
the effect of topography is discussed in section [ topography ] .
all the simulations performed in this study were forced initially in a cold and dry state , which assumes : 1 . a uniform and complete ice cover .
2 . atmospheric temperatures arbitrarily fixed to 230 kelvins everywhere .
no water vapor , no clouds .
depending on co@xmath1 partial pressure , obliquity , or parameterization of clouds , the simulations evolve in different steady state climate regimes that are discussed in the next section .
[ cols= " < , < " , ] \1 . melting , freezing , condensation , evaporation , sublimation and precipitation of h@xmath1o physical processes are all included in the model . in the atmosphere
, water vapor can condense into water ice particles clouds . at the surface
, we fix the h@xmath1o ice albedo at 0.6 and we use an emissivity of 1 . \2 . in our model , co@xmath1 can condense to form co@xmath1 ice clouds and surface frost if the temperature drops below the saturation temperature .
atmospheric co@xmath1 ice particles are sedimented and thus can accumulate at the surface .
the co@xmath1 ice layer formed at the surface can sublimate and recycle the co@xmath1 in the atmosphere .
the co@xmath1 ice on the surface contributes to the surface albedo calculation : if the co@xmath1 ice layer exceeds a threshold value of 1 mm thickness , then the local surface albedo is set immediately to the albedo of co@xmath1 ice ( 0.6 in this work ) . on mars ,
the albedo of co@xmath1 ice can substantially vary @xcite with insolation and presence of dust . without dust ,
the albedo can become very high so that 0.6 is probably a lower estimate .
for co@xmath1 ice , we use an emissivity of 0.9 .
the radiative effect of co@xmath1 ice clouds is discussed in details in section [ co2_cloud_section ] physical parameters used for both co@xmath1 and h@xmath1o ices are summarized in table [ param_ices ] .
what happens once co@xmath1 ice caps have reached their maximum size , as calculated in section [ max_reservoir_co2 ] ? using calculations , we show in the following lines that , depending on few parameters , the co@xmath1 ice caps when full may ( or may not ) be stable . the total mass of co@xmath1 available at the surface and in the atmosphere is : @xmath16 with a the area of the co@xmath1 ice caps , s the total area of the surface ( i.e. 4@xmath17r@xmath18 ) and @xmath19 the thickness of the co@xmath1 ice caps averaged over a. when co@xmath1 ice caps are full , @xmath20 .
let s assume that the system initially with full co@xmath1 ice caps is sightly perturbated from @xmath21 to @xmath22 . by conservation of co@xmath1 mass ,
the new mass of co@xmath1 ice caps is @xmath23 $ ] = @xmath24\footnote{hereafter , ' [ ' and ' ] ' are used to bracket variables . }
$ ] .
we know first from gcm simulations that the area of the ice caps a is not a monotonic function of @xmath33 ( see figure [ condens_plots ] ) .
instead , as @xmath33 grows , @xmath34 should be positive and then at some point become negative .
figure [ condens_plots]b ( 23.5@xmath35 obliquity , inactive co@xmath1 clouds ) tells us that the maximum of a(@xmath33 ) should roughly lie at 1 bar in this specific configuration .
it is possible to derive an analytical - complicated yet - expression of @xmath36 using the relation that served to compute figure [ 2d_basal_melting ] .
it tells us that , whatever the configuration , @xmath36 is in fact always negative , because as pco@xmath1 increases , surface temperature also increases , which limits the thickness of co@xmath1 ice caps shows that the mean thickness of co@xmath1 ice caps is proportional to the maximum thickness calculated by basal melting . ] ( see equation [ conductivity ] ) . for the experiment described in previous section ( 1.30 au
, 23.5@xmath35 obliquity , inactive co@xmath1 clouds , co@xmath1 partial pressure of 1 bar ) , we assume @xmath37 and we have therefore ( with @xmath38 , see section [ co2_rad_extent ] ) : @xmath39 from our calculations , this condition is valid for internal heat flux lower than 80 mw m@xmath4 .
it means that , for internal heat flux lower than 80 mw m@xmath4 : ( 1 ) co@xmath1 ice caps when full would not be stable , and ( 2 ) the maximum amount of co@xmath1 that can be trapped in the @xmath40surface , atmosphere@xmath41 system is attained for pco@xmath1 lower than 1 bar . for internal heat flux
higher than 80 mw m@xmath4 , because a significant fraction of co@xmath1 is in the gaseous phase : ( 1 ) co@xmath1 ice caps when full would be stable ( until @xmath34 term becomes significant ) , and ( 2 ) the maximum amount of co@xmath1 trapped in the @xmath40surface , atmosphere@xmath41 system occurs for pco@xmath1 larger than 1 bar . ,
b. , forget , f. , wordsworth , r. , leconte , j. , millour , e. , codron , f. , and spiga , a. ( 2013 ) . exploring the faint young sun problem and the possible climates of the archean earth with a 3-d gcm .
, 118:414431 . , f. , musat , i. , bony , s. , braconnot , p. , codron , f. , dufresne , j .- l . ,
fairhead , l. , filiberti , m .- a .
, friedlingstein , p. , grandpeix , j .- y . , krinner , g. , levan , p. , li , z .- x . , and lott , f. ( 2006 ) . .
, 27:787813 . , l. s. , gordon , i. e. , babikov , y. , barbe , a. , benner , d. c. , bernath , p. f. , birk , m. , bizzocchi , l. , boudon , v. , brown , l. r. , campargue , a. , chance , k. , coudert , l. h. , devi , v. m. , drouin , b. j. , fayt , a. , flaud , j .-
m . , gamache , r. r. , harrison , j. j. , hartmann , j. m. , hill , c. , hodges , j. t. , jacquemart , d. , jolly , a. , lamouroux , j. , le roi , r. j. , li , g. , long , d. a. , lyulin , o. m. , mackie , c. j. , massie , s. t. , mikhailenko , s. , mller , h. s. p. , naumenko , o. v. , nikitin , a. v. , orphal , j. , perevalov , v. i. , perrin , a. , polovtseva , e. r. , richard , c. , smith , m. a. h. , starikova , e. , sung , k. , tashkun , s. a. , tennyson , j. , toon , g. c. , tyuterev , v. g. , and wagner , g. ( 2013 ) . .
, 130:455 .
toon , o. b. , mckay , c. p. , ackerman , t. p. , and santhanam , k. ( 1989 ) .
rapid calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres .
, 94:16,28716,301 . | it is widely believed that the carbonate@xmath0silicate cycle @xcite is the main agent - through volcanism - to trigger deglaciations by co@xmath1 greenhouse warming on earth and on earth - like planets when they get in frozen state .
here we use a 3d global climate model ( gcm ) to simulate the ability of planets initially completely frozen to escape from glaciation episodes by accumulating enough gaseous co@xmath1 .
the model includes co@xmath1 condensation and sublimation processes and the water cycle .
we find that planets with earth - like characteristics ( size , mass , obliquity , rotation rate , ... ) orbiting a sun - like star may never be able to escape from a glaciation era , if their orbital distance is greater than @xmath2 1.27 astronomical units ( flux @xmath3 847 w m@xmath4 , s@xmath5 @xmath3 0.62 ) , because co@xmath1 would condense at the poles here the cold traps forming permanent co@xmath1 ice caps .
this limits the amount of co@xmath1 in the atmosphere and thus its greenhouse effect .
furthermore , our results indicate that for ( 1 ) high rotation rates ( p@xmath624 h ) , ( 2 ) low obliquity ( obliquity@xmath723.5@xmath8 ) , ( 3 ) low background gas partial pressures ( @xmath91bar ) , and ( 4 ) high water ice albedo ( h@xmath1o albedo@xmath100.6 ) , this critical limit could occur for significantly lower equivalent distance ( or higher insolation ) . for each possible configuration
, we show that the amount of co@xmath1 that can be trapped in the polar caps depends on the efficiency of co@xmath1 ice to flow laterally as well as its graviational stability relative to subsurface water ice .
the flow of co@xmath1 ice from polar regions to the equator is mostly controlled by the bottom temperature , and hence by the internal heat flux of the planet .
we find that a frozen earth - like planet located at 1.30 au of a sun - like star could store as much as 1.5/4.5/15 bars of dry ice at the poles , for internal heat fluxes of 100/30/10 mw m@xmath4 .
but these amounts are in fact lower limits . for planets with a significant water ice cover ,
we show that co@xmath1 ice deposits should be gravitationnally unstable .
they get burried beneath the water ice cover in very short timescales of 10@xmath11 - 10@xmath12 yrs , mainly controlled by the viscosity of water ice . for water ice cover exceeding about 300 meters ,
we show that the co@xmath1 would be permanently sequestred underneath the water ice cover , in the form of co@xmath1 liquids , co@xmath1 clathrate hydrates and/or dissolved in subglacial water reservoirs ( if any ) .
this would considerably increase the amount of co@xmath1 trapped and further reduce the probability of deglaciation .
our results may have implications for the search for life - suitable extrasolar planets orbiting in the habitable zone of sun - like stars . |
when low- and intermediate mass stars enter the agb phase at the end of their lives , the mass - loss rate exceeds the nuclear burning rate and so dominates the subsequent evolution . in this process , a circumstellar envelope ( cse ) of gas and dust is formed which expands at a rate of about @xmath5km@xmath6 ( see for example @xcite ) .
the agb mass loss undergoes variations on different time scales .
the mass loss gradually increases over a time scale of several hundred thousands of years to reach a maximum on the tip of the thermally pulsing - agb @xcite .
the pulsations of the central star cause variations over several hundreds of days .
strong variations in the mass - loss rate , probably related to thermal pulses occurring every @xmath7-@xmath5 @xmath8yr @xcite , can lead to the formation of circumstellar detached shells .
@xcite have recently studied 7 carbon stars with known detached molecular shells .
they find that the shells are caused by periods of very intense mass loss ( @xmath9 ) and that these shells are running into a previous low mass - loss - rate agb wind .
after the intense mass - losing period , the mass loss decreases to a few @xmath10 , on a time scale of a few thousand years .
the question then arises if these types of mass - loss variations can be deduced from the sed . to answer this question
, we modelled the sed of a carefully selected sample of nearby agb stars , post - agb stars and supergiants . for modelling purposes it proved desirable to obtain millimetre observations of the stars in our sample , as there are not many observations available in the literature in this wavelength range .
still , a considerable part of the dust envelope is so cold that it emits its radiation at millimetre wavelengths , making these fluxes necessary to constrain the models for the seds .
+ the outline of this article is as follows .
first , the obtained fluxes at @xmath0 mm are presented .
sect.[observations ] contains information on the sample selection , the observations with simba and the data reduction with mopsi .
sect.[aperture ] is devoted to the aperture photometry . in sect.[models ] the constructed models for the seds are presented and the quality of these models and the indications for variable mass loss are discussed . in sect.[variations ] , the variability at @xmath11 mm is analysed on the basis of our observations .
the conclusions are summarised in sect.[conclusions ] .
the agb stars in the sample include m- and c - stars .
we have also observed some post - agb stars and supergiants that are known to have circumstellar shells . to improve the sensitivity to very faint circumstellar emission , the selection was restricted to objects with low mm - background emission based on the _ iras _ 60 and @xmath12 m data ( typically the cirr3 flag , which is the total @xmath13 m sky surface brightness , @xmath14 ) and the sample was further restricted to stars within 1kpc ( see table [ results ] ) .
there are a few exceptions , such as the unique f - type supergiant irc@xmath15 .
the data were taken with the 37-channel hexagonal bolometer array simba installed at the 15-m sest telescope , during @xmath16 observation runs : 2002 september 510 , 2003 may 913 and 2003 july 1315 .
the channels have a half power beam width ( hpbw ) of 24arcsec and two adjacent channels are separated by 44arcsec .
the filter bandpass is centered on 1.2 mm or 250ghz and has a full width half max ( fwhm ) of 90ghz .
simba works without a wobbling secondary mirror ; the maps were made with the fast - scanning technique .
the scans were performed in azimuthal direction by moving the telescope at a speed of @xmath17 with a separation in azimuth of 8arcsec .
the size of the scans varies between 500arcsec x 360arcsec and 600arcsec x 480arcsec .
4 to 8 consecutive scans were made of each source .
this procedure was repeated several times for each source during the observation runs .
although simba has a hexagonal array design , there are still gaps in the spatial coverage . because the telescope is set up in horizontal coordinates , the scan direction on the sky changes with the hour angle . by assembling scans taken at different hour angles ,
the gaps in the spatial coverage are reduced .
of course the assembling of the different scans also increases the signal - to - noise ratio .
the mopsi software was used to reduce the data .
basically the procedure described in the section on mopsi in the simba user - manual @xcite was followed , but the reduction was further divided into 3 different steps . in the first step some fundamental operations like despiking , opacity correction and sky - noise reduction
are performed on each of the individual scans .
also , the 4 to 8 consecutive scans of each source are put together to form one map . in a second step ,
the maps made during different nights are assembled .
if the source was detected in the individual maps , the maps were recentered before the assembling . out of this map information
is gained about the position of the source , which is used in the last step to define a proper baseline and to improve the sky - noise reduction .
for the absolute calibration , scans were made of uranus , typically at the beginning and/or end of each observing night .
the data reduction is basically the same as for the scientific sources , although a few steps were altered because uranus is a relatively strong and extended source .
only low order baseline fits were used ( with an appropriate base range definition ) and neither despiking nor sky - noise reduction were carried out , as recommended in the manual .
the flux of uranus at 250ghz was estimated with the subprogram ` planet ' in mopsi .
table [ tabelvarianties ] gives the resulting calibration factors for the 3 observation runs .
k , amc @xmath20 , @xmath21 , @xmath22k , @xmath23 between @xmath24 and @xmath25 , @xmath26 between @xmath25 and @xmath27 .
the upper figure shows the photometric data ( asterisk ) and the model ( full line ) .
error - bars are shown , but most of the time they fall within the symbols .
a reversed triangle represents an upper limit .
the lower figure shows the lrs spectrum ( plus signs ) and the model ( full line ) . as a comparison ,
the dotted line shows the corresponding hydrodynamical model . ] | it is generally acknowledged that the mass loss of asymptotic giant branch ( agb ) stars undergoes variations on different time scales .
we constructed models for the dust envelopes for a sample of agb stars to assess whether mass - loss variations influence the spectral energy distribution ( sed ) . to constrain the variability , extra observations at millimetre wavelengths ( @xmath0 mm ) were acquired . from the analysis of the dust models , two indications for the presence of mass - loss variations can be found , being ( @xmath1 ) a dust temperature at the inner boundary of the dust envelope that is far below the dust condensation temperature and ( @xmath2 ) an altered density distribution with respect to @xmath3 resulting from a constant mass - loss rate . for 5 out of the 18
studied sources a two - component model of the envelope is required , consisting of an inner region with a constant mass - loss rate and an outer region with a less steep density distribution . for one source an outer region with a steeper density distribution was found .
moreover , in a search for time variability in our data set at 1.2 mm , we found that wx psc shows a large relative time variation of @xmath4% which might partially be caused by variable molecular line emission .
[ firstpage ] stars : agb and post - agb stars : mass - loss stars : variables : other radio continuum : stars . |
99 heyman p and garcia - molina h 2006 collaborative creation of communal hierarchical taxonomies in social tagging systems _ technical report infolab 2006 - 10 .
department of computer science , stanford university , stanford , ca , usa _
schmitz c , grahl m , hotho a , stumme g , cattuto c , baldassarri a , loreto v and servedio vdp 2007 network properties of folksonomies _ proceedings of the sixteenth international world wide web conference ( www2007 ) _ | we analyze _ citeulike _ , an online collaborative tagging system where users bookmark and annotate scientific papers . such a system can be naturally represented as a tripartite graph whose nodes represent papers , users and tags connected by individual tag assignments .
the semantics of tags is studied here , in order to uncover the hidden relationships between tags .
we find that the clustering coefficient reflects the semantical patterns among tags , providing useful ideas for the designing of more efficient methods of data classification and spam detection .. the recent development of the world wide web is characterized by a growing number of online social communities . in many such cases ,
individuals provide bits of information - about either their tastes , opinions or interests - and software applications gather and organize them into a database , allowing the browsing of the whole information collected so .
a class of such collaborative systems focusses on collecting users online bookmarks with either a general approach or a more specialized one . in particular , some websites have been recently born to store user generated scientific bibliographies . in these systems ,
the elementary contribution , the `` post '' , is made of three ingredients : a user , an article and an annotation of it by a number of tags chosen by users . in exchange for this voluntary contribution
, a user can browse others bibliographies and annotations .
tags are an alternative classification method with respect to traditional taxonomies , where items belong to `` taxa '' represented as a tree like set of categories : here , each category contains in turn a number of more specialized sub categories , and so on until the desired resolution of classification is been reached . instead , in tagging systems items are tagged by users characterized by diverse tagging strategies depending on a number of individual variables .
the set of tag resource relations in such a community is called a `` folksonomy '' .
such communities are now extremely popular , storing hundreds of thousands posts and more .
the tagging system we analyze here , _ citeulike _
@xcite , has been built , at the time of our survey , by ca .
180000 references annotated by ca .
48000 tags supplied by ca .
6000 users .
our dataset includes about 550000 `` tag assignments '' : each assignment is a t - uple ( user , resource , tag ) .
the sequence of chronologically ordered tags , in particular , can be interpreted as a stream of words , to which one can applies the traditional statistical text analysis to uncover how human behavior affects it .
the statistical analysis of word occurrences in a written text has shown that word frequencies are power law distributed according to the zipf s law , according to which a large number of words appears in a text only a few times , while a few words occur orders of magnitude more often @xcite .
such feature has been modeled by many models based on the preferential attachment principle , that is , the assumption that authors employ already used words with a probability proportional to the current word frequency .
moreover , it has been observed that the rate of new words decrease with the text
length @xcite , that is , the number of distinct word @xmath0 in a text of length @xmath1 scale as @xmath2 with @xmath3 .
however , models in literature assume that new words are introduced at a constant growth rate , so that their total number , i.e. the vocabulary , is a linear constant of the total number of words ( both new or repeated ones ) used so far @xcite . yet , to discover the semantical properties of _ citeulike _ , one rather represents it by means of the network formalism , which proved fruitful in the analysis of many natural and social phenomena involving unsupervised interacting units : in a network perspective , elementary interacting agents or objects are represented by nodes , interactions by edges connecting them
. the widespread success of such approach has been triggered by the discovery that many networks instances one encounters in reality share common statistical properties with no external tuning .
for example , the degree @xmath4 , that is , the number of edges pointing to a node , follows in many cases a broad distribution @xmath5 with long tail decaying algebraically as @xmath6 with @xmath7 .
if edges have varying intensities , each of them is attached a weight @xmath8 representing its intensity ; accordingly , a node is characterized by its @xmath9 , equal to the sum of the weights of edges pointing to it .
the distribution of @xmath10 , too , is power
law distributed in many real weighted network instances .
furthermore many such networks exhibit a strong transitivity , i.e. with high probability , the neighbors of a node are themselves connected by an edge , with respect to purely random realization of a network with equal number of nodes and links .
networks sharing the above properties are currently named `` complex networks '' @xcite .
the network approach has also been recently adopted to analyze the semantical structure of tagging systems @xcite .
tags can be represented by networks in different ways , in order to study how the behavior of users maps into the dynamical or topological features .
a more recent stream of research deals with the organization of tags , which are implicitly linked by hierarchical and logical associations emerging despite the diversity of users as their number is large enough .
the underlying semantical organization of tags reveals the dominant trends within a tagging community and allows to improve its navigability .
recently , algorithms have been introduced in order to infer a taxonomy of tags from a folksonomy @xcite .
the statistical properties we observed in the _ citeulike _ data are consistent with the findings obtained in similar surveys , confirming that tags in collaborative systems form complex networks indeed .
moreover , we have investigated how the underlying semantics of tags reflects on the topology of the network . as a matter of facts ,
tags provided by users come with no explicit hierarchy beside the chronological ordering , leading authors to analyze the stream of tags as a text like sequence of words .
interestingly , the time ordered sequence of tags displays statistical properties already observed in written texts , such as the fat tails in the word frequency distributions or the sub - linear vocabulary growth .
our analysis confirms the sub - linear vocabulary growth observed in written texts .
the number of distinct tags @xmath11 introduced by users after @xmath12 assignments grows approximately as @xmath13 , as shown in figure [ sublinear ] although the pace is slightly smaller than in other collaborative tagging systems already surveyed @xcite .
the frequency of tags , too , reported in [ wordsfreq ] , reminds that of words observed in written texts , algebraically decaying according to the zipf s law @xcite .
however , the sole frequency of tags as a function of time does not convey much information about the semantics , although it reflects the different centrality of associated concepts in the underlying knowledge organization . to investigate tag pair relations
, one has to represent the unit elements of a tagging system as nodes of a network .
the dataset we focus on can be naturally represented as a tri partite network , where each node represents either a user @xmath14 , a resource @xmath15 or a tag @xmath12 ; if a tag assignment @xmath16 exists , an edge is drawn from @xmath14 to @xmath15 , and from @xmath15 to @xmath12 . since in a single user s
post a resource can be tagged more than once , one post can correspond to multiple tag assignments @xcite .
although efficient algorithm have been developed to analyzed such tri partite network @xcite , the heterogeneity of nodes discourages in general the application of traditional network methods , mainly conceived to deal with network connections representing peer - to - peer relationships .
thus , to study how tags are organized we chose to project the tri partite networks on the tag space . as a result
, the tag co occurrence network we study is composed by nodes representing tags only , between which an undirected edge of weight @xmath8 is drawn if @xmath8 distinct resources are labeled by both tags .
the resulting network displays some of the typical features of weighted scale free networks .
we have measured the distribution of the sum @xmath17 of the weights of edges pointing to a given node , or the _ strength _ of the node : such distribution @xmath18 , plotted in figure [ strength - dist ] , exhibits a clear power
law decay @xmath19 , with @xmath20 for large values of @xmath17 .
interestingly , the heterogeneity of the observed nodes weights does not necessarily reflects the centrality of corresponding concepts , that are supposed to be assigned together with a wider range of more specialized concepts , in the underlying hierarchy of tags .
as it has been already shown @xcite , reshuffling the tag assignment in order to destroy the logical association among words does not change dramatically the shape of @xmath18 , which proves that the @xmath21 heterogeneity is more a consequence of frequency distribution broadness than of the varying roles of concepts in the semantical organization of the whole vocabulary .
nevertheless , the tag co occurrence network unveils some semantical feature of the underlying ontology if , instead of focussing on the properties of single nodes , one turns to the inspection of quantities involving its environment .
an example of such is represented by the analysis of the neighbor average degree @xmath22 of nodes with degree @xmath4 , where the degree is the number of incoming edges of a node . in our study
we examined instead the clustering properties of the tag co occurrence network through the clustering coefficient .
such coefficient @xmath23 counts the average density of triangles involving nodes with degree @xmath4 or , in other words , the probability that the nearest neighbors of a node with degree @xmath4 are in turn connected one to each other .
this reads @xmath24 where @xmath25 is 1 if a link exists between @xmath26 and @xmath27 and 0 otherwise , and @xmath28 is the frequency of nodes with degree @xmath4 .
this quantity has been found to characterize most complex networks found in nature and society , where it takes substantially larger values with respect to a purely random networks @xcite .
the properties of the clustering coefficient are often associated to the hierarchical organization of nodes @xcite .
indeed , the clustering coefficient appears to encode a signature of semantical relations between words . as represented in figure [ clustering - real ]
, the clustering coefficient @xmath23 in _ citeulike _ decays algebraically for large values of the degree @xmath4 , according to @xmath29 .
however , the clustering value displays an apparent fluctuation at @xmath30 . by inspecting the nodes corresponding to such value
, one discovers that the sharp rise taking place at al @xmath30 corresponds to a non existing resource labelled by @xmath31 distinct uncorrelated randomly chosen tags , which mimics the a spam contribution to the collaborative systems .
one is led thus to conjecture that the overall semantical organization of concept represented by tags is encoded in a characteristic behavior of the clustering coefficient @xmath23 , so that tags assigned in a semantically inconsistent way fall far away from this behavior . to verify such conjecture ,
we have performed the same statistical analysis after removing from the data set the tag assignments related to the spam like page . as shown in figure
[ clustering - real ] , after the removal the clustering coefficient follows a more regular behavior , confirming that the strong fluctuation observed above was due indeed to the presence of a single meaningless set of assignments involving a single resource .
tags assigned only to the spam resource form a complete co occurrence network , so that their clustering coefficient is equal to @xmath32 .
thus , the behavior of clustering coefficient of the tag co occurrence networks can be used as a test for models representing the tag semantical organization or , equivalently , how users choose tags when annotating a resource . as noted in literature @xcite
, users typically use tags hierarchically , labelling a resource by tags related to the same topics but with different generality , adding more specialized tags as the number of collected resources grows . on a very basic level , we have tested how such hierarchical tagging , affects the topology of the tag co occurrence network by a simple toy model defined in the following .
let us assume that tags are organized on a taxonomy , that is , a tree like structure stemming from a seed node , where each node corresponds to a tag and is an offspring of another tag belonging to the same branch of knowledge with higher generality . at discrete time steps
, a new post is added to the system , with a new resource and 2 tags .
the first tag can be a new one , with probability @xmath33 : in such case , the new tag is an offspring of a tag randomly chosen among the already employed ones .
otherwise , the first tag is chosen at random among the already employed ones .
the second tag is either chosen at random from within the whole set of used tags or , with probability @xmath34 , it is chosen according to hierarchy : in such case , the second tag is drawn at random among the nodes that lie on the shortest path length from the first tag to the seed node on the tree like taxonomy .
the tag co occurrence network resulting from the above algorithm share some features of the _ citeulike _ one , if we assume a time dependent @xmath33 which reproduces the sub - linear vocabulary growth observed in reality , and by a suitable choice of the parameter @xmath34 , which mimics the relevance of hierarchy in tagging activity . to reproduce the growth rule ,
we have set @xmath35 and imposed that @xmath36 and @xmath37 where the number of resources @xmath38 , the number of tag assignments @xmath39 , the number of tags @xmath40 and @xmath41 are set to the same values they take in _
citeulike_. as a result , this yields @xmath42 and @xmath43
. as shown in figure [ strength - dist ] , the strength distribution @xmath18 of tags is a scale free one with a good agreement with reality in the decaying exponent for large values of @xmath17 if one sets @xmath44 . for such choice of the parameter , the clustering coefficient reproduces qualitatively the algebraic decay observed in _
citeulike _ , as shown in figure [ summarymodel ] , although the absolute value differs of orders of magnitude .
we have found , thus , a simple model that captures the complex features of a tag co occurrence network issued from the dataset describing an online collaborative tagging system , _
citeulike_. in particular , by assuming that users label resources by hierarchically associated tags , the probability distribution of nodes strength is reproduced for a suitable choice of the parameters .
moreover , the model reproduces qualitatively the decaying asymptotic behavior of the clustering coefficient @xmath23 .
such quantity encodes a signature of the semantical organization of concepts represented by tags , so that malicious or meaningless tag assignments can be detected by inspecting the perturbation to the clustering coefficient they generate . establishing a relationship between clustering and semantics may suggest tools and algorithms for technological tasks such as automatic categorization of resources , recommendation and spam detection techniques .
the authors acknowledge useful discussions with francesca colaiori , stefano leonardi , ciro cattuto , vito d.p .
servedio and andrea baldassarri .
the authors acknowledge the european project delis for support and r. cameron for providing the data . as a function of time @xmath12 , where time is measure in chronologically ordered tags assignments ( plus symbols ) .
solid line represents @xmath45 for a comparison.,scaledwidth=80.0% ] of tag frequencies @xmath46 ( plus symbols ) .
solid line represents @xmath47 for a comparison.,scaledwidth=80.0% ] of the node strengths @xmath17 in the tag co occurrence network .
the best fitting power law exponent , represented by the solid curve , yields @xmath48 .
, scaledwidth=80.0% ] of the tag co occurrence network as a function of the nodes degree @xmath4 before ( circles ) and after ( plus symbols ) the removal of a spam post from the dataset .
the solid line represents a decay @xmath49 and the dashed vertical ruler is set at @xmath30.,scaledwidth=80.0% ] ( plus symbols ) ; the solid line represents the decay @xmath50 for a comparison with real data .
inset : the clustering coefficient in the co occurrence network derived from the model with @xmath51 ( plus symbols ) .
the solid line represents the decay @xmath49 for a comparison with real data.,scaledwidth=80.0% ] |
let @xmath2 be the set of all square matrices of order @xmath3 with entries in @xmath4 and @xmath5 be the group of all invertible matrices of @xmath2 .
a map @xmath6 is called an affine map if there exist @xmath7 and @xmath8 such that @xmath9 , @xmath10 .
we denote @xmath11 , we call @xmath12 the _ linear part _ of @xmath13 . the map @xmath13 is invertible if @xmath14 .
denote by @xmath15 the vector space of all affine maps on @xmath1 and @xmath16 the group of all invertible affine maps of @xmath17 .
let @xmath0 be an abelian affine sub - semigroup of @xmath18 . for a vector @xmath19
, we consider the orbit of @xmath0 through @xmath20 : @xmath21 .
denote by @xmath22 the closure of a subset @xmath23 .
the semigroup @xmath0 is called _ hypercyclic _ if there exists a vector @xmath24 such that @xmath25 . for an account of results and bibliography on hypercyclicity , we refer to the book @xcite by bayart and matheron .
we refer the reader to the recent book @xcite and @xcite for a thorough account on hypercyclicity .
costakis and manoussos in @xcite localize the concept of hypercyclicity using j - sets . by analogy
, we generalize this notion to affine case as follow : suppose that @xmath0 is generated by @xmath26 affines maps @xmath27 @xmath28 then for @xmath29 , we define the extended limit set j@xmath30 to be the set of @xmath31 for which there exists a sequence of vectors @xmath32 with @xmath33 and sequences of non - negative integers @xmath34 for @xmath35 with @xmath36 such that @xmath37 note that condition ( 1.1 ) is equivalent to having at least one of the sequences @xmath38 for @xmath39 containing a strictly increasing subsequence tending to @xmath40 .
we say that @xmath0 is _ locally hypercyclic _ if there exists a vector @xmath41 such that j@xmath42 .
so , the question to investigate is the following : when an abelian sub - semigroup of @xmath17 can be hypercyclic ?
the main purpose of this paper is twofold : firstly , we give a general characterization of the above question for any abelian _ sub - semigroup _ of @xmath17 using j - sets .
secondly , we generalize the results proved in @xcite , by a.ayadi and h.marzougi , for linear semigroups , which answers negatively , the question raised in the paper of costakis and manoussos @xcite : is it true that a locally hypercyclic abelian semigroup @xmath43 generated by matrices @xmath44 is hypercyclic whenever j@xmath45 for a finite set of @xmath10 whose vector space is equal @xmath1 ?
similarly for @xmath46 .
denote by @xmath47 the canonical basis of @xmath1 .
let @xmath48 .
let introduce the following notations and definitions .
denote by : + let @xmath49 be fixed , denote by : + @xmath50 , @xmath51 and @xmath52 .
+ @xmath53 the canonical basis of @xmath54 and @xmath55 the identity matrix of @xmath56 . + for each @xmath57 , denote by : + @xmath58 the set of matrices over @xmath4 of the form @xmath59 + @xmath60 the group of matrices of the form ( [ eq1 ] ) with @xmath61 .
+ let @xmath62 and @xmath63 such that @xmath64 in particular , @xmath65 .
write + @xmath66 in particular if @xmath67 , then @xmath68 and @xmath69
. + @xmath70 .
+ @xmath71 where @xmath72 , for @xmath73 .
so @xmath74 .
+ @xmath75 the second projection defined by @xmath76 .
+ define the map @xmath77 + @xmath78 we have the following composition formula @xmath79 then @xmath80 is an injective homomorphism of groups .
write + @xmath81 , it is an abelian subgroup of @xmath82 . + let consider the normal form of @xmath83 : by proposition [ p:2 ] , there exists a @xmath84 and a partition @xmath85 of @xmath86 such that @xmath87 .
for such a choice of matrix @xmath88 , we let + @xmath89 .
so @xmath90 , since @xmath91 .
+ @xmath92 .
we have @xmath93 .
+ @xmath94 .
+ denote by @xmath95 , @xmath96 and @xmath97 , then @xmath98 for such choise of the matrix @xmath99 , we can write @xmath100,\ \ \mathrm{with}\ \ \
q\in gl(n , { \mathbb{c}}).\ ] ] we have @xmath101 , @xmath102 and @xmath103 .
we have @xmath104 is an abelian semigroup of @xmath105 .
our principal results are the following : [ t:1 ] let @xmath0 be a finitely generated abelian semigroup of affine maps on @xmath1 . if @xmath106 for some @xmath107 then @xmath108 .
[ c:1 ] under the hypothesis of theorem [ t:1 ] , the following are equivalent : * @xmath0 is hypercyclic . *
* @xmath110 .
[ c:2 ] under the hypothesis of theorem [ t:1 ] , set @xmath111 .
if @xmath0 is not hypercyclic then @xmath112 , ( @xmath113 ) where @xmath114 are @xmath0-invariant affine subspaces of @xmath1 with dimension @xmath115 .
[ p:2 ] let @xmath0 be an abelian sub - semigroup of @xmath116 and @xmath81 .
then there exists @xmath117 such that @xmath118 is a sub - semigroup of @xmath119 , for some @xmath65 and @xmath120 .
[ p:002]@xmath121@xcite , proposition 2.1@xmath122 let @xmath0 be an abelian subgroup of @xmath123 and @xmath81 .
then there exists @xmath117 such that @xmath118 is a subgroup of @xmath124 , for some @xmath65 and @xmath120 .
suppose first , @xmath125 .
let @xmath126 be the group generated by @xmath83 .
then @xmath126 is abelian and by proposition [ p:002 ] , there exists a @xmath117 such that @xmath127 is an abelian subgroup of @xmath128 , for some @xmath129 and @xmath130 .
in particular , @xmath131 .
suppose now , @xmath132 .
for every @xmath133 , there exists @xmath134 such that @xmath135 ( one can take @xmath136 non eigenvalue of @xmath12 ) . write @xmath137 be the group generated by @xmath138 .
then @xmath137 is an abelian subsemigroup of @xmath82 .
hence by above , there exists a @xmath139 such that @xmath140 , for some @xmath130 . as @xmath141 then @xmath142 .
this proves the proposition .
let @xmath143 be the semigroup generated by @xmath83 and @xmath144 .
then @xmath143 is an abelian sub - semigroup of @xmath145 . by proposition [ p:2 ]
, there exists @xmath91 such that @xmath118 is a sub - semigroup of @xmath146 for some @xmath65 and @xmath120 and this also implies that @xmath147 is a sub - semigroup of @xmath146 .
+ + @xmath152 is obvious since @xmath153 by construction .
+ @xmath154 let @xmath31 and @xmath155 be a sequence in @xmath143 such that @xmath156 .
one can write @xmath157 , with @xmath158 and @xmath159 , thus @xmath160 , so @xmath161 .
therefore , @xmath162 .
hence , @xmath163 .
+ @xmath164 since @xmath165 and for every @xmath166 , @xmath167 , we get @xmath168 hence @xmath169
. therefore , @xmath178 and sequences of non - negative integers @xmath34 for @xmath39 such that @xmath179 hence @xmath180 .
+ @xmath181 since @xmath182 , then there exists a sequence of vectors @xmath183 with @xmath184 and sequences of non - negative integers @xmath34 for @xmath185 with @xmath186 such that @xmath187 suppose that @xmath106 with @xmath107 . by proposition [ p:2 ] , we can assume that @xmath194 and @xmath195 .
by lemma [ l:1 ] , we have @xmath196 . then by theorem [ t:5 ] , @xmath197 .
it follows by lemma [ ll1l:9 ] , that @xmath198 . with @xmath211^{t},\ x_{k}\in\{0\}\times\mathbb{c}^{n_{k}-1},\ x_{i}\in\mathbb{c}^{n_{i } } , \
\mathrm{if}\ i\neq k\right\}$ ] .
it follows that @xmath212 with @xmath213 is an affine space with dimension @xmath115 . | we give a characterization of hypercyclic using ( locally hypercyclic ) of semigroup @xmath0 of affine maps of @xmath1 .
we prove the existence of a @xmath0-invariant open subset of @xmath1 in which any locally hypercyclic orbit is dense in @xmath1 . |
solving lattice qcd to high precision requires the use of dynamical ginsparg - wilson light quarks .
however , this is computationally expensive . therefore , as a starting place , we take improved staggered quark configurations , which have the advantage of light sea quarks , and use an overlap valence quark action , which has the correct chiral and flavour symmetries .
this has its own disadvantages .
firstly , the overlap inversion is still relatively expensive and , secondly , because we have different actions for the sea and valence quarks , it is not straightforward to interpret the results .
mixed actions are inevitable in the improved staggered programme , because we do not yet have a local version of the sea quark action to use for the valence quarks . also , it is complicated to measure some quantities in the improved staggered formalism .
for example , in order to measure the mass of the nucleon one has a choice of o(100 ) different nucleon operators . without measuring a representative set ,
the effect of taste symmetry breaking is unquantified and uncontrolled .
the simulations were performed on twenty coarse ( milc ) dynamical configurations with 2 + 1 flavours @xcite .
ten configurations have a light isodoublet with mass @xmath0 and ten have @xmath1 .
both have a lattice spacing @xmath2 fm and linear size @xmath3 fm .
three iterations of hyp - smearing were applied to each configuration @xcite . the overlap operator from szin code @xcite
was then used to calculate propagators .
these were created with seven different valence quark masses using the overlap multi - mass solver : four light and three heavy @xcite . even for the baryon spectrum
we get a remarkably good signal on ten configurations . as a check
, we applied several iterations of hyp - smearing to 624 quenched ukqcd configurations at @xmath4 with a volume of @xmath5 .
planar wilson loops were used to extract the quark - antiquark potential .
hyp - smearing quickly alters the short - distance behaviour , while the medium - to - long distance behaviour remains relatively unchanged for a small number ( @xmath6 ) of iterations .
smearing the configuration helps to speed up the convergence of the overlap operator , renders the effective interaction more local , and makes the eigenvalue spectrum more like that for an overlap sea @xcite .
we perform simultaneous fits to three different correlators in order to extract the pseudoscalar meson mass ( see figure [ effective_mass ] ) .
the fluctuations in a@xmath7 are larger than the apparent statistical errors , but this is probably due to underestimation of the variance on ten configurations .
all the analysis is carried out partially quenched - we hold the sea quark mass fixed and vary the input valence quark mass . since we have multiple input valence masses , we can construct non - degenerate light meson correlators .
a two - dimensional fit was performed to @xmath8 versus valence masses @xmath9 and @xmath10 , which allowed evaluation of the average @xmath11 and @xmath12 quark mass , @xmath13 , from @xmath14 where @xmath15 is the physical pion mass squared .
this in turn allows us to evaluate the strange quark mass from @xmath16 where @xmath17 is the physical kaon mass and @xmath18 is the strange quark mass .
we define @xmath19 as @xmath20 we obtain @xmath21 from the axial ward identity @xmath22 which we can express in terms of the pseudoscalar correlator , @xmath23 , and the pseudoscalar axial correlator , @xmath24 .
@xmath25 cancels in eq.([fps ] ) and hence we only require @xmath23 in order to evaluate @xmath19 . once again we perform a 2-d linear fit to the light non - degenerate pseudoscalars to calculate @xmath19 ( see figure [ pseudoscalardecay ] ) and extract the ratio of @xmath26 ( see table [ table1 ] ) .
the value increases slightly with decreasing light sea quark mass in the right direction to agree with experiment .
this is also evident from the slight change of the gradient in figure [ pseudoscalardecay ] . versus @xmath27 for the two ensembles . ]
.pseudoscalar meson decay constants [ cols="<,<,<",options="header " , ] + we measure the masses of the nucleon and delta baryon .
it is remarkable that we can see a signal for the negative parity partner of the nucleon on as few as ten configurations .
figure [ nucleonlinear ] shows the nucleon mass versus the pseudoscalar meson mass squared .
the lines shown are uncorrelated linear fits to our data .
the values calculated by the milc collaboration @xcite on their corresponding full ensembles are also shown .
heavy quarks essentially come for free in the overlap propagator calculation due to the multi - mass solver .
however , lattice artefacts are @xmath28@xmath29 and the heaviest input valence quark mass used is @xmath30 and hence @xmath31 . with the lattice spacing of @xmath32gev
, we are at best on the limit of simulating charm . because of the rapid decay in euclidean time ,
we require double precision . however , this does not slow the solver down appreciably as we need less reorthogonalisations of the krylov subspace than in single precision .
these heavy quark propagators were used to calculate @xmath33 ( see table [ table1 ] ) .
the value of @xmath33 increases with decreasing light sea quark mass , in the direction of the experimental value , as can be seen from the change of gradients in figure [ fds ] .
vs inverse heavy - strange pseudoscalar meson mass . ]
we have shown that , even with very low statistics , it is possible to calculate light hadron and charm physics using an overlap valence operator on an improved staggered sea .
this could be an alternative to staggered valence quarks for probing sea quark effects , although for our data , the effect of small changes in the sea quark mass is minimal . | we present exploratory results for the hadron mass spectrum and pseudoscalar meson decay constants using mixed actions .
we use improved staggered sea quarks and hyp - smeared overlap valence quarks .
we obtain good signals on 10 configurations at one lattice spacing and two different sets of sea quark masses . |
the recent results from rhic ( see e.g. @xcite ) have attracted renewed interest in better understanding the dynamics of particle production , not only in nuclear collisions .
quite different approaches have been used to describe the particle spectra from the nuclear collisions @xcite . the model in ref.@xcite with an educated guess for ugd describes surprisingly well the whole charged particle rapidity distribution by means of gluonic mechanisms only .
such a gluonic mechanism would lead to the identical production of positively and negatively charged hadrons .
the recent results of the brahms experiment @xcite put into question the successful description of ref.@xcite . in the light of this experiment , it becomes obvious that the large rapidity regions have more complicated flavour structure .
i discuss the relation between ugd s in hadrons and the inclusive momentum distribution of particles produced in hadronic collisions .
the results obtained with different ugd s @xcite are shown and compared .
at sufficiently high energy the cross section for inclusive gluon production in @xmath2 can be written in terms of the ugd s `` in '' both colliding hadrons @xcite @xmath3 above @xmath4 and @xmath5 are ugd s in hadron @xmath6 and @xmath7 , respectively .
the longitudinal momentum fractions are fixed by kinematics : @xmath8 .
the argument of the running coupling constant is taken as @xmath9 . here
i shall not discuss the distributions of `` produced '' gluons , which can be found in @xcite .
instead i shall discuss what are typical values of @xmath10 and @xmath11 in the jet ( particle ) production .
average value @xmath12 and @xmath13 , shown in fig.[fig : x1_x2 ] , only weakly depend on the model of ugd . for @xmath14 0 at the rhic energy w = 200 gev one tests ugd s at @xmath15 = 10@xmath16 - 10@xmath17 .
when @xmath18 grows one tests more and more asymmetric ( in @xmath10 and @xmath11 ) configurations . for large @xmath18 either @xmath10 is extremely small ( @xmath19 10@xmath20 ) and @xmath21 1 or @xmath22 1 and @xmath11 is extremely small ( @xmath23 10@xmath20 ) .
these are regions of gluon momentum fraction where the ugd s is rather poorly known . the approximation used in obtaining ugd s are valid certainly only for @xmath24 0.1 . in order to extrapolate the gluon distribution to @xmath25 1
i multiply the gluon distributions from the previous section by a factor @xmath26 , where n = 5 - 7 . and @xmath13 for @xmath27 0.5 gev and at w = 200 gev .
[ fig : x1_x2 ] , width=302 ]
in ref.@xcite it was assumed , based on the concept of local parton - hadron duality , that the rapidity distribution of particles is identical to the rapidity distribution of gluons . in the present approach i follow a different approach which makes use of phenomenological fragmentation functions ( ff s ) . for our present exploratory study
it seems sufficient to assume @xmath28 .
this is equivalent to @xmath29 , where @xmath30 and @xmath31 are hadron and gluon pseudorapitity , respectively .
then @xmath32 where the transverse mass @xmath33 . in order to introduce phenomenological
ff s one has to define a new kinematical variable . in accord with @xmath34 and @xmath35 collisions
i define a quantity @xmath36 by the equation @xmath37 .
this leads to the relation @xmath38 where @xmath39 is given in ref.@xcite .
now we can write the single particle distribution in terms of the gluon distribution as follows @xmath40 in the present calculation i shall use only lo ff s from @xcite
. 0.2 gev .
the experimental data of the ua5 collaboration are taken from @xcite .
[ fig : eta_glue ] , width=302 ] let us analyze now how the results for pseudorapidity distributions depend on the choice of the ugd . in fig.[fig :
eta_glue ] i compare pseudorapidity distribution of charged pions for different models of ugd s . in this calculation ff from @xcite has been used .
in contrast to ref.@xcite , where the whole pseudorapidity distribution , including fragmentation regions , has been well described in an approach similar to the one presented here , in the present approach pions produced from the fragmentation of gluons in the @xmath41 mechanism populate only midrapidity region , leaving room for other mechanisms in the fragmentation regions .
these mechanisms involve quark / antiquark degrees of freedom or leading protons among others .
this strongly suggests that the agreement of the result of the @xmath41 approach with the phobos distributions @xcite in ref.@xcite in the true fragmentation region is rather due to approximations made in @xcite than due to correctness of the reaction mechanism . in principle , this can be verified experimentally at rhic by measuring the @xmath42 ratio in proton - proton scattering as a function of ( pseudo)rapidity in possibly broad range .
the brahms experiment can do it even with the existing apparatus . in fig.[fig
: pt_glue ] i compare the theoretical transverse momentum distributions of charged pions obtained with different gluon distributions with the ua1 collaboration data @xcite .
the best agreement is obtained with the karzeev - levin gluon distribution .
the distribution with the gbw model is much too steep in comparison to experimental data .
this is probably due to neglecting qcd evolution in @xcite .
, width=302 ]
i have calculated the inclusive distributions of gluons and associated charged @xmath1 s in the nn collisions through the @xmath43 mechanism in the @xmath44-factorization approach .
the results for several ugd s proposed recently have been compared .
the results , especially @xmath45 distributions , obtained with different models of ugd s differ considerably .
contrary to a recent claim in ref.@xcite , we have found that the gluonic mechanism discussed does not describe the inclusive spectra of charged particles in the fragmentation region , i.e. in the region of large ( pseudo)rapidities for any ugd from the literature .
clearly the gluonic mechanism is not the only one .
since the mechanism considered is not complete , it is not possible at present to precisely verify different models of ugd s .
the existing ugd s lead to the contributions which almost exhaust the strength at midrapidities and leave room for other mechanisms in the fragmentation regions .
it seems that a measurement of @xmath0 distributions of particles at rhic should be helpful to test better different ugd s . | the inclusive distributions of gluons and pions for high - energy nn collisions are calculated .
the results for several unintegrated gluon distributions ( ugd s ) from the literature are compared .
we find huge differences in both rapidity and @xmath0 of gluons and @xmath1 s in nn collisions for different models of ugd s .
the karzeev - levin ugd gives good description of momentum distribution of charged hadrons at midrapidities .
we find that the gluonic mechanism discussed does not describe the inclusive spectra of charged particles in the fragmentation region . |
it has recently become possible to collect large samples of high resolution cloud particle images in real time , opening up the modelling of cloud dynamics to detailed comparison with nature .
figure 1 shows ice crystal aggregates from a cirrus cloud over the usa , captured by non - contact aircraft - based imaging .
such aggregates can be seen to be comprised of varied rosette ice crystal types , and detailed statistics have recently been published on both the cluster aspect ratios [ _ korolev and isaac _ 2003 ] and size distributions [ _ field and heymsfield _ 2003 ] in cirrus clouds .
such aggregation is a key feature of cloud development in the troposphere and can be quite crucial to the development of precipitation , whether it reaches the ground as snow or melts first to arrive as rain .
the openness of the aggregates significantly accelerates their growth .
two clusters ( labelled by @xmath0 ) pass approach with their centres closer than the sum of their radii @xmath1 at a rate proportional to@xmath2 where for each cluster the sedimentation speed @xmath3 varies inversely with its radius @xmath4 and mass @xmath5 as @xmath6 here @xmath7 and @xmath8 are the viscosity and density of the air , @xmath9 is the acceleration due to gravity , and we have assumed that only one geometrical radius is relevant : _
mitchell _ [ 1996 ] discusses an elaboration .
given the above , the rates of aggregation per unit time for fixed cluster masses vary linearly overall with the cluster radii , and openness of aggregate structure enhances aggregation rates despite lowering fall speed . for real aggregates
this is a significant factor : using data from _ heymsfield et al .
_ , [ 2002 ] , one finds that rosette aggregates 2 mm across ( which yield 0.5 mm droplets ) aggregate four times faster than when melted . for cloud particles it is also relevant to consider the rates of aggregation per unit of distance fallen ( rather than per unit time ) , which at fixed mass is proportional to the square of radius , leading to 16 times enhancement for ice over water in the example cited .
we have made computer simulations of ice aggregation based on equations ( [ eq : kernel ] ) and ( [ eq : fallspeed ] ) , tracing trajectories through possible collisions to obtain accurate collision geometries .
we assumed that all collisions led to rigid irreversible joining of clusters , as the openness of the experimentally observed clusters suggests little large scale consolidation of structure upon aggregation , and that cluster orientations were randomised in between collisions but did not change significantly during them .
we took the sedimentation speeds to be governed by inertial flow , for which the mass dependence function in equation ( [ eq : fallspeed ] ) is given by @xmath10 .
details of implementation are given in a longer paper [ _ westbrook et al .
_ , 2004 ] .
some representative computer aggregates are shown in figure 1 alongside the experimental ones .
our simulations used three dimensional cross shapes for the initial particles as a crude representation of the experimental bullet rosettes . figure 2 shows a quantitative comparison of aggregate geometry , in terms of the ratio of cluster spans perpendicular to and along the direction of maximal span , as measured from projections in an arbitrary plane of observation .
we find that different initial particle geometries ( rosettes , rods ) approach a common asymptotic average cluster value . the aspect ratio of cpi images have been similarly calculated [ _ korolev and isaac _ 2003 ] , the results of which have been overlayed onto figure 2 , and these appear to approach the same value .
this universality of aspect ratios provides direct support for our hypothesis of rigid cluster joining upon contact . a deeper indicator of universality is provided by the fractal scaling of ice crystal aggregates , where one tests the relation @xmath11 between aggregate mass @xmath5 and linear span @xmath12 . our simulations and experimental observations [ _ heymsfield et al .
_ , 2002 ] , rather accurately agree on the fractal dimension @xmath13 and in _ westbrook et al . _
[ 2004 ] we discuss theoretical arguments leading to @xmath14 .
our simulations conform well to dynamical scaling of the cluster size distribution .
this means that number of clusters per unit mass varies with mass and time together as a single scaling function,@xmath15 where @xmath16 is the weight average cluster mass .
this relationship is confirmed in figure 3 , where we rescale the mass distribution from different times in the simulations onto a universal curve . the scaling function which we observe in figure 3 exhibits power law behaviour with @xmath17 for @xmath18 with @xmath19 .
this is not intrinsically surprising ( and indeed it matches theoretical expectations [ _ van dongen and ernst _ , 1985 ] ) but it has forced us to abandon the way experimentally observed distributions of cluster linear size have hitherto been plotted .
the problem is that given equation ( [ eq : dyn.scalg ] ) and its observed power law form , we must expect that the distribution of clusters by linear span @xmath20 should at small @xmath20 take the form @xmath21 which diverges as @xmath22 using our observed exponents
. for small enough crystal sizes this behaviour will be modified by the role of growth processes other than aggregation , but that lies outside the scaling regime . because of the divergence one has to take great care in constructing a characteristic linear size @xmath23 , where the natural choices are @xmath24 and the lowest whole number @xmath25 for which the denominator is not dominated by the smallest clusters is @xmath26 .
the simplest natural scaling ansatz for the cluster span distribution is then found [ _ westbrook et al .
_ , 2004 ] to be@xmath27 where @xmath28 .
figure 4 shows that this scaling ansatz works acceptably for our simulation data and well for the experimental observations .
the latter are rich data because cluster span is one of the simplest automated measurements to take .
the rescaled distributions from simulation and experiment agree fairly well but not perfectly , as shown in figure 4 .
one experimental reservation is the fall - off of experimental observation efficiency at small sizes , where clusters can be missed .
however our scaling procedure itself is in effect expressly designed to avoid sensitivity to this , and the superposition of the experimental data down to small reduced sizes looks good .
indeed it looks so good that the transient flattening around @xmath29 , which is absent from the simulations , appears to be significant .
one suggestion for the flattening around the middle of the rescaled distribution is that it might be associated with the peculiar feature of the collision rate being zero between clusters of equal sedimentation speed .
our simulations include this feature but for low relative approach speeds , where each cluster has more time to adjust its momentum in response to the other perturbing the local airflow , our approximation of ignoring hydrodynamic interactions ( and hence phenomena such as wake capture ) is less accurate . in summary , we have a fairly complete understanding of the geometry of the atmospheric ice crystal aggregates , dominated by sticking upon encounter .
further details of the sticking mechanism ( which we did not include ) appear not to be important for the cluster geometry , and the excellent scaling superposition of the experimental cluster size distributions suggests sticking efficiency does not favour aggregation at particular sizes .
the simplest interpretation of these observations is that although the sticking probability might be low for a single microscopic event , many such contacts will be attempted during a cluster - cluster encounter so that eventual escape is unlikely .
the actual sticking mechanism between ice crystals remains an intriguing open question , particularly for the low temperatures of figure 1 .
the fact that the same evolution is seen for differing initial monomer populations ( rods and rosettes ) suggests that a single set of geometric relationships for ice aggregates can successfully be applied in a wide range of cloud conditions .
this would lead to greater accuracy in retrieving cloud properties such as precipitation rate and predicting the radiative affect of ice crystal aggregates upon the climate system .
c to @xmath30c ( @xmath319 km altitude ) , using a cloud particle imager ( cpi , spec inc .
the pictures shown are aggregates of rosette ice crystal types .
( b ) aggregates as simulated by our computer model which assumed rigid joining when clusters collide under differential sedimentation .
, width=317 ] divided into the span perpendicular to the longest @xmath32 .
grey lines show cloud data of _ korolev and isaac _ [ 2003 ] plotted against longest span in microns for a range of temperatures between @xmath33c and @xmath34c .
black lines show simulation data plotted against longest span in arbitrarily scaled units , where the initial particles were three dimensional crosses ( solid line ) and simple rods ( dashed ) .
, width=317 ] c ) to 6.6 km ( @xmath37c ) in the cirrus cloud of _ field and heymsfield _ [ 2003 ] obtained during an arm ( atmospheric radiation measurement program ) flight ( 9th march 2000 ) .
each experimental size distribution represents an in - cloud average over 15 km .
black lines show simulation data .
, width=317 ] | aggregation of ice crystals is a key process governing precipitation .
individual ice crystals exhibit considerable diversity of shape , and a wide range of physical processes could influence their aggregation ; despite this we show that a simple computer model captures key features of aggregate shape and size distribution reported recently from cirrus clouds .
the results prompt a new way to plot the experimental size distributions leading to remarkably good dynamical scaling .
that scaling independently confirms that there is a single dominant aggregation mechanism at play , albeit our model ( based on undeflected trajectories to contact ) does not capture its form exactly . |
systems with asymmetric transport characteristics are also known as ratchets and brownian motors since they can be used to generate dc currents from an ac or noisy voltage .
this mechanism has important applications in physics and biology @xcite . as specific examples , we mention diodes and photovoltaic current rectifiers . here
we address the possibility of realizing such effects in luttinger liquids , which is of interest in connection with nanostructured devices .
motivated by recent experiments on quantum dots @xcite , carbon nanotubes @xcite , and quantum hall systems @xcite , we examine ratchet effects caused by two unequal constrictions as point scatterers .
we consider a one - dimensional spinless electron liquid at zero temperature subject to an impurity potential @xmath0 and a pair interaction @xmath1 with the hamiltonian @xmath2 the impurity potential @xmath0 is chosen to describe two unequal point scatterers at a distance @xmath3 . in the absence of interactions , the application of a voltage @xmath4 leads to a current @xmath5 with a finite conductance @xmath6 .
the conductance is proportional to @xmath7 with the transmission probability @xmath8 for electrons with incident energy @xmath9 in the vicinity of the fermi energy @xmath10 . as a consequence of time reversal symmetry , @xmath8
does not depend on the direction of the incoming momentum and therefore noninteracting electrons have a symmetric transport characteristic with an odd function @xmath11 .
therefore , the inclusion of interactions is mandatory for the analysis of ratchet effects .
for the inclusion of interactions , the bosonized representation of the model is particularly convenient . the bosonization technique @xcite maps the quantum dynamics of the electron liquid onto a path integral for a bosonic field @xmath12 which essentially describes collective displacements of the electron liquid . in terms of this field , the particle density of the electrons reads @xmath13 } + \rm{h.c . }
\right ) \ .
\label{rho}\end{aligned}\ ] ] here , @xmath14 is the fermi wave vector and @xmath15 is a microscopic cutoff length scale of the order of @xmath16 .
the particle current is given by @xmath17 , and the charge current by @xmath18 . in terms of the field
@xmath12 , the relevant contributions to the action corresponding to the hamiltonian ( [ h ] ) read @xmath19 } + { \rm h.c . } ] \nonumber \\ & & - \frac{w_0}{\pi^{3/2 } \alpha } \partial_x \vartheta ( x ) [ e^{i [ 2 k_f x + 2 \sqrt \pi \vartheta(x ) ] } + { \rm h.c . } ] \bigg\ } \ . \label{s}\end{aligned}\ ] ] forward scattering by the interaction is included in the `` free '' bosonic theory via the luttinger parameter @xmath20^{-1/2}$ ] which is less than unity for repulsive interaction .
assuming that @xmath1 is short ranged due to screening effects , only its weight @xmath21 is effective .
the second and third lines of eq .
( [ s ] ) describe backscattering off the impurity potential and by the interaction , respectively . for a single point - like scatterer , @xmath22 , it was shown @xcite that repulsive electron interactions ( @xmath23 ) lead to a vanishing linear conductance .
a weak scatterer was found to suppress the conductance according to @xmath24 where @xmath25 is conductance change due to the presence of the scatterer . on the other hand , for a strong scatterer
, the conductance vanishes like @xmath26 with the amplitude @xmath27 for hopping across the scatterer .
we subsequently focus on the weak - barrier case , deferring the strong currugation limit to ref . @xcite .
the suppression of the conductance in the presence of interactions can be attributed to the backscattering of electrons from a hartree - type potential caused by friedel oscillation in the vicinity of the impurity . in the framework of the bosonic action ( [ s ] )
, this backscattering arises from the second - line contribution , and the third - line contribution is irrelevant for the asymptotics ( [ dg ] ) . to illustrate the mechanism at work ,
it is instructive to briefly recall the scattering features of single electrons by a double barrier @xmath28 . we assume the amplitudes @xmath29 and @xmath30 to be positive .
@xmath3 is the distance between the two barriers . comparing the probability density @xmath31 for a particle incident from @xmath32 with wave vector @xmath33 to the density @xmath34 for a particle incident from @xmath35 with wave vector @xmath36
, one observes that the densities are not only different but also _ not _ related by reflection symmetry , @xmath37 ) . in this term , the hartree approximation amounts to replacing @xmath38 which is proportional to the slowly varying part of the density , cf .
( [ rho ] ) by its average value @xmath39 .
this average is readily calculated from the action perturbatively to second order in @xmath40 .
then , the third - line contribution can be absorbed into the second - line contribution by replacing the bare potential @xmath0 with the effective potential @xmath41 including the correction @xmath42 .
in analogy to the analysis @xcite yielding eq .
( [ dg ] ) for a single scatterer , one then can calculate the corrections to conductance to second order in this effective potential . to estimate the strength of this effect , it is important to notice that , to leading order , this correction is proportional to the backscattering current off the impurities , i.e. , one expects @xmath43 corresponding to eq .
( [ dg ] ) .
the reinsertion of this correction into eq .
( [ dg ] ) suggests subleading ratchet corrections to the conductance of order @xmath44 .
performing the systematic calculation outline above , we obtain an asymmetric ratchet contribution to the conductance @xmath45 \label{res}\end{aligned}\ ] ] with the function @xmath46 invoking the bessel function @xmath47 .
equation ( [ res ] ) was obtained within the hartree approximation .
it becomes exact in a model of many bands @xmath48 interacting through the coupling @xmath49 .
however , the order - of - magnitude estimate of the current is valid in a more general case including our one - band model ( [ s ] ) .
this can be verified by analyzing the expression for the current in the forth order of the perturbation theory .
equation ( [ res ] ) is our main result .
its proportionality to @xmath50 reflects the fact that the ratchet effect vanishes in the absence of interactions .
it is valid provided the backscattering current can be obtained within perturbation theory .
this is the case for weak scattering , more specifically for @xmath51 within this limit , one can distinguish two regmies . * at lower voltages @xmath52 , @xmath53 and the effect is in agreement with the above estimate .
additional oscillating factors reflect resonances due to quantum interferences @xcite .
the absolute value of the ratchet current grows with decreasing voltage for @xmath54 .
* in the high - voltage regime @xmath55 , @xmath56
. then @xmath57 . in this regime
, the ratchet current grows with decreasing votalge for @xmath58 .
this result shows that the ratchet effect can be increasing with decreasing voltage . at low voltages beyond the point where the condition ( [ valid ] ) breaks down and the total current vanishes with decreasing voltage ,
also the ratchet current has to vanish .
nevertheless , it can give a sizeable contribution to the total current .
this explains the pronounced asymmetry observed experimentally in corrugated nanotubes @xcite .
although the hamiltonian ( [ h ] ) does not describe quantum hall systems , the bosonized form ( [ s ] ) captures tunneling of electron or quasiparticles between edges @xcite . in a fractional quantum hall state with filling factor
@xmath59 , the tunneling of quasiparticles corresponds to the case @xmath60 .
thus , the interesting regime with small @xmath61 is physically accessible . | we investigate a one - dimensional electron liquid with two point scatterers of different strength . in the presence of electron interactions ,
the nonlinear conductance is shown to depend on the current direction .
the resulting asymmetry of the transport characteristic gives rise to a ratchet effect , i.e. , the rectification of a dc current for an applied ac voltage . in the case of strong repulsive interactions , the ratchet current grows in a wide voltage interval with decreasing ac voltage . in the regime of weak
interaction the current - voltage curve exhibits oscillatory behavior .
our results apply to single - band quantum wires and to tunneling between quantum hall edges
. ratchets , luttinger liquids , conductance , current rectification , bosonization , impurity scattering , hartree approximation |
in gauge theories , the coulomb gauge has special position .
the number of dynamical variables is the same as the number of physical degrees of freedom . moreover ,
if we go to the hamiltonian , phase - space , first - order formalism , there are no ghosts ; and , because of the existence of a hamiltonian , unitarity should be manifest .
nevertheless , there are complications , if not problems , with the coulomb gauge . in the lagrangian , second - order , formalism , there are ` energy - divergences ' in individual feynman graphs
. these are divergences over the energy - integration , @xmath0 , in a loop , for fixed values of the 3-momentum @xmath1 .
these are difficult to regularize : dimensional regularization does not touch them , and any other regularization risks doing violence to gauge - invariance ( but see leibbrandt et al for a modified form of dim .
these energy - divergences do cancel when all graphs are combined @xcite ; but it makes one uneasy to be manipulating divergent and unregulated integrals .
the problem of energy - divergences is eased by going to the hamiltonian , phase - space , first - order formalism , in which time derivatives of the gluon field @xmath2 are eliminated in favour of the conjugate momentum field @xmath3 .
this has the advantage of being a true hamiltonian formalism , and unitarity should be manifestly obeyed . also , there are no ghosts ( ghost loops cancel part of the closed coulomb loops ) . for a sample calculation in this formalism
see @xcite , and for possible connection to confinement see @xcite .
but there are still problems .
there is a question of operator - ordering in the hamiltonian @xcite ( see also @xcite , @xcite ) , which may require higher - order terms .
it has been shown @xcite that these operator - ordering problems are connected with ambiguous multiple energy - integrals in higher orders . in this paper , we are concerned with a simpler problem , which arises at 2-loop order . in general , in the hamiltonian formalism to this order , the two integrals over the internal energies converge with the two internal spatial momenta held fixed . however , renormalization demands that we first perform the energy and momentum integrals for each subgraph , then make subtractions for ultraviolet divergences , and then perform the remaining energy and momentum integrals . with this sequence of operations ,
one does in general find an energy - divergence in the final energy integral .
we illustrate this with a simple example in which quark - loop subgraphs are inserted into the second - order gluon self - energy graphs .
we perform the energy - momentum integral in the subgraph first , then do the renormalization subtraction .
individual graphs now have energy - divergences in the final energy integral , but these cancel when graphs are combined .
we show that the cancellation is a consequence of the ward identities obeyed by the quark - loop sub - diagrams .
of course , it is reassuring to check that the energy - divergences do cancel .
but we are back in the uncomfortable position of having to handle divergent ( and unregularized ) integrals at intermediate stages of the cancellation .
this contrasts with the feynman gauge , where all integrals to all orders are unambiguously regularized by dimensional regularization .
*p * bf
p lorentz indices are denoted by greek letters , spatial indices by @xmath4 , and colour indices by @xmath5 .
we use the metric tensor @xmath6 , where @xmath7 lorentz vectors are written @xmath8 we define the lorentz tensor @xmath9 by @xmath10 and for any vector @xmath11 we define the vector @xmath12 by @xmath13 ( of course , these definitions refer to the particular time - like vector @xmath14 with respect to which we have chosen to define the coulomb gauge . )
we define a spatial transverse tensor @xmath15 by @xmath16 so that @xmath17 in terms of colour matrices @xmath18 , @xmath19 is defined by @xmath20 and in terms of the structure constants @xmath21 , @xmath22 is defined by @xmath23 the renormalized coupling constant is @xmath24 .
quarks have mass @xmath25 .
we use dimensional regularization with spacetime dimension @xmath26 .
the lagrangian density in the phase - space formalism is @xmath27 where @xmath28.\ ] ] the hamiltonian form of the coulomb gauge has dynamical , conjugate fields @xmath29 .
the coulomb potential @xmath30 is not a dynamical variable
. it could be eliminated , but we find it convenient to leave it in the feynman rules .
we use a continuous line to represent @xmath3 , a dashed line for @xmath2 and a dotted line for @xmath30 .
the propagators are not diagonal in @xmath31 .
the propagators are shown in fig.1 ( the arrows on the lines show the direction of the momentum @xmath32 ) .
only one vertex will be relevant to our calculation , that shown in fig.2 .
, dashed lines @xmath33 and dotted lines @xmath34 .
the arrow indicates the sense of momentum flow.,width=234 ] its value is @xmath35 in the hamiltonian formalism , this is the only vertex involving the coulomb field .
it is this feature which implies there are no energy - divergences to 1-loop order .
we are going to insert quark loops into a gluon diagram , so we need a notation for quark 1-loop effective action .
let the 2-gluon term in this effective action be ( in momentum space ) @xmath36 we will require to know @xmath37 only for @xmath38 in this region , we have @xmath39,\ ] ] ( using minimal subtraction with a mass unit @xmath40 ) . the 3-gluon term in the effective action will be denoted by @xmath41 where @xmath42 , and the quantum numbers of the three gluons are @xmath43 ( all momenta are directed into the vertex ) .
we will not need to know the value of @xmath44 in general .
finally the 4-gluon term in the effective action will be denoted as @xmath45 where the quantum numbers are @xmath46 .
again , we do not need to know the value of @xmath47 in general .
both @xmath48 and @xmath47 have the symmetries required for bose symmetry .
note that the effective action due to quark loops is a functional of @xmath49 , and does not depend upon @xmath3 .
there are terms in the effective action which involve the coulomb field @xmath30 , and this is the reason that energy - divergences re - appear .
renormalization requires also the presence of counter - terms with a different structure from the interactions in the original formalism .
the effective action obeys the following ward identities : @xmath50,\ ] ] @xmath51 @xmath52 these identities express the gauge invariance of the quark loop contribution to the effective action .
they are a special case of the brs identities ( see for example itzykson and zuber equation ( 12 - 144 ) ) when there are no ghost contributions @xcite .
we shall show that these identities are sufficient to ensure the cancellation of energy - divergences between graphs .
the simplest example of the energy - divergences occurs in the gluon 2-point function , to 2-loop order .
the relevant graphs are shown in fig.3 , where the thick circles represent terms from the quark - loop effective action ( in ( 12 ) , ( 14 ) and ( 15 ) ) . in fig.3(vi ) , the sum of the three subgraphs shown corresponds to ( 15 ) .
we then see that ( 19 ) , ( 20 ) and ( 21 ) are each divergent as integrals over @xmath62 for fixed @xmath1 .
( actually , for @xmath63 this is true only of the contributon from the subtraction term in ( 13 ) . )
if we take the limit @xmath64 first , then we get a double log energy - divergence . to find the behaviour of the integrals in ( 22 ) , ( 23 ) and ( 24 ) , it is sufficient to use the ward identities ( 16 ) and ( 17 ) in the large @xmath62 limit
. then ( 16 ) gives @xmath65 also , @xmath66 @xmath67 similarly , ( 17 ) implies that @xmath68\ ] ] @xmath69 using ( 27 ) again . from ( 27 ) , ( 28 ) and ( 29 ) , we see that all the integrals in ( 18 ) have energy - divergences of the same kind , and the divergent part has the form @xmath70,\ ] ] where @xmath71 @xmath72 @xmath73 @xmath74@xmath75 @xmath76 these last six expressions cancel , so the energy - divergences in the separate terms in ( 18 ) cancel out in the sum .
probably similar cancellations occur in two - loop graphs made entirely of gluon lines .
but in this case there is the extra complication of the ambiguous integrals connected to the christ - lee terms @xcite @xcite .
+ acknowledgement .
this work was supported by mzos of the republic of croatia under contract no . 0098003
( a.a . ) .
we are grateful to dr .
g. duplani for drawing the figures .
99 g. heinrich and g. leibbrandt , nucl .
b * 575 * , 359 ( 2000 ) r.n .
mohapatra , phys .
rev . d4 * 22*,378 , 1007 ( 1971 ) a. andrai , eur .
j. c * 37 * , 307 - 313 ( 2004 ) a. cucchieri , d. zwanziger , phys .
d * 65 * , 014002 ( 2002 ) n. christ , t. d. lee , phys .
rev . d*22 * , 939 ( 1980 ) p. doust , ann . of phys . *
177 * , 169 ( 1987 ) ; p. doust , j. c. taylor , phys .
lett . * 197 * , 232 ( 1987 ) j. c. taylor , in physical and nonstandard gauges , proceedings , vienna , austria 1989 , edited by p. gaigg , w. kummer , m. schweda j. schwinger , phys . rev . *
127 * , 234 ( 1962 ) ; phys . rev . * 130 * 406 ( 1963 ) h. cheng , e. c. tsai , phys
b * 176 * 130 ( 1986 ) ; phys .
* 57 * 511 ( 1986 ) c. itzykson and j. b. zuber , quantum field theory , international series in pure and applied physics , mcgraw - hill inc . | in the coulomb gauge of nonabelian gauge theories there are in general , in individual graphs , ` energy - divergences ' on integrating over the loop energy variable for fixed loop momentum .
these divergences are avoided in the hamiltonian , phase - space formulation .
but , even in this formulation , energy - divergences re - appear at 2-loop order .
we show in an example how these cancel between graphs as a consequence of ward identities .
+ pacs numbers : 11.15.bt ; 11.10.gh + keywords : coulomb gauge ; renormalization ; qcd |
fig . 1 . : : \(a ) analyses of data for s + pb @xmath45 reaction by eq .
( [ eq : ratio ] ) .
( b ) the same but with coulomb corrections switched off for @xmath46 limit .
( results for @xmath47 pair production looks similar with only change being in the value of @xmath48 which depend on the value of radius parameter @xmath38 . ) fig . 2 . : : flow chart for our procedure of `` seamless fitting ( sf ) '' . fig . 3 . : : results of sf for bec for kaons produced in s + pb collisions ; ( a ) for @xmath47 pairs ; ( b ) for @xmath49 pairs . fig .
4 . : : results of sf for bec for kaons produced in @xmath1 + pb @xmath45 reaction .
5 . : : results of sf for bec for pions produced in s + pb @xmath50 reaction . | we applied an improved coulomb correction method developed by us recently to data on identical @xmath0-pairs production in s + pb and @xmath1 + pb reactions at 200 gev / c obtained by na44 collaboration . to analyse
the whole range of the momentum transfers measured the method of `` seamless fitting '' has been proposed and used together with the asymptotic expansion formula for the coulomb wave function .
we found that such coulomb corrections lead sometimes to different than previously reported ( by na44 collaboration ) interaction region and strongly influence the long range correlations .
+ preprint * dpsu-95 - 4 * ( july , 1995 ) = -45pt = 0 cm = 0 cm = 23.7 cm = 16 cm * introduction : * recently na44 collaboration has reported their data on the bose - einstein correlations ( bec ) of @xmath2 pairs produced in s + pb and @xmath1 + pb reactions at 200 gev / c @xcite . in our previous work
@xcite we have analysed these data by making use of the various source functions with the long range correlation ( without , however , invoking any sort of coulomb corrections ) .
the data @xcite have been corrected for coulomb interactions by applying only the gamow factor . as was pointed out some time ago by bowler
this is , however , not sufficient @xcite . in our recent works @xcite the still improved method of coulomb corrections was presented but not yet applied to any concrete data set . in the present letter , we apply it therefore to the analysis of data for @xmath2 pairs production in s + pb and @xmath1 + pb reactions mentioned above ( in the whole measured momentum transfer region ) and compare our results with those obtained before in @xcite . to be able to analyse the whole range of measured momentum transfer @xmath3 and to avoid wild oscillations developing at large @xmath3 s ( cf .
fig .
1a ) we have to use the the asymptotic expansion of the coulomb wave function together with the procedure of `` seamless fitting '' ( sf ) explained below ( cf . figs .
1b and 2 ) . +
* theoretical formula of bec with coulomb wave function : * to write down an amplitude @xmath4 satisfying bose - einstein statistics it is convenient to decompose the wave function of identical ( charged in our case ) bosons with momenta @xmath5 and @xmath6 into the wave function of the center - of - mass system ( c.m . ) with total momentum @xmath7 and the inner wave function with relative momentum @xmath8 .
it allows us to express @xmath4 in terms of the confluent hypergeometric function @xmath9 @xcite : @xmath10\ : , \label{eq : a}\\ \psi({\mbox{\bf q}},{\mbox{\bf r } } ) & = & \gamma(1+i\eta)e^{-\pi \eta/2 } e^{i{\mbox{\scriptsize \bf q}}\cdot{\mbox{\scriptsize \bf r } } } \phi(-i\eta;1;iqr(1 - \cos \theta))\:,\nonumber\\ \psi_s({\mbox{\bf q}},{\mbox{\bf r } } ) & = & \gamma(1+i\eta)e^{-\pi \eta/2 } e^{-i{\mbox{\scriptsize \bf q}}\cdot{\mbox{\scriptsize \bf r } } } \phi(-i\eta;1;iqr(1 + \cos \theta ) ) \:,\nonumber\end{aligned}\ ] ] where @xmath11 and the parameter @xmath12 .
assuming factorization in the source functions , @xmath13 ( here @xmath14 ) , one obtains the following expression for theoretical bec formula @xcite including the improved coulomb correction @xcite : @xmath15 \label{eq : bec}\\ & = & ( 1 + \delta_{{\mbox{\scriptsize 1c } } } ) + ( \delta_{{\mbox{\scriptsize ec } } } + e_{{\mbox{\scriptsize 2b}}}),\label{eq : result}\end{aligned}\ ] ] where @xmath16 denotes gamow factor and the first and the second parentheses in eq .
( [ eq : result ] ) correspond to the first and the second terms in eq .
( [ eq : bec ] ) and @xmath17 see @xcite .
] and @xmath18 to analyse data corrected only by the gamow factor using our formulae we should use the following ratio : @xmath19 ( 1 + \gamma q).\hspace{1 cm } \label{eq : ratio}\end{aligned}\ ] ] it should be noted that the normalization and an effective degree of coherence , i.e. , the denominator of the ratio @xmath20 , are related to each other .
notice also that other parameters like the additional normalization factor @xmath21 , the long range correlation @xmath22 and @xmath23 are introduced by hand .
+ * source function : * to obtain an explicit expression , we have to decide on some form of the source function . in the present letter , we shall use the gaussian source distribution , @xmath24 . for this type of source function
we have the following formulae for the elements of eqs .
( [ eq : result ] ) and ( [ eq : ratio ] ) @xcite : @xmath25
to analyze data corrected by the coulomb wave function as was done in @xcite , we should modify the formula ( [ eq : ratio ] ) replacing it by the following one : @xmath26 ( 1 + \gamma q ) .
\label{eq : a21}\end{aligned}\ ] ] for the sake of reference , we write down here also the conventional formula ( i.e. , a kind of standard formula without corrections due to the final state interactions ) : @xmath27 ( 1 + \gamma q ) .
\label{eq : a22}\ ] ] * asymptotic expansion of the coulomb wave function : * first of all , it should be noted that the expansion in eq .
( [ eq : result ] ) has to be the limited to @xmath28 only due to mathematical properties of the confluent hypergeometric function used @xcite .
this can be seen as wild oscillation developing in fig . 1 ( a ) where the eq . ( [ eq : ratio ] ) has been simply used .
if we , instead , set the coulomb correction to zero in the region @xmath29 limit , a small step appears as seen in fig . 1 ( b ) . therefore in order to analyse in a consistent way the whole region of the momentum transfer measured we have to use the following asymptotic expansion of the coulomb wave function : @xmath30 \ : , \label{eq : asym}\\ \psi^{{\mbox{\scriptsize asym } } } ( { \mbox{\bf q } } , { \mbox{\bf r } } ) & \!\!\ ! = & \!\!\ ! \exp\{i(qz - \eta\ln(r - z))\}\times \left(1+\frac{\eta^2 } { iq(r - z)}\right)\nonumber\\ & \!\!\ ! & \!\!\ !
+ f(\theta ) \frac{\exp\{i(qr - \eta \ln(2qr))\}}r\ : , \label{eq : asym1}\\ \psi_{{\mbox{\scriptsize s}}}^{{\mbox{\scriptsize asym } } } ( { \mbox{\bf q } } , { \mbox{\bf r } } ) & \!\!\ ! = & \!\!\ ! \exp\{i(-qz - \eta \ln(r+z))\}\times
\left(1+\frac{\eta^2}{iq(r+z)}\right ) \nonumber\\ & \!\!\ ! & \!\!\ !
+ f(\pi - \theta ) \frac{\exp\{i(qr - \eta \ln(2qr))\}}r\ : , \label{eq : asym2}\end{aligned}\ ] ] where @xmath31 and @xmath32 in analyses we should assure a smooth connection between both regions of @xmath33 . to avoid the divergence of denominators @xmath34 , we have to introduce a cutoff parameter @xmath35 ( of the order of @xmath36 ) such that @xmath37 always depends on the magnitude of the interaction region ( @xmath38 ) . ] .
this procedure , shown as a flow chart in fig . 2 ,
is called the `` seamless fitting ( sf ) '' .
+ * analyses of data by sf method : * our results obtained in terms of the new formula ( [ eq : ratio ] ) are shown in table i and figs . 3 and 4 . whereas the parameter @xmath22 ( representing here the influence of long range correlations ) increases now noticeably in comparison with that obtained previously in @xcite , we find that the interaction region represented by @xmath39 remains s + pb reactions almost the same . only in @xmath1 + pb collisions the estimated @xmath38 becomes larger with inclusion of coulomb correction than that obtained in @xcite .
these facts suggest that we should be careful in interpreting any data ( at least those for kaons ) which were corrected for coulomb interactions only by the gamow factor . + * concluding remarks : * we have proposed the possible method of applying the coulomb correction for the bec in the whole region of momentum transfer , the seamless fitting " ( sf ) . we confirm that this method works well when analysing data corrected only by the gamow factor .
+ our analyses of data of @xmath0 pairs in s + pb reaction @xcite shows ( cf . table i ) that @xmath40 = 4 fm and @xmath41 = 3 fm ( i.e. , they differ substantially ) , contrary to the estimation provided in @xcite that @xmath42 @xmath43 3 fm .
this is an important result for the study of signals of the quark gluon plasma ( qgp ) ( see refs .
@xcite ) .
moreover , we found that the long range correlations are strongly affected by coulomb corrections ( most probably because of the long range character of coulomb interactions ) .
+ for the sake of reference , we show also in table ii and fig .
5 results of our analysis of data for s + pb @xmath44 reaction @xcite ( which were corrected by the coulomb wave function method @xcite ) performed by using both eq .
( [ eq : a21 ] ) and the `` standard '' formula ( eq . ( [ eq : a22 ] ) ) . as one can see there are no significant differences between parameters estimated by means of these two formulae , in particular the magnitude of the interaction region is in both cases almost the same . +
* acknowledgements : * the authors would like to thank s. esumi , t. nishimura , and s. d. pandey ( members of na44 collaboration ) for useful conversations and correspondences .
this work is partially supported by japanese grant - in - aid for scientific research from the ministry of education , science and culture ( # 06640383 ) .
99 h. beker et al .
( na44 collaboration ) , _ z. phys .
_ * c 64 * ( 1994 ) 209 .
m. biyajima , t. mizoguchi , y. nakata and g. wilk , _ prog .
theor .
phys . _
* 92 * ( 1994 ) 1223 .
m. g. bowler , _ phys .
lett . _ * b270 * ( 1991 ) 69 .
m. biyajima and t. mizoguchi , _ coulomb wave function correction to bose - einstein correlations _ , preprint suldp-94 - 9 ( dec .
1994 ) .
m. biyajima , t. mizoguchi , t. osada and g. wilk , _ phys .
lett . _ * b353 * ( 1995 ) 340 .
h. bggild et al.(na44 collaboration ) , _ phys .
lett . _
* b302 * ( 1993 ) 510 .
l. i. schiff , _ quantum mechanics _ , 2nd ed .
( mcgraw - hill , new york , 1955 ) , p. 117 . s. nagamiya , _ nucl .
phys . _ * a544 * ( 1992 ) 5c .
s. pratt , t. csrg and j. zimanyi , _ phys .
rev . _
* c42 * ( 1990 ) 2646 .
.parameters of kaonic bec obtained from s + pb and @xmath1 + pb reactions . [ cols="^,^,^,^,^,^,^",options="header " , ] |
during last few years many exciting experimental results and theory development are obtained in sidis on the transversely polarized target . up to now
only the measurements @xcite of sivers and collins asymmetries were performed by hermes and compass collaborations and together with data from belle @xcite they allow a first extraction the transversity and sivers transverse momentum dependent ( tmd ) distribution functions ( dfs ) and collins fragmentation function ( ff ) .
in addition to these , the general expression of sidis cross section @xcite contains six more target transverse polarization dependent azimuthal asymmetries . here
we present the preliminary results on these asymmetries for the first time measured by compass from the 2002 - 2004 data . in the following the notations of ref .
@xcite are used .
there are eight azimuthal modulations related to the target transverse polarization : @xmath2 where first two correspond to sivers and collins effects .
the expression for the cross section in interest can be represented as @xmath3 where @xmath4 is the target transverse polarization .
we factored out the explicitly calculable depolarization factors , @xmath5 , and defined the asymmetries as the ratios of corresponding structure functions to unpolarized one : @xmath6 where @xmath7 or @xmath8 corresponds to beam polarization dependent or independent part of asymmetry .
the depolarization factors entering in eq .
( [ eq : cros - sect - short ] ) depend only on @xmath9 and are given as @xmath10 the asymmetries extracted from the data as amplitudes of corresponding azimuthal modulations ( raw asymmetries ) are then given by @xmath11 where @xmath12 is the target polarization dilution factor . in the qcd parton model the asymmetries @xmath13 and @xmath14
are given by the ratio of convolutions of spin - dependent to spin - independent twist two dfs and ffs , for example @xmath15 and can be used for extraction of dfs @xmath16 and @xmath17 describing the quark longitudinal and transverse ( along quark transverse momentum ) polarization in the transversely polarized nucleon .
the other asymmetries can be interpreted as cahn kinematic corrections to spin effects on the transversely polarized nucleon @xcite , for example : @xmath18
the event selection and asymmetry extraction are done as described in @xcite .
the following kinematic cuts were imposed : @xmath19 ( gev / c)@xmath20 , @xmath21 gev , @xmath22 , @xmath23 gev / c and @xmath24 . in figs .
[ fig:1 ] and [ fig:2 ] for the first time we present six target transverse spin dependent asymmetries extracted from compass 20022004 data collected on deuterium target .
the estimated systematic errors are smaller than statistical
. all six newly measured asymmetries are compatible with zero within statistical errors .
v. y. alexakhin _ et al . _ [ compass collaboration ] , phys .
lett . *
94 * , 202002 ( 2005 ) [ arxiv : hep - ex/0503002 ] .
e. s. ageev _ et al .
_ [ compass collaboration ] , nucl .
b * 765 * , 31 ( 2007 ) [ arxiv : hep - ex/0610068 ] ; r. seidl _ et al .
_ [ belle collaboration ] , phys .
lett . * 96 * , 232002 ( 2006 ) [ arxiv : hep - ex/0507063 ] .
a. kotzinian , nucl .
b * 441 * , 234 ( 1995 ) [ arxiv : hep - ph/9412283 ] .
a. bacchetta , m. diehl , k. goeke , a. metz , p. mulders and m. schlegel , jhep * 0702 * , 093 ( 2007 ) [ arxiv : hep - ph/0611265 ] . | in semi - inclusive dis of polarized leptons on a transversely polarized target eight azimuthal modulations appear in the cross - section . within qcd parton model four azimuthal asymmetries
can be interpreted at leading order , two of them being the already measured collins and sivers asymmetries .
the other two leading twist asymmetries , related to different transverse momentum dependent quark distribution functions , and also additional four asymmetries which can be interpreted as twist - three contributions have been measured for the first time at compass , using a 160 gev / c longitudinally polarized ( @xmath0 ) muon beam and a transversely polarized @xmath1 target .
we present here the preliminary results from the 2002 - 2004 data . |
it has been studied years ago that the supersymmetric generalizations of the bosonic cp(n-1 ) sigma model is automatically an @xmath2 supersymmetric theory by the virtue of that the target space cp(n-1 ) is a khler manifold @xcite .
recently edalati and tong suggested and built an @xmath3 cp(n-1 ) heterotic sigma model by study of the low - energy dynamics of vortex strings in @xmath4 four - dimensional gauge theories@xcite .
later shifman and yung formulated a geometric representation for this heterotic model with the cp(n-1 ) target space for bosonic fields and an extra right - handed fermion which couples to the fermion fields of the @xmath5 cp(n-1 ) model@xcite , and thus breaks the supersymmetry to @xmath3 . in this paper , we follow the geometric formulation to discuss the fermionic zero modes of @xmath3 heterotic cp(1 ) sigma model in the instanton background .
nontrivial homotopy group structure of target space cp(1 ) allows for the bosonic instanton background of the form of a holomorphic function @xmath6 , where @xmath7 and @xmath8 are instanton size and center respectively . under such background
, the fermionic zero modes can be obtained by acting supercharges and superconformal charges to the instanton solution . since the heterotic deformation of the standard cp(1 ) sigma model only preserves half of four original supercharges , the supersymmetries and superconformal symmetries are partly broken .
the remaining fermionic generators are not sufficient to generate all fermionic zero modes from the instanton background .
therefore we will find zero modes by solving dirac equations . in section 2
, we will calculate the chiral anomaly at first to give the number of zero modes . in section 3
we will explicitly solve dirac equations of zero modes and use the result of section 2 to pick up those linear independent modes . in the last section we generalize this result to cp(n-1 ) heterotic sigma models .
we start from the chiral anomaly of the standard cp(1 ) sigma model .
the notations are in accordance with the reference @xcite .
the lagrangian of cp(1 ) is given as follows : @xmath9\nonumber\\ & = & \frac{2}{g_{0}^2\chi^2}\partial_{\mu}\phi^{\dagger}\partial^{\mu}\phi+\frac{2i}{g_{0}^2}\bar{\xi}\gamma^{\mu}(\partial_{\mu}\xi - ia_{\mu}\xi)+\frac{2}{g_{0}^2}(\bar{\xi}\xi)^2\end{aligned}\ ] ] where @xmath10 , @xmath11 and @xmath12 for convenience to calculate the chiral anomaly .
it has a chiral symmetry and thus an axial current : @xmath13 the chiral anomaly is well - known@xcite as : @xmath14 this anomaly term corresponds to the tadpole diagram : + now we are going to consider the chiral anomaly of heterotic cp(1 ) sigma model .
the lagrangian of the heterotic model for bilinear fermion terms is deformed from eq.(1 ) by adding terms with an extra right - handed fermion field @xmath15 @xcite .
since only bilinear terms of fermions need to be considered when calculating one loop diagrams , we just write them up : @xmath16 + \frac{2i}{g_{0}^2\chi^2}\bar{\psi}\gamma^{\mu}(\partial_{\mu}\psi-\frac{2}{\chi}\phi^{\dagger}\partial_{\mu}\phi\psi)\nonumber\\ & = & i\bar{\zeta}\gamma^{\mu}\frac{1+\gamma_5}{2}\partial_{\mu}\zeta+(\bar{\zeta}\gamma^{\mu}\frac{1+\gamma_5}{2}b_{\mu}\xi+h.c.)+ \frac{2i}{g_{0}^2}\bar{\xi}\gamma^{\mu}(\partial_{\mu}\xi - ia_{\mu}\xi)\end{aligned}\ ] ] where we define @xmath17 and @xmath18 . it is easy to see @xmath19 and the lagrangian is invariant under @xmath20 and @xmath21
. therefore the corresponding axial current is : @xmath22 we will show that the chiral anomaly of the heterotic model will not be corrected by the extra @xmath23 terms , and thus prove that the number of zero modes is the same as the standard cp(1 ) model . actually , to calculate this anomaly one needs to consider diagrams as follows : + + the diagrams b and c cancel with each other because both of them are finite , and thus free to shift integral variables .
the diagrams d and e also cancel each other
. it can be proved by using momentum @xmath24 times the sum of these two diagrams , @xmath25 + + by multiplying @xmath26 , the original converged digrams d and e become two divergent parts respectively .
however they are all logarithmically divergent , and thus still free to shift integral variables to prove the cancellation .
therefore the anomaly of heterotic case is still only from the tadpole diagram , and is the same as in the standard cp(1 ) case , see equation ( 3 ) .
for the standard cp(1 ) model , @xmath27 has four zero modes , under the instanton background @xmath28@xcite .
since the chiral anomaly is not corrected in the heterotic case , the number of zero modes should be still four .
we now proceed to derive the dirac equations for @xmath27 and @xmath23 from the heterotic lagrangian and wick - rotate them to euclidean space by @xmath29 .
we only keep linear terms in the equations of motion and solve them .
we will see that the solutions are also satisfied with the equations of motion when we add nonlinear terms . since we have already shown that the number of independent zero modes is four , the solutions solved in the equations of motions up to linear terms are all zero modes . from eq .
( 4 ) and instanton background @xmath30 , in spinor components we have : @xmath31 notice that eqs .
( 8) ( 9 ) and ( 11 ) are the same as in the standard cp(1 ) case
. therefore the solutions to these three equations should be the same as before .
they give all four zero modes .
since we have argued that the total number of zero modes is four , there is no extra zero modes raised from field @xmath32 , although the equation of motion of @xmath32 ( 10 ) is deformed by the @xmath33 term .
therefore we have : @xmath34 by the same argument , fermionic field @xmath23 and @xmath35 can not provide extra zero modes . from eqs .
( 6 ) ( 7 ) and ( 10 ) , we get : @xmath36 at first sight , the solutions seem inconsistent with the anomaly calculation , which gives the number of the difference between left and right handed fermions under instanton background , @xmath25 @xmath37 from solutions ( 12)-(15 ) , it seems that the first two solutions are right handed fermions while the last two are left handed , thus the number of the difference is zero .
however , because we wick - rotated to euclidean space to perform the calculation , in which the complex conjugate is not a well - defined involution for chiral fermions , the field @xmath38 is thus totally independent of @xmath27 .
moreover in euclidean space , the lagrangian is @xmath39 invariant .
therefore the field @xmath38 transformed under @xmath39 is the same as @xmath40 .
bearing this in mind , we can be back to the lagrangian ( 4 ) : @xmath41 now it is clear that , when wick - rotated to euclidean space , the field @xmath42 and @xmath43 we solved in eqs .
( 10 ) and ( 11 ) are in fact the fields @xmath44 and @xmath45 respectively , while the field @xmath38 plays the same role as @xmath40 in euclidean space . therefore the four solutions are all right handed fermions .
it is consistent with the anomaly calculation . as for the field @xmath23 , solution
( 16 ) shows that the extra field @xmath23 mixes with field @xmath27 , however it is linearly dependent of field @xmath27 , and thus does not produce extra zero modes as what we also expected from the result of the chiral anomaly calculation ( 17 ) . at last ,
one more worthy to mention is the solutions of field @xmath27 .
they are of the same form as in the standard cp(1 ) zero modes .
it means that not only the number of zero modes does not change , the zero modes of @xmath27 also receive no correction in the heterotic model .
in fact it is easy to understand this result from equation ( 8) and ( 9 ) .
although the supersymmetries are partly broken by deformation in the heterotic case , the classical equation of motion of @xmath27 up to linear terms are still @xmath1 supersymmetic invariant . therefore in this sense
the zero modes of @xmath27 still can be generated by supercharges and superconformal charges from the instanton background , even though half of the symmetries are broken in the heterotic model .
in addition , one can check that these solutions are satisfied with the equations of motion when adding nonlinear terms of fermions .
our conclusion to the heterotic cp(1 ) model is that the zero modes of @xmath27 are the same as in the standard cp(1 ) case , while the extra fermion @xmath23 does not provide extra zero modes .
this result can be simply generalized to the heterotic cp(n-1 ) model .
for the heterotic cp(n-1 ) case , the lagrangian containing bilinear terms of fermions is@xcite :
@xmath46 + ig_{i\bar{j}}\bar{\psi}^{\bar{j}}\gamma^{\mu}(\partial_{\mu}\psi^{i}+\gamma^{i}_{lk}\partial_{\mu}\phi^{l}\psi^{k})\end{aligned}\ ] ] hence , the equations of motion up to linear terms under instanton backgroud @xmath47 are : @xmath48 it is not hard to see the solutions are : @xmath49 where @xmath50 is the khler potential . from these solutions
we see that the number of zero modes in the heterotic cp(n-1 ) model is still @xmath51 , while @xmath23 can be linearly expressed by the zero modes of @xmath27 and thus not extra zero mode .
i am grateful for m. shifman who led me to the subject , and a. vainshtein for very useful and fruitful discussions and reviewing the final version of the manuscript .
i also want to thank m. sasseville for proofreading the text .
+ b. zumino , phys . lett . *
b87 * , 203 ( 1979 ) m. edalati and d. tong , jhep * 0705 * , 005 ( 2007 ) m. shifman and a. yung , phys . rev . *
d77 * , 125016 ( 2008 ) v. a. novikov , m. a. shifman , a. i. vainshtein and v. i. zakharov , phys . rept . * 116 * , 103 ( 1984 ) m. shifman , a. vainshtein and r. zwicky , j. phys . *
a39 * , 13005 ( 2006 ) | we discuss instanton fermionic zero modes in the heterotic @xmath0 modification of the cp(1 ) sigma model in two dimensions . by calculating its chiral anomaly
we prove that the number of fermionic zero modes is same as in the standard @xmath1 cp(1 ) case , and determine their explicit form . |
this work was supported in part by doe grant de - fg02 - 91er-40690 .
j. d. bekenstein , phys .
d * 7 * , 2333 ( 1973 ) . j. d. bekenstein , lett .
nuovo cim . * 11 * , 467 ( 1974 ) . c. rovelli and l. smolin , nucl .
b * 442 * , 593 ( 1995 ) [ erratum - ibid .
b * 456 * , 753 ( 1995 ) ] [ arxiv : gr - qc/9411005 ] .
k. s. .
thorne , r. h. .
price and d. a. .
macdonald , _ new haven , usa : yale univ .
( 1986 ) 367p _ o. lunin and s. d. mathur , phys .
lett . * 88 * , 211303 ( 2002 ) [ arxiv : hep - th/0202072 ] ; o. lunin , j. m. maldacena and l. maoz , arxiv : hep - th/0212210 ; i. kanitscheider , k. skenderis and m. taylor , jhep * 0706 * , 056 ( 2007 ) [ arxiv:0704.0690 [ hep - th ] ] . s. giusto , s. d. mathur and a. saxena , nucl .
b * 710 * , 425 ( 2005 ) [ arxiv : hep - th/0406103 ] ; i. bena and n. p. warner , adv .
* 9 * , 667 ( 2005 ) [ arxiv : hep - th/0408106 ] ; v. jejjala , o. madden , s. f. ross and g. titchener , phys .
d * 71 * , 124030 ( 2005 ) [ arxiv : hep - th/0504181 ] .
v. balasubramanian , e. g. gimon and t. s. levi , arxiv : hep - th/0606118 ; j. de boer , f. denef , s. el - showk , i. messamah and d. van den bleeken , jhep * 0811 * , 050 ( 2008 ) [ arxiv:0802.2257 [ hep - th ] ] ; s. d. mathur , arxiv:0810.4525 [ hep - th ] .
s. d. mathur , arxiv:0706.3884 [ hep - th ] .
v. cardoso , o. j. c. dias , j. l. hovdebo and r. c. myers , phys .
d * 73 * , 064031 ( 2006 ) [ arxiv : hep - th/0512277 ] ; b. d. chowdhury and s. d. mathur , class .
* 25 * , 135005 ( 2008 ) [ arxiv:0711.4817 [ hep - th ] ] .
s. d. mathur , arxiv:0805.3716 [ hep - th ] .
s. d. mathur , int .
j. mod .
d * 18 * , 2215 ( 2009 ) [ arxiv:0905.4483 [ hep - th ] ] .
p. hayden and j. preskill , jhep * 0709 * , 120 ( 2007 ) [ arxiv:0708.4025 [ hep - th ] ] ; y. sekino and l. susskind , jhep * 0810 * , 065 ( 2008 ) [ arxiv:0808.2096 [ hep - th ] ] . j. m. maldacena , adv .
* 2 * , 231 ( 1998 ) [ int .
j. theor .
phys . * 38 * , 1113 ( 1999 ) ] [ arxiv : hep - th/9711200 ] .
m. parikh and f. wilczek , phys . rev .
d * 58 * , 064011 ( 1998 ) [ arxiv : gr - qc/9712077 ] ; t. shimomura , t. okamura and t. mishima , int .
j. mod .
d * 11 * , 789 ( 2002 ) ; p. kovtun , d. t. son and a. o. starinets , jhep * 0310 * , 064 ( 2003 ) [ arxiv : hep - th/0309213 ] ; v. cardoso , o. j. c. dias and l. gualtieri , int .
j. mod .
d * 17 * , 505 ( 2008 ) [ arxiv:0705.2777 [ hep - th ] ] ; m. natsuume , phys . rev .
d * 78 * , 066010 ( 2008 ) [ arxiv:0807.1392 [ hep - th ] ] ; n.
iqbal and h. liu , phys .
d * 79 * , 025023 ( 2009 ) [ arxiv:0809.3808 [ hep - th ] ] ; h. culetu , arxiv:0906.0920 [ gr - qc ] ; c. eling and y. oz , jhep * 1002 * , 069 ( 2010 ) [ arxiv:0906.4999 [ hep - th ] ] . | are there any degrees of freedom on the black hole horizon ? using the ` membrane paradigm ' we can reproduce coarse - grained physics outside the hole by assuming a fictitious membrane just outside the horizon . but to solve the information puzzle we need ` real ' degrees of freedom at the horizon , which can modify hawking s evolution of quantum modes .
we argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon ; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius .
the collective behavior of these microstate solutions may give a realization of the membrane paradigm , with the fictitious membrane now replaced by real , explicit degrees of freedom .
epsf = = = = = = = = ============= == = = membrane paradigm realized ?
+ + department of physics , + the ohio state university , + columbus , oh 43210 , usa + .2 in mathur@mps.ohio-state.edu 1.0 true in a longstanding puzzle in quantum gravity is the following : is there anything at the black hole horizon ?
there are many reasons to take the horizon seriously as a place where ` physics happens ' .
the bekenstein entropy @xmath0 of the hole is proportional to the area of the horizon @xcite .
this suggests that we attach one ` bit ' of information to each planck area of the horizon , and perhaps quantize the horizon area to give an integral number of bits @xcite . in loop quantum gravity
the entropy arises from spin degrees of freedom on links that intersect the horizon @xcite . in the schwarzschild
coordinate frame , all matter that ever fell towards the horizon appears to be frozen forever just outside the horizon .
this picture was concretized in the ` membrane paradigm ' @xcite , where one puts an artificial cutoff surface just outside the horizon , and finds boundary conditions at this surface which will reproduce correct mechanical and thermal effects in the region outside this surface .
these boundary conditions can be summarized by imagining a fictitious membrane placed at this surface , with appropriate mechanical and thermal properties . in particular , there is a very high temperature near the membrane ,
so one might imagine that an infalling observer would get burnt up and eventually reradiated out to infinity @xcite .
this would be good , because to avoid the information paradox we need to have some way of returning the information in infalling objects back to infinity .
but there turns out to be a flaw in these attempts to assign genuine dynamics to the horizon .
it is well known that the schwarzschild coordinate system fails at the horizon , and the regular coordinates there the kruskal coordinates show that _ nothing _ special happens at the horizon of the traditional black hole .
nothing can ` stay ' at the horizon ; all matter must fall in towards the singularity .
the high temperature in the schwarzschild frame disappears in the kruskal frame ; it is seen to be nothing but the rindler tempertaure observed in an accelerated system of coordinates .
careful renormalization of the stress tensor shows that there is no energy density at the horizon @xcite ; the energy of rindler quanta is cancelled by vacuum polarization energy , since the physical vacuum at the horizon is naturally described in kruskal rather than schwarzschild coordinates . what then , about the fate of information falling into the hole ? over the past decade , many physicists had settled down to the following set of beliefs ( i ) information is not lost ; it emerges in the hawking radiation from the hole ( ii ) nothing special happens at the horizon , because the kruskal description looks like the logical one ( iii ) the above two beliefs are consistent because we need only small delicate correlations among hawking quanta to carry the information , and subleading corrections to hawking s computation @xcite should be able to encode the required information in the quanta .
but if these beliefs were correct , one has to wonder why over the years no one produced a model showing how it was possible for information to get encoded in the radiation while preserving a near - semiclassical hamiltonian at the horizon .
the reason for this failure emerged last year , when it was proved that ( iii ) is in fact incorrect : it is _ not _ possible to make small corrections to hawking s leading order state and recover any significant information in the radiation @xcite .
more precisely , if matrix elements of the hamiltonian for low energy modes are within @xmath1 of their semiclassical values , then no more than a fraction @xmath2 of the information can be encoded in the radiation .
the proof of this theorem used a well known inequality from quantum information theory called ` strong subadditivity ' @xcite .
but no _ elementary _ proof of this inequality is known , so it is perhaps not surprising that its consequences were not built into our naive thinking about encoding of information in the radiation .
it would now seem that we are back to square one on the information puzzle .
must we reconcile ourselves to information loss ?
we will now argue that another set of results over the past few years gives us a picture of how there can be real dynamics at the horizon , which will lead to an escape of information in the radiation .
a black hole has given values of of its conserved quantum numbers : mass , charge and angular momentum . in earlier work ,
one assumed a simple ansatz for the metric .
thus for the nonrotating hole , one assumed independence of the angular directions @xmath3 for all metric components . in a higher dimensional gravity theory ,
the extra directions have to be assumed compact , and the ansatz assumed no dependence of the metric on the compact coordinates @xmath4 either .
einstein s equations then gave a unique solution , possessing a horizon and a singularity the traditional black hole .
but it has been now recognized that there are @xmath5 $ ] _ different _ solutions of einstein s equations with the _ same _ quantum numbers @xcite .
all are regular , with no horizon and no singularity .
none of them are spherically symmetric , and all involve the compact directions in a nontrivial way .
so it was the simplicity of our initial ansatz which led us to miss these solutions .
further , string theory has allowed us to list all possible states for simple sets of quantum numbers .
the regular states mentioned above map in a one - to one and onto way onto the set of all allowed states , while the spherical solution with horizon and singularity is not realized at all .
this situation gives us an appealing way out of the information problem : \(a ) the region far from the hole has an infinite dimensional phase space due to its infinite volume .
very close to the horizon , however , there is again a very large phase space @xcite , from the @xmath5 $ ] solutions termed microstates giving the entropy of the hole ( fig.[fone ] ) .
\(b ) most of these solutions have nontrivial structure only very close to the horizon .
this is because rapid variation of the metric with position costs a lot of energy , and the large redshift near @xmath6 is needed to lower this to the given total energy @xmath7 .
the detailed structure of the solutions can be inferred from the explicitly solutions which have been constructed .
the geometry has _ ergoregions _ , with the direction of frame dragging changing rapidly from place to place ( fig.[ftwo ] ) .
this rapid space - time time dependence is what keeps the geometrical structure from collapsing towards @xmath8 .
( for an analogy , see fig.[fthree ] ; a circular elastic band shrinks to a point , but an rapidly vibrating band stays open with a nontrivial average radius . )
\(c ) consider a spherically symmetric shell made of gravitational radiation , collapsing to make a hole .
the motion upto @xmath9 is described by traditional dynamics in the schwarzschild frame ( @xmath10 ) .
but at @xmath11 the wavefunction of the shell can spread over the @xmath5 $ ] alternative solutions of einstein s equations .
the amplitude for this spread can be estimated by computing the _ tunneling _
amplitude between the shell and one of the microstate solutions .
this amplitude @xmath12 $ ] is very _ small _ , since the involved objects are macroscopic and the classical action of tunneling @xmath13 is big . but
the _ number _ of states that we can tunnel to very _ large _
, given by @xmath5 $ ] .
it turns out that @xmath14 @xcite , so instead of making a long lived black hole , the shell state becomes a linear superposition of microstate solutions in a time which is much shorter than the hawking evaporation time @xcite .
\(d ) it has been checked that ergoregion emission from the microstate solutions reproduces exactly the hawking radiation rate expected from those solutions @xcite . but this emission does not involve information loss , since there is no horizon .
\(e ) the further evolution of the collapsing shell is given by the evolution of the linear superposition of microstates into which it has tunneled .
it is plausible that the short time evolution of the collective modes of these complicated microstates can be mimicked by evolution in the interior of the traditional black hole geometry .
this effective evolution would then corresponds to the interior of the black hole in the penrose diagram .
it is important to note here that the typical microstate is not a classical solution in which infalling quanta scatter around in a zig - zag path .
instead , the large phase space of fuzzball solutions creates a very large ` coordination number ' the number of states that can be reached from a given state by a small action @xmath15 .
( this may make the black hole a ` fast scrambler ' @xcite . )
an infalling heavy object excites a linear combination of fuzzball states , similar to the ` fermi - golden rule ' absorption encountered when we have a closely spaced band of energy levels .
different objects excite different degrees of freedom to leading order , since the number of excitable states is so large ; the small overlap between different sets of excited states gives the residual interaction that mimics the usual ( weak ) gravitational interaction between different quanta ( the dual cft description of this effect was noted in @xcite ) .
thus the effective dynamics of absorption into fuzzballs gets related to motion in gently curved space , in a manner similar to absorption by the large number of open string degrees of freedom on a stack of d - branes : the infalling quantum excites these open strings , different quanta typically excite different strings ( due to the large number of these strings ) , and the small overlap between the set of excited strings generates the effective gravitational interactions between infalling quanta .
thus in this picture we would think of both ads / cft duality @xcite and the above mentioned effective description of fuzzballs as arising from the same underlying physics : absorption into a dense set of levels with high coordination number .
with this picture we seem to have an explicit realization of the membrane paradigm . in several earlier works , effective gravitational dynamics or dual cft descriptions
have been used to infer an imaginary ` membrane ' that may sit at the horizon @xcite . by contrast
, we are now addressing how gravity manages to actually produce something at the horizon that is capable of sending information back out in the hawking radiation . in our description
the membrane has real degrees of freedom on it , given by the rapidly oscillating solutions of einstein s equations that correspond to the black hole microstates
. it would be exciting to explore if the collective dynamics of the microstates reproduces the very precise properties of the fictitious membrane of the membrane paradigm . |
one of the techniques to register ultra - high energy extensive air showers ( eas ) is measuring strength of radio pulse by antennas . unlike traditional techniques , including optic measurements of air shower propagation radio technique can operate in any atmospheric condition except during thunderstorm conditions for whole observation period , which dramatically increases effective time of air showers registration .
it is easier to use and much cheaper than other ground detectors in existing air showers array . the yakutsk array measured three components of air shower : the total charged component , the muon component and cherenkov radiation . from these components using average lateral distribution function ( ldf ) the integral characteristics of air shower , the total number of charged particles , the total number of muons and full flux of cherenkov light at the sea level are recovered .
all these shower characteristics are used for further model - free air shower energy estimation as shown in [ 1 ] .
cherenkov light registered at the sea level moreover is used to recover air shower longitudinal distribution and it characteristics , cascade curve and depth of maximum x@xmath4 [ 2][3 ] .
using this , in future is possible to find a relation between the characteristics of the radio emission and characteristics of the eas , including slope of the radio emission ldf with depth of maximum , as shown in [ 4 ] .
for the season 2008 - 2012 were recorded 600 air shower events with radio emission .
showers energy were above 3@xmath010@xmath1 ev , and zenith angle @xmath5 @xmath6 70@xmath7 .
for further analysis were selected only 421 showers , appropriate selection criteria of this paper .
therefore , for analysis at the yakutsk array we use following criteria : 1 .
the shower selected if adc prehistory contains radio pulse with amplitude 5 times more than noise level and pulse is localized within time gate equal to delay of `` master '' from small or large arrays . 2 .
extensive air shower axis must be within perimeter of central array with radius 600 m. zenith angle @xmath5 @xmath6 35@xmath7 .
azimuth angle @xmath8 chosen such a way as to exclude influence of polarization effect .
that is , the amplitude of the crossed antennas were equal or were nt go beyond limit ( 3 - 5 ) @xmath9 . with selected events
, we plotted dependence of maximum amplitude of radio pulse from zenith angle ( fig .
@xmath10 ) .
approximation curve is given by power function : @xmath11 in fig .
@xmath12 is shown dependence of maximum amplitude of radio signal from shower energy .
approximation is given by : @xmath13 as seen from fig .
@xmath14 , slope of the ldf changes with the distance . at large distance signal of radio emission attenuates
slowly . from equation ( 1 ) and ( 2 ) we derived formula for calculating energy in individual showers : 10@xmath2 ev , 4.38@xmath010@xmath2 ev and 1.32@xmath010@xmath3 ev.,scaledwidth=40.0% ] @xmath15 with : @xmath5 - zenith angle , r - distance of antennas to the shower axis , e@xmath16 - the primary particle energy . in fig .
@xmath17 dependence of radio emission ldf from depth of the air shower maximum .
the depth was determined by cherenkov detectors measurements of yakutsk array .
the slopes were determined from the ratio of the amplitudes , taken at 80 and 200 m ( fig .
@xmath14 ) for three energies : 1.73@xmath010@xmath2 ev , 4.38@xmath010@xmath2 ev and 1.32@xmath010@xmath3 ev . .
the slope was determined from the ratio of the amplitudes , taken at 80 and 200 m using averaged ldf and xmax from cherenkov light measurements .
, scaledwidth=40.0% ]
yakutsk array measurements are showing : a ) there is a correlation between measured maximum amplitude of radio signal and air shower energy determined measurements of the main components at observation level .
it follows from the formula ( 2 ) derived empirically from the joint consideration of radio signal amplitude and eas energy ; b ) the shape of ldf depends on the depth of air shower maximum x@xmath4 ( fig .
@xmath17 ) . | this paper presents the set of measurements of ultra - high energy air shower radio emission at frequency 32 mhz in period of 2008 - 2012 .
the showers are selected by geomagnetic and azimuth angles and then by the energy in three intervals : 3@xmath010@xmath1 3@xmath010@xmath2 ev , 3@xmath010@xmath2 6@xmath010@xmath2 ev and 6@xmath010@xmath2 5@xmath010@xmath3 ev . in each energy interval
average lateral distribution function using mathematically averaged data from antennas with different directions are plotted . in the paper , using experimental data the dependence of radio signal averaged amplitude from geomagnetic angle , the shower axis distance and the energy are determined .
depth of maximum of cosmic ray showers xmax for the given energy range is evaluated .
the evaluation is made according qgsjet model calculations and average lateral distribution function shape . |
charge symmetry is a special case of the general flavour symmetry of qcd , which at its simplest distinguishes the proton and the neutron ( or @xmath6 and @xmath7 quarks ) .
it is , of course , trivially broken by the electromagnetic interaction , notably the coulomb force in comparisons of the @xmath8 and @xmath9 systems and by the magnetic interaction in the @xmath3 system .
other well known sources are the @xmath3 mass difference and @xmath10- as well as @xmath11-meson mixing . these in turn may be related to the up- and down - quark mass difference - the microscopic flavour symmetry breaking in qcd .
one might consider remarkable the fact that , although the relative quark mass difference is large ( @xmath12 ) , the symmetry breaking at the observable hadron level is two orders of magnitude smaller . in the mirror system
@xmath8 vs. @xmath9 csb has been studied for many decades @xcite , while its appearance in the @xmath3 system was first seen only a decade ago @xcite as the difference @xmath13 of elastic analyzing powers .
different csb observables have been seen in calculations to be sensitive to different combinations of sources .
for example , in @xmath3 scattering above 300 mev the @xmath3 mass difference in ope dominates , while at and below @xmath14 200 mev @xmath11 meson mixing and the magnetic interaction become about equally important@xcite .
in contrast , the @xmath8 vs. @xmath9 difference is dominated by @xmath11 meson mixing @xcite .
the csb effects in the @xmath3 system change the total isospin of the two nucleons ( class iv in the terminology of ref .
@xcite ) , whereas in @xmath8 and @xmath9 the isospin must be conserved ( class iii ) .
it is easily seen that in the reaction @xmath15 the isospin change @xmath16 implies a csb asymmetry of the unpolarized cross section about 90@xmath17 and vice versa .
namely , due to the generalized pauli principle and conservation of the angular momentum and parity , with isospin one initial states for odd @xmath18 only singlet - even initial states are possible and for even @xmath18 only triplet - odd states .
the presence of some isospin zero component in the initial state introduces opposite spin - parity assignments and the initial spin states will then have both parities involved .
this minor asymmetry is being measured in an on - going experiment at triumf @xcite . since class iv forces mentioned above
change the isospin , as an initial state interaction they can quite naturally give rise to @xmath19 final states even from initial @xmath20 @xmath3 states .
further , although in a purely nucleonic basis @xmath10 mixing force conserves the isospin ( class iii ) , it can cause a @xmath20 @xmath21 admixture even in initial isospin zero states @xcite and thus contribute to pion production from these states .
in addition @xmath10 mixing can contribute very explicitly in the final actual production vertex in the form of production first of an isoscalar @xmath22 meson which then transforms into a pion . of traditional csb mechanisms in pion production @xmath10 mixing
is important and was seen to dominate at threshold @xcite , while the @xmath3 mass difference becomes more important at higher energies , where the two @xmath10 mixing mechanisms described above tend to cancel @xcite . exploiting the fact that chiral symmetry gives predictions for effects arising from the small but explicit breaking of this symmetry generated by the quark masses , ref . @xcite
employed a csb effective lagrangian based on chiral symmetry and including the @xmath6 and @xmath7 quark mass differences @xmath23 to describe pion - nucleon @xmath24-wave rescattering in @xmath25 .
this rescattering dominates isospin conserving production at threshold . here
@xmath26 represents the pauli matrices in isospin space , @xmath27 mev is the pion decay constant , and @xmath28 , though for simplicity @xmath29 was used .
it is important to note that the pion - nucleon interaction in the second term is linked by chiral symmetry to the first term , which in turn is directly related to the neutron - proton mass difference giving @xmath30 . here
@xmath31 is an electromagnetic `` hard photon '' exchange contribution to the neutron - proton mass difference also related to the isospin violating pion - nucleon interaction in the effective lagrangian @xmath32 this csb rescattering mechanism is presented in fig .
1a . above
, the quark mass difference is by no means small as compared with their sum but rather @xmath33 with @xmath34 , although the individual parameters @xmath35 and @xmath31 are not completely uniquely determined and remain model dependent .
their values have reasonable ranges 23 mev and ( 0.5)(1.5 ) mev , respectively . at the triumf experiment energy 279.5 mev the integrated forward - backward asymmetry @xmath36 } { \int_0^\pi d\omega \ ; \sigma(\theta)}. \label{asym}\ ] ]
was obtained in ref .
@xcite in terms of the above mass differences as @xmath37 where the conventional meson contributions in the first term have been taken from ref .
@xcite . due to the dominance of the @xmath10 mixing
, the uncertainties in its strength directly scale that term .
apart from minor pionic effects due to the @xmath3 mass difference , it is proportional to @xmath38 .
the values @xmath39 and @xmath40 mev@xmath41 have been used for this result .
( in addition , the analogous effect from @xmath42 with the same coupling and the mixing matrix element 5500 mev@xmath41 was icluded @xcite . )
since in eq .
( [ afb ] ) @xmath35 and @xmath31 add constructively , the latter term arising from the new effective lagrangian easily dominates the total @xmath43 making it change sign . with the given first term , the total @xmath43 would vary in the range 0.30.6% .
it is unlikely that the first term is an overestimate , so the range might rather be even more positive . with the anticipated experimental resolution of 0.12% @xcite this is a significant result .
if the uncertainties in the @xmath10 mechanisms ( notably the @xmath44 coupling constant ) can be solved , csb pion production could set constraints also on @xmath35 and @xmath31 .
since the new effective csb interaction gave such a large contribution in pion production , one is prone to worry how much this @xmath45 rescattering might contribute to elastic @xmath1 scattering possibly breaking the consensus there . in ref . @xcite the csb @xmath1 two - pion exchange interaction depicted in fig .
1b was shown in lowest order ( in the static approximation for baryons ) to be of the form of class iii @xmath46 [ \mu^2+({\bf k } -{\bf q}/2)^2]},\ ] ] where @xmath47 is the pion - nucleon coupling constant and @xmath48 the pion mass . a similar expression resulted for exchanges involving an intermediate @xmath49 isobar ( fig . 1c ) .
contrary to pion production , in this case , although the integrals and parameters are rather large , the two mass differences cancel to a large extent leaving only rather small contributions to the difference between @xmath9 and @xmath8 scattering . to see this , one need only compare the range of the factor @xmath50 [ + 0.8(-0.2 ) mev ] with the range of @xmath51 [ 2.23.4 mev ]
correspondingly , the contributions to the scattering length and effective range differences @xmath4 and @xmath5 vary between 0.17 fm and 0.05 fm , and 0.003 and 0.001 fm , respectively .
also the contribution from this source to the @xmath52h@xmath52he binding energy difference is expected to be small .
99 g. a. miller , b. m. k. nefkens and i. slaus , phys .
rep . * 194 * , 1 ( 1990 ) .
r. abegg _ et al .
lett . * 56 * , 2571 ( 1986 ) , phys .
d * 39 * , 2464 ( 1989 ) ; l. d. knutson _
lett . * 66 * , 1410 ( 1991 ) ; s. e. vigdor _
c * 46 * , 410 ( 1992 ) ; j. zhao _ et al .
c * 57 * , 2126 ( 1998 ) .
a. g. williams , a. w. thomas and g. a. miller , phys .
c * 36 * , 1956 ( 1987 ) ; m. j. iqbal and j. a. niskanen , phys .
c * 38 * , 2259 ( 1988 ) .
s. a. coon and r. c. barrett , phys .
c * 36 * , 2189 ( 1987 ) . g. f. de tramond , proc .
symposium / workshop on spin and symmetries , triumf , vancouver , june 30july 2 , 1989 , tri-89 - 5 , eds . w. d. ramsay and w. t. h. van oers , p. 235 .
e. m. henley and g. a. miller , in _ mesons and nuclei _ ,
i , eds . m. rho and d. h. wilkinson , north holland ( amsterdam 1979 ) .
triumf experiment e704 , spokespersons a. opper and e. korkmaz .
j. a. niskanen , few - body systems * 26 * , 241 ( 1999 ) .
j. a. niskanen , m. sebestyen , and a. w. thomas , phys .
c * 38 * , 838 ( 1988 ) .
j. a. niskanen , proc . of meson2000 workshop ,
cracow , may 2000 , acta physica polonica * b 31 * , 2683 ( 2000 ) .
u. van kolck , j. a. niskanen and g. a. miller , phys .
b 493 , 65 ( 2000 ) ; nucl - th/0006042 .
j. a. niskanen , phys .
c * 65 * , 037001 ( 2002 ) ; nucl - th/0108015 . | chiral effective field theory predicts a charge symmetry violating ( csb ) amplitude for pion - nucleon scattering .
this mechanism provides a very large contribution also to the csb forward - backward asymmetry in the angular distribution of the reaction @xmath0 .
this contribution was so large that it had a potential to cause a large effect also in csb elastic @xmath1 scattering and to disturb its present understanding .
however , it can be seen that , contrary to pion production , in this case the @xmath2-quark mass difference and electromagnetic contribution to the @xmath3-mass difference tend to cancel causing the total effect in the effective range parameters @xmath4 and @xmath5 to be relatively small . in the lowest order and within the static approximation for the nucleons csb pion - nucleon rescattering does not influence @xmath3 scattering .
= by -1 |
brown dwarfs substellar objects with masses below the hydrogen burning limit of 0.08@xmath1 are ideal to test the mass dependence of critical parameters in stellar evolution .
one example for such a parameter is the lifetime of circumstellar disks , which is an important constraint for the core - accretion scenarios for planet formation .
the disk lifetime is affected by a number of physical processes , e.g. disk ionisation by the central object and cosmic rays , accretion , grain growth ( e.g. @xcite ) .
our understanding of the relative importance of these processes and how they change with object mass is still incomplete , i.e. observational guidance is important to advance the theory .
the clear majority of low - mass stars lose their disk within less than 5myr @xcite .
maybe the best test for the longevity of disks is the upper scorpius ob assocation ( upsco in the following ) , the oldest nearby star forming region with a substantial number of brown dwarfs .
upsco is often assumed to have an age of 5myr @xcite but recently @xcite have derived an older age of 10myr for this region . in upsco , @xcite derived a disk frequency of @xmath2% for f and g stars and @xmath3% for k0-m5 stars ( with 1@xmath4 binomial confidence intervals ) . the brown dwarfs in this region exhibit a disk fraction of @xmath5% , based on an examination of 35 objects @xcite .
thus , the spitzer data tentatively shows that the disk fractions _ in upsco increase monotonically with decreasing object mass for early f- to late m - type objects_. this would imply a mass dependence in the disk evolution , resulting in long - lived disks in the substellar regime .
so far , the brown dwarf disk frequency in upsco is affected by low number statistics . here
we set out to test previous findings based on a much enlarged number of brown dwarfs in upsco , identified from ukidss . to identify the objects in our sample that have a disk ( class ii objects ) and those that do not ( class iii objects ) , we use data from the wide - field infrared survey explorer ( wise)@xcite . as will be shown , with improved statistics we find a disk fraction for brown dwarfs that is consistent with the value published for low - mass stars in this region . | we present a census of the disk population for ukidss selected brown dwarfs in the 5 - 10 myr old upper scorpius ob association . for 116 objects originally identified in ukidss ,
the majority of them not studied in previous publications , we obtain photometry from the wise database . the resulting colour - magnitude and
colour - colour plots clearly show two separate populations of objects , interpreted as brown dwarfs with disks ( class ii ) and without disks ( class iii ) .
we identify 27 class ii brown dwarfs , 14 of them not previously known .
this disk fraction ( 27 out of 116 or 23% ) among brown dwarfs was found to be similar to results for k / m stars in upper scorpius , suggesting that the lifetimes of disks are independent of the mass of the central object for low - mass stars and brown dwarfs .
5 out of 27 disks ( 19% ) lack excess at 3.4 and 4.6@xmath0 m and are potential transition disks ( i.e. are in transition from class ii to class iii ) .
the transition disk fraction is comparable to low - mass stars .
we estimate that the timescale for a typical transition from class ii to class iii is less than 0.4myr for brown dwarfs .
these results suggest that the evolution of brown dwarf disks mirrors the behaviour of disks around low - mass stars , with disk lifetimes on the order of 5 - 10myr and a disk clearing timescale significantly shorter than 1myr .
[ firstpage ] techniques : photometric techniques : brown dwarfs open clusters and associations : individual : upper scorpius infrared : stars . |
the spectra of hot stars show often excess emission at ir and radio wavelengths that can be ascribed to free - free and free - bound ( ff - fb ) emission from their wind zones ( see e.g. panagia & felli @xcite ) .
waters & lamers ( @xcite ) have investigated this excess emission for @xmath4 m and winds with a @xmath1-law velocity distribution of varying @xmath1 , pointing already to the sensitivity of the wind emission to the chosen velocity distribution . over the last few years
, two major effects have become obvious that both strongly influence the wind continuum emission : ( i ) the winds of hot stars seem to be clumped , and ( ii ) many ob supergiants have winds with @xmath5 ( see table [ kraus : tab1 ] ) .
we investigate the wind continuum emission of ob supergiants especially at optical wavelengths .
first , the influence of high @xmath1 values is discussed , and later on the effects of clumping are studied .
the calculation of the continuum emission of a typical ob supergiant is performed in three steps : ( i ) we first calculate the stellar emission of the supergiant with no stellar wind , ( ii ) then we calculate the emission of the wind with the stellar parameters ( @xmath6 ) as boundary conditions , ( iii ) and finally we combine the two continuum sources whereby the stellar emission still has to pass through the absorbing wind . to simulate a typical ob supergiant
we adopt the following set of stellar parameters : @xmath7k , @xmath8 , @xmath9 , and @xmath10 . with these parameters
we compute the stellar continuum emission with the code of kubt ( @xcite ) , suitable for the calculation of nlte spherically - symmetric model atmospheres .
.range of @xmath1 values found for ob supergiants in the galaxy ( markova et al .
@xcite = ma ; crowther et al .
@xcite = cr ; kudritzki et al .
@xcite = ku ) and the magellanic clouds ( evans et al .
@xcite = ev ; trundle & lennon @xcite = tl ; trundle et al .
@xcite = tr ) .
[ cols="<,^,<",options="header " , ] the spherically symmetric wind is assumed to be fully ionized , isothermal , and in lte .
this reduces the problem to a pure 1d treatment of the simplified radiation transfer ( e.g. panagia & felli @xcite ) .
the electron temperature is fixed at 20000k , and the density distribution in the wind follows from the equation of mass continuity , relating the density at any point in the wind to the mass loss rate and the wind velocity . the velocity of hot star winds can be approximated with a @xmath1-law @xmath11 where @xmath1 describes the steepness of the velocity increase at the base of the wind , and @xmath12 defines the velocity on the stellar surface . a more detailed description of the calculations will be given elsewhere .
the range in @xmath1 found for galactic and magellanic cloud ob supergiants is listed in table[kraus : tab1 ] . increasing @xmath1 means that the wind is accelerated more slowly .
consequently , the density in these regions is enhanced because @xmath13 . these density peaks close to the stellar surface with respect to the wind density with @xmath14
are shown in fig.[kraus : dens ] .
even though these density peaks are rather narrow in radius , they strongly influence the optical depth and therefore the emission of the ff and especially the fb processes .
now , the wind can become ( at least partially ) optically thick even at optical wavelengths .
this leads to an enhanced wind emission meanwhile the stellar flux suffers from the simultaneously increasing wind absorption .
our test supergiant is assumed to have a wind with @xmath15yr@xmath16 , @xmath17kms@xmath16 , and we calculate the continuum emission for @xmath18 , and 3 .
the results are shown in fig.[kraus : beta ] .
it is obvious that with increasing @xmath1 the wind creates a near - ir excess , absorbs more of the stellar emission , and contributes to the total emission even at optical wavelengths . )
that grow with increasing @xmath1.[kraus : dens ] ] hillier et al .
( @xcite ) introduced a formalism to account for the presence of wind clumping , and in our calculations we use their filling factor defined by @xmath19 and setting @xmath20kms@xmath16 , and @xmath21 .
since @xmath22 depends on the velocity distribution , this filling factor is a function of radius as well , constructed such that it quickly reaches its terminal value ( top panel of fig.[kraus : dens_cl ] ) .
this way of clumping introduction requests , however , that in order to maintain the same radio flux , the mass loss rate has to be decreased , i.e. @xmath23 , while the absorption coefficient of the ff - fb processes increases , @xmath24 , due to its density squared dependence .
our clumped models automatically account for this mass loss reduction . at those positions in the wind
where @xmath25 there is no difference between the clumped and the unclumped wind .
however , in those regions where @xmath26 , which are also the regions where @xmath1 has its strongest influence , the wind opacity is sensitive to the clumping .
but while @xmath1 enhances the density , clumping ( for the same input @xmath27 ) reduces the density again . a wind with high @xmath1 and clumping
will therefore have a different opacity in the innermost wind region than a wind with low @xmath1 and clumping , and the clumped wind will have a different opacity than the smooth wind .
this is shown in the lower panel of fig.[kraus : dens_cl ] where we plotted the opacity ratio of the clumped with respect to the smooth wind for different values of @xmath1 .
the higher @xmath1 , the stronger the effect . in fig.[kraus : clumped ] we compare the continuum of a clumped with an unclumped wind for @xmath28 . .
shown are the stellar emission having passed through the absorbing wind ( dotted ) , the ff - fb emission from the wind ( dashed ) and the total continuum ( solid ) .
[ kraus : beta ] ] .
bottom : opacity ratio between clumped wind model and unclumped wind model .
[ kraus : dens_cl ] ] it is obvious that the clumped model generates less wind emission for @xmath29 m . for a better visualization we calculated the flux ratios between unclumped and clumped models ( fig.[kraus : ratio ] ) .
they show a maximum of up to 30% at near - ir wavelengths .
continuum observations at these wavelengths are therefore an ideal tool to discriminate whether the winds of ob stars with @xmath30 are clumped . .
the clumped model produces less wind emission for @xmath31 m , resulting in a lower total near - ir flux .
[ kraus : clumped ] ]
for ob supergiants with high @xmath1 values the ff and especially the fb emission can strongly influence the total continuum , even at optical wavelengths .
clumping , introduced by the filling factor approach , also influences the wind opacity and therefore the continuum emission . whether the wind of an ob supergiant is clumped or not can be checked based on continuum observations in the optical and near - ir region .
especially winds with high @xmath1 are found to have fluxes that differ by about 30% ( see fig.[kraus : ratio ] ) .
the optical and near - ir continuum are therefore ideal to discriminate between clumped and unclumped winds .
crowther , p. a. , lennon , d. j. , & walborn , n. r. 2006 , a&a , 446 , 279 evans , c. j. , crowther , p. a. , fullerton , a. w. , & hillier , d. j. 2004 , apj , 610 , 1021 hillier , d. j. , lanz , t. , heap , s. r. , et al .
2003 , apj , 588 , 1039 kubt , j. 2003 , in modelling of stellar atmospheres , ed . n. piskunov , w. w. weiss , & d. f. gray ( san francisco : asp ) , iau symp . , 210 , a8 kudritzki , r. p. , puls , j. , lennon , d. j. , et al . 1999 ,
a&a , 350 , 970 markova , n. , puls , j. , repolust , t. , & markov , h. 2004 , a&a , 413 , 693 panagia , n. , & felli , m. 1975 , a&a , 39 , 1 trundle , c. , & lennon , d. j. 2005 , a&a , 434 , 677 trundle , c. , lennon , d. j. , puls , j. , & dufton , p. l. 2004 , a&a , 417 , 217 waters , l. b. f. m. , & lamers , h. j. g. l. m. 1984 , a&as , 57 , 327 | the influence of the wind to the total continuum of ob supergiants is discussed . for wind velocity distributions with @xmath0 ,
the wind can have strong influence to the total continuum emission , even at optical wavelengths .
comparing the continuum emission of clumped and unclumped winds , especially for stars with high @xmath1 values , delivers flux differences of up to 30% with maximum in the near - ir .
continuum observations at these wavelengths are therefore an ideal tool to discriminate between clumped and unclumped winds of ob supergiants . * wind emission of ob supergiants + and the influence of clumping * + _ * m .
kraus@xmath2 , j. kubt@xmath2 & j. krtika@xmath3 * _ + _ @xmath2astronomick stav , akademie vd esk republiky , ondejov , czech republic _
+ _ @xmath3stav teoretick fyziky a astrofyziky pf mu , brno , czech republic _ 2 |
the human eye is distinguished from commercially available electronic cameras by virtue of having much better resolution in the fovea near the optical axis .
the eccentricity of the retina , which produces a large field of view and high acuity at the fovea , causes the human visual system to have quick jerky eye movements - i.e. , saccades .
it was shown that an artificial visual system equipped with saccades could reduce the number of processing units required for pattern recognition @xcite and could greatly simplify the calculations in low - level vision systems @xcite .
the saccades involve two subtasks ; i.e. , a location task and an identification task .
the location task fixates the location of a pattern in a wide field of view using _ a priori knowledge of the pattern class of interest . on the other hand
, the identification task determines the class of a pattern under the assumption that the location of the pattern can be fixated .
these subtasks are therefore cooperative .
recently , hopfield and his colleagues have shown that a symmetric interconnected neural network ( a hopfield neural network ) can perform error corrections in associative retrieval @xcite and lead to appropriate solutions in optimization problems @xcite . in this letter
, we treat the saccades as the optimization problem and apply the hopfield network to the emulation of saccades .
computer simulation confirms that the network performs these subtasks cooperatively .
it also suggests that the network is applicable to shift - invariant pattern recognition . _
the network ( shown in fig.[figure01 ] ) comprises three blocks of neurons called the saccades ( s ) block , hidden ( h ) block , and output(o ) block , respectively .
its energy function is defined as follows : @xmath0 where @xmath1 and @xmath2 where @xmath3 is a gaze position , @xmath4 a pixel image of an input pattern , @xmath5 a window function , @xmath6 and activity of the @xmath7th neuron of @xmath8 block , @xmath9 the output of the @xmath7th neuron of @xmath8 block ( @xmath10 ) , @xmath11 the @xmath12th template embedded in the weights between the @xmath13 and @xmath14 blocks , @xmath15 positive constants .
the @xmath16 block is a matrix representation of the location of an input pattern relative to a gaze position represented as the @xmath17th neuron .
the most - activated neuron in the @xmath14 block indicates the class of the input pattern whose location would be represented by the @xmath16 block .
the location and identification tasks are obtained by minimizing the first and second terms in the energy function , respectively .
the third and fourth terms represent winner - take - all constraints in the @xmath16 and @xmath14 blocks , respectively .
a gaze position is updated by the following rule : @xmath18 where @xmath19 is an index of the most - activated neuron in the @xmath16 block . when the gaze position is unchanged by the updating rule , the tasks are complete . and @xmath14 block .
fully interconnected between the @xmath16 and @xmath13 block and between the @xmath13 and @xmath14 block . ]
the first simulation confirmed that the network can perform cooperative subtasks in the saccades .
positive constants in the energy function and the number of neurons of each block were chosen to be @xmath20 , @xmath21 , @xmath22 , @xmath23 and @xmath24 , @xmath25 , @xmath26 , respectively . four templates ( @xmath27 binary - valued pixels ) are depicted in fig.[figure02 ] .
the stable states of the network are illustrated in fig.[figure03](a)-(d ) , where one side of each square represents an output level of the corresponding neuron , an empty circle in @xmath4 a gaze position , and a directed line in the s block a saccadic vector .
it is also seen that the activation pattern of the @xmath28 block resembles the template of the class of the target pattern .
the network was next applied to shift - invariant pattern recognition .
positive constants in the energy function and the number of neurons of each block were chosen to be @xmath29 , @xmath21 , @xmath30 , @xmath31 and @xmath32 , @xmath33 , @xmath34 , respectively . ten templates ( @xmath35 binary - valued pixels )
are depicted in fig.[figure04 ] . in the experiment ,
160 input patterns shifted in any direction by one pixel and deformed by no more than eight hits ( hamming distance ) , including the patterns shown in fig.[figure05 ] , were recognized perfectly .
the behavior of the network is illustrated in fig.[figure06 ] .
figure [ figure06](a ) and ( b ) show the stable states before and after a saccade by one pixel to the upper left , respectively .
we can see the identification task was completed by the saccade that resulted from the location task .
a hopfield neural network for saccades has been proposed .
computer simulations confirmed that the network performs the location and the identification tasks in a cooperative fashion .
it has also been demonstrated that the network can be applied to shift - invariant pattern recognition . since
out network is a standard hopfield - type neural network , it is suitable for vlsi and optical implementations and therefore can speed up saccadic tasks and shift - invariant pattern recognition significantly . used in the first simulation . ]
used in the second simulation . ]
the author thanks the reviewer who originally recommended the publication of this letter and dr . y. tomita of the university of electro - communications for his helpful comments .
ballard , `` behavioral constraints on animate vision , '' image and vision computing , vol.7 , no.1 ( 1989 ) .
j. j. hopfield , `` neural networks and physical systems with emergent collective computational abilities , '' proc .
sci . u.s . , vol.79 ( 1982 ) .
k. nakano , m. niizuma , and t. omori , `` model of neural visual system with self - organizing cells , '' biolog .
cybern . , vol.60 ( 1989 ) .
m. takeda and j. w. goodman , `` neural networks for computation : number representations and programming complexity , '' appl .
vol.25 , no.18 ( 1986 ) .
d. w. tank and j. j. hopfield , `` simple neural optimization networks : an a / d converter , signal decision circuit , and a linear programming circuit , '' ieee trans . circuits and syst . ,
vol.cas-33 , no.5 ( 1986 ) | human eye movement mechanisms ( saccades ) are very useful for scene analysis , including object representation and pattern recognition . in this letter , a hopfield neural network to emulate saccades
is proposed .
the network uses an energy function that includes location and identification tasks .
computer simulation shows that the network performs those tasks cooperatively .
the result suggests that the network is applicable to shift - invariant pattern recognition . |
electromagnetic radiation represents penetrating probes mapping out the full space - time history of strongly interacting matter in the course of heavy - ion collisions .
particularly interesting is the stage of maximum temperature , where a quark - gluon plasma might be formed .
various properties of the quark - gluon plasma are calculable from first principles exploiting numerical lattice qcd techniques .
the results , such as thermodynamical properties , can be interpreted within quasi - particle models @xcite .
other quantities , such as the electromagnetic emission rates , are accessible within perturbation theory @xcite .
the motivation to measure electromagnetic signals in ultralrelativistic heavy - ion collisions is based on the hope to have a direct access to the hottest and densest stages of matter ( cf .
@xcite ) . according to the present understanding of the dynamics of central heavy - ion collisions at cern - sps , the temperature range covered is @xmath0 mev ( where @xmath1 mev is the confinement temperature ) . in this regime
the electromagnetic emission rates from deconfined and confined hadronic matter are fairly similar ( cf .
@xcite ) . indeed , taking into account the empirical electromagnetic formfactors from the reaction @xmath2 and including vector - axial vector mixing @xcite one gets a dilepton rate which coincides with the lowest - order @xmath3 rate for invariant masses
@xmath4 gev @xcite . below 1.1 gev the dilepton spectrum of hadronic matter
is determined by the sharp @xmath5 and @xmath6 peaks and the broad @xmath7 peak .
hadronic reactions broaden the @xmath7 peak so much that the net dilepton spectrum again resembles that from the @xmath3 rate down to @xmath8 mev @xcite .
it is therefore tempting to entirely describe the spectra at @xmath9 mev by the lowest - order @xmath3 rate , thus treating it as a convenient parameterization .
analog arguments are not available for the real photon rate .
therefore , we use as a working hypothesis the lowest - order born rates of the processes @xmath10 and @xmath11 for thermal photons .
many hadron observables at cern - sps energies can be described by thermal models . in line with this finding
we will describe the secondary real and virtual photons by a thermal source which adds to the drell - yan - like yields and hadron decay contributions ( hadronic cocktail and correlated semi - leptonic decays of open charm mesons ) .
by now the following experimental data are available : ( i ) lead beam at 158 a@xmath12gev and au , pb targets : ceres ( low - mass @xmath13 ) , na50 ( intermediate - mass @xmath14 ) , wa98 ( direct photons ) , ( ii ) lead beam at 40 a@xmath12gev and au target : ceres ( low - mass @xmath13 ) , ( iii ) sulfur beam at 200 a@xmath12gev and au , u , w targets : ceres ( low - mass @xmath13 ) , na38 ( intermediate - mass @xmath14 ) , helios/3 ( low- and intermediate - mass @xmath14 ) , wa80 ( upper bounds on direct photons ) .
in addition , data with proton beams at these energies and also 450 gev for various target nuclei are at our disposal .
the lowest - order rates are in boltzmann approximation @xmath15 , \label{rates_1}\ ] ] where @xmath16 ( @xmath17 ) is the virtual ( real ) photon s 4-momentum ; effects of a finite chemical potential @xmath18 can be absorbed in an additional normalization factor .
note the necessary occurrence of the medium s
4-velocity @xmath19 to build up lorentz - invariant rates .
to reduce the number of parameters in the space - time integration , we replace in ( [ rates_1 ] ) @xmath20 , @xmath21 and @xmath22 yielding @xmath23 thus not relying on a particular model for @xmath24 , @xmath25 and @xmath26 ( for the explicit form of ( [ rates_2 ] ) cf .
this approach is in the spirit of the usual parameterization of the transverse momentum spectra of hadrons by an exponential with a slope parameter and a normalization factor . as an example
we show in figure 1 our results for the invariant mass spectra of dileptons and the momentum spectrum of photons for the experiments of group ( i ) ( cf .
@xcite for more details ) .
also the transverse momentum spectra of dileptons are described very well @xcite .
the na50 acceptance is incorporated only in an approximate way here ; the use of the correct filter reproduces the data perfectly @xcite .
a comparison of our model with the preliminary ceres data @xcite of the experiment group ( ii ) is shown in figure 2 for @xmath27 mev and a fairly large value of @xmath28 .
deliver a better description of the spectral shape but need even larger @xmath28 . ] since the experiments of group ( iii ) cover a large rapidity range an additional gaussian smearing of the source in ( [ rates_2 ] ) needs to be included @xcite . in figure 3 the strength distributions of the thermal dilepton source without and with smearing
are displayed .
as shown in @xcite the shape of the spectra can be well described by @xmath29 mev , however , different values of @xmath28 are needed .
this might be attributed to an inadequate rapidity distribution of our thermal source and different centrality selections in the experiments .
( -3.5,-2.45)(-3.55,-1.55 ) ( -2.9,-2.6)thermal ( -3.0,-2.2)(-3.0,-1.9 ) ( -2.7,-2.3)cocktail ( -2.3,-1.4)(-2.88,-1.68 ) ( -1.5,-1.4)drell - yan ( -3.1,-2.9)(-2.76,-2.66 ) ( -3.6,-2.9)charm ( -2.85,-3.41)(-2.65,-3.35 ) ( -3.5,-3.4)thermal ( -2.6,-2.77)(-2.,-2.2 ) ( -2.5,-2.9)thermal ( -2.5,-3.25)(@xmath30 ) ( -3.3,-2.3)(-2.95,-1.28 ) ( -3.3,-2.5)pqcd + ( 2.,1.7)(2.0,2.3 ) ( 2.,1.5)cocktail ( 2.8,3.56)(2.33,3.23 ) ( 3.5,3.6)thermal + + by using a model for @xmath31 and @xmath32 and neglecting spatial gradients one can equally well describe the dilepton spectra of the ceres and na50 collaborations .
as shown in @xcite , there is virtually no difference with the results displayed in figure 1 .
the needed initial temperature is 210 mev , for a given freeze - out temperature of 120 mev .
while the analysis of the low - mass dileptons uses a hadronic cocktail and is normalized to the mean multiplicity of charged hadrons , the analyses of the intermediate - mass dileptons and photons need careful estimates of the hard drell - yan - like yields and the open charm contribution .
we used the pythia event generator with charm quark mass of 1.5 gev , intrinsic parton transverse momentum distribution width of 0.8 gev and photon cut - off parameter of 1 gev .
the parameter adjustments are done by comparing with @xmath33 and @xmath34 data , and then scaling to heavy - ion collisions .
the possible subtleties of this procedure are described in @xcite .
in summary we have demonstrated that the superposition of background contributions and a thermal source of real and virtual photons describes the shape of all data from central heavy - ion collisions at cern - sps .
we find evidence for a large and long - lived thermal source in lead beam experiments at 158 a@xmath12gev .
the normalization factor @xmath28 translates into a lifetime of 23 fm / c , in accordance with @xcite , when assuming a spatial volume of the fireball 1440 @xmath35 as found for a radius of 7 fm .
the space - time averaged temperature of @xmath36 mev coincides with both the confinement temperature and the temperature needed to describe the hadron multiplicity ratios in thermal models . using a model for the temperature and volume evolution of the fireball we find a maximum temperature of 210 mev indicating an initial state in the deconfinement region .
the sulfur beam data point to a similar value of @xmath37 mev , while the recent preliminary lead beam data at 40 a@xmath12gev can be described by @xmath38 mev .
the present analysis strategy needs to be extended to understand the centrality dependence of the intermediate - mass dileptons as measured by the na38/50 collaborations @xcite .
the results of the high - statistic data sampling of dileptons in the lead beam induced reactions at 158 a@xmath12gev by the ceres collaboration is eagerly waited for to decide whether a smooth @xmath3-like rate is still sufficient .
we used it here as a convenient parameterization , and this is not a substitute to a more detailed microscopic calculation .
the consistent description of the real and virtual photon data makes an interpretation of the na50 data by an anomalous open charm enhancement unlikely .
nevertheless , the explicit measurement of the charm yield , as envisaged by the na60 collaboration , is needed to arrive at a better understanding of the various dilepton sources .
9 a. peshier , b. kmpfer , o.p .
pavlenko , g. soff , phys . rev .
d 54 ( 1996 ) 2399 , + a. peshier , b. kmpfer , g. soff , phys .
c 61 ( 2000 ) 045203 .
p. aurenche , f. gelis , r. kobes , h. zaraket , phys .
d 60 ( 1999 ) 076002 .
k. gallmeister , b. kmpfer , o.p .
pavlenko , prog .
42 ( 1999 ) 333 .
j. kapusta , p. lichard , d. seibert , phys .
d 44 ( 1991 ) 2774 .
li , c. gale , phys .
c 58 ( 1998 ) 2914 , phys .
81 ( 1998 ) 1572 .
z. huang , phys .
b 361 ( 1995 ) 131 .
r. rapp , j. wambach , hep - ph/9909229 , adv .
phys . , in press .
k. gallmeister , b. kmpfer , o.p .
pavlenko , phys .
c 62 ( 2000 ) 057901 .
k. gallmeister , b. kmpfer , o.p .
pavlenko , c. gale , hep - ph/0010332 , nucl .
a , in press . l. capelli ( na50 ) , this volume ; ph.d .
thesis , univ .
de lyon 2001 .
b. lenkeit ( ceres ) , nucl . phys . a 661 ( 1999 ) 23c ; ph.d .
thesis , heidelberg 1998 .
e. scomparin ( na50 ) , nucl .
phys . a 610 ( 1996 ) 331c , j. phys .
g 25 ( 1999 ) 235c .
aggarwal et al .
( wa98 ) , phys .
85 ( 2000 ) 3595 .
s. damjanovic , k. filimonov ( ceres ) , poster p084 at qm2001 .
k. gallmeister , b. kmpfer , o.p .
pavlenko , phys .
b 473 ( 2000 ) 20 . k.o .
gallmeister , ph.d .
thesis , tu dresden 2001 .
. hung , e.v .
shuryak , phys .
c 57 ( 1998 ) 1891 . | a unique parameterization of secondary ( thermal ) dilepton and photon yields in heavy - ion experiments at cern - sps is proposed . adding those thermal yields to background contributions the spectral shapes of the ceres / na45 , na38 , na50 , helios/3 and wa98 data from experiments with lead and sulfur beams can be well described . |
quantum game theory @xcite is a new field of science having its roots in both game theory and quantum information theory . for about a decade
quantum computer scientists have been searching for new methods of quantum algorithm design .
thorough investigation of different quantum games may bring new insight into the development of quantum algorithms .
it was shown that grover s algorithm @xcite can be treated as an example of a quantum parrondo s paradox @xcite .
operators used in grover s algorithm can be treated as parrondo games having separately zero expected values , however , if they are interwired , the expected value fluctuates .
this effect is well known in grover s algorithm .
implementation of a quantum parrondo s paradox has been described in papers @xcite . in this paper
we present a new implementation scheme of a capital - dependent parrondo s paradoxical games on a relatively small number of qubits .
parrondo s paradox consists of a sequence of games , where each game can be interpreted as a toss of an asymmetrical coin .
every success means that the player gains one dollar , every loss means that the player loses one dollar .
there are two games .
game @xmath2 has probability of winning @xmath3 .
game @xmath4 depends on the amount of capital accumulated by player .
if his capital is a multiple of three , the player tosses coin @xmath5 , which has probability of wining @xmath6 , otherwise the player tosses coin @xmath7 which has probability of wining @xmath8 .
originally @xmath9 , but generally it can be any small real number . both games @xmath2 and @xmath4 are biased and have negative expected gain .
but when a player has the option to choose which game he wants to play at each step of the sequence , he can choose such a combination of games which allows him to obtain positive expected gain .
it is known that sequences @xmath10 or @xmath11 give relatively high expected gain .
this fact is known as _ parrondo s
in @xcite the quantum versions of parrondo games were proposed .
the scheme introduced in @xcite realizes a history - dependent version of parrondo s paradox .
its disadvantage is that it needs a large number of qubits to store the history of the games . on the
other hand the scheme by meyer and blumer @xcite uses brownian motion of particle in one dimension and does not consume large amounts of quantum resources . the scheme presented by flitney , abott and johnson in @xcite
is based on multi - coin discrete quantum history - dependent random walk .
the implementation of the capital - dependent quantum parrondo s paradox introduced in this paper uses only @xmath0 qubits , where @xmath1 is the number of games played .
this allows to perform simulation even when a relatively large number of games are played ; for instance , if a strategy consists of five elementary games then 400 iterations require only 15 qubits .
to implement games @xmath2 and @xmath4 , three arbitrary - chosen one - qubit quantum gates @xmath12 , @xmath5 and @xmath7 are used .
each gate is described by four real parameters and our scheme as a whole is described by set of parameters : * @xmath13 : real numbers describing gates @xmath14 ; * @xmath15 : strategy any sequence of games @xmath2 , @xmath4 ; * @xmath1 : size of @xmath16 outcome register ( see below ) ; * @xmath17 : initial capital offset .
each gate is composed of elementary gates as presented in eq .
( [ equ : gate - comp ] ) : @xmath18 where @xmath19 and + @xmath20 .
the quantum register used to perform this scheme consists of three subregisters : * @xmath21 : one - qubit register representing the coin , * @xmath16 : @xmath1-qubit register storing player s capital , * @xmath22 : three - qubit auxiliary register .
register @xmath21 holds the state of the _
quantum coin_. gates @xmath12 , @xmath5 and @xmath7 acting on this register represent _ quantum coin tosses_. one should note that the register @xmath21 does not store information about history of the games .
after every execution of gates @xmath12 , @xmath5 and @xmath7 , the state of the register @xmath16 is changed according to the result of the _ quantum coin toss_. this register is responsible for storing the history of the games , that is , player s capital .
register @xmath22 is an ancillary register , which one need to check if the state of the @xmath16 register is a multiple of three . at the beginning of the scheme and after the application of the games gates this register is always set to @xmath23 .
games @xmath2 and @xmath4 are implemented using the conditional incrementation
decrementation ( cid ) gate and gates @xmath12 , @xmath5 and @xmath7 described above .
in addition , game @xmath4 uses gate @xmath24 . gate @xmath24 sets @xmath25 and @xmath26 registers to state @xmath27 iff the @xmath16 register contains a number that is a multiple of three : @xmath28 the cid gate is responsible for increasing and decreasing the player s capital . the circuit for this gate is presented in fig .
[ fig : cid ] .
this gate increments register @xmath16 if @xmath21 is in state @xmath27 and decrements if it is in state @xmath29 .
game @xmath2 is directly implemented by gate @xmath12 as presented in fig .
[ fig : game - a ] .
game @xmath4 , presented in fig .
[ fig : game - b ] , is more complicated . it uses gate @xmath24 to check if the player s capital is a multiple of three .
if it is the case gate @xmath7 is applied to register @xmath21 , otherwise , @xmath5 is applied .
one can easily check that all gates used in this scheme are unitary because they are composed of elementary unitary operations .
+ the game procedure is composed of the following steps : 1 .
preparation of @xmath21 in state @xmath30 .
2 . preparation of @xmath16 in state @xmath31 , where @xmath17 is a small integer number , 3 .
preparation of @xmath32 in @xmath23 state .
4 . application of gates @xmath12 and @xmath33 in some chosen order @xmath15 . after each application of gate @xmath12 or
@xmath33 the number stored in register @xmath16 is either incremented or decremented .
the initial state of register @xmath16 must be chosen in such way that integer overflow is avoided .
the maximum number of elementary games can not exceed the capacity of the register @xmath16 .
if our scheme is implemented on a physical quantum device it should be finalized by measurement .
this would give a single outcome representing the final capital .
thus , to obtain expected gain , the experiment should be repeated several times .
simulation allows to observe the state vector of the quantum system . using this property
the expected gain is calculated as the average value of @xmath34 in state @xmath35 obtained after tracing out the register with respect to coin and auxiliary subregisters : @xmath36
simulations of a quantum parrondo s paradox presented in this article were performed using qcl @xcite .
the source code of the implementation can be found on the webpage listed in ref .
@xcite . to carry out the simulation ,
gates @xmath12 , @xmath5 and @xmath7 were prepared with coefficients listed in table [ tab : ex1 ] .
those coefficients were chosen arbitrarly .
.coefficients of the experiment [ cols="^,^,^,^",options="header " , ] in fig .
[ fig : sim - res ] the selection of results is presented .
as one can see there are strategies that give positive expected values . for @xmath37 ,
strategy @xmath38 gives a gain of @xmath39 after 400 steps .
for @xmath40 , strategy @xmath41 gives a gain of @xmath42 after 400 steps .
+ simulations have shown that finding the winning strategy for a given initial set of parameters is not trivial because they are uncommon .
we found that the initial value kept in register @xmath16 heavily influences the outcome , for example , see fig .
[ fig : sim - res ] . for different offsets different winning strategies can be found .
one should note that behavior of the strategy can change if the initial offset is altered , for example see , fig .
[ fig : sim - res - comp ] .
is wining for @xmath40 and losing for @xmath37 . ]
we have shown that it is possible to create a capital - driven scheme for quantum parrondo games using less than 20 qubits .
the main advantage of this scheme is that the size of the register grows as @xmath0 , where @xmath1 is the number of steps .
we have found that the initial value of the register @xmath16 is important for selection of strategy .
simulations have shown that for an analyzed set of strategies composed of five elementary games , winning strategies are uncommon .
this paper has been supported by the polish ministry of scientific research and information technology under the ( solicited ) grant no .
pbz - min-008/p03/2003 . | we propose a quantum implementation of a capital - dependent parrondo s paradox that uses @xmath0 qubits , where @xmath1 is the number of parrondo games .
we present its implementation in the quantum computer language ( qcl ) and show simulation results . |
in this section , we give explicit expressions for the _
su_(4 ) superoperators for @xmath0 two - level atoms in terms of the pauli spin - operators . following hartmann @xcite , 18 superoperators @xmath15 , @xmath16 and @xmath17 are defined , where @xmath18 , @xmath109 although this list , eq .
( [ super ] ) , contains 18 operator definitions , only 15 of them are independent ( it is possible to write @xmath110 , @xmath111 , @xmath112 in terms of the others ) .
one can demonstrate that the 15 remaining superoperators are linear combinations of the familiar gell - mann matrices that are the generators of the _
su_(4 ) group , @xmath113 @xcite . in order to see this , consider first the fundamental one atom case , where we interpret the @xmath114 density matrix as a @xmath115 vector in the representing vector space ( _ i.e. _ liouville space ) .
@xmath116 the linear combinations are given by @xmath117 the commutation relations of the superoperators are given in both ref .
@xcite and @xcite
. we can also identify six _
su_(2 ) subalgebras , @xmath118=2\mathcal{o}_3,\;\;\ ; [ \mathcal{o}_3,\mathcal{o}_{\pm}]=\pm\mathcal{o}_{\pm},\ ] ] so that it is useful to define six corresponding quadratic superoperators @xmath119 , which commute with @xmath120 .
su_(4 ) group has 3 casimir operators , one of which is quadratic in the generators , and the others are of higher order .
the quadratic casimir operator @xmath121 can be expressed in terms of superoperators @xmath122
the fundamental representation of the _
su_(4 ) group , adapted to serve as basis of the single - spin density matrix , is given by @xmath19 , @xmath20 , @xmath21 , @xmath22 .
higher order representations can then be obtained from the fundamental representation and the symmetry type , which is described by the young tableau .
the basis for the fully symmetrical case is defined as @xmath23 which are eigenstates of both @xmath123 and @xmath17 @xcite , with eigenvalues @xmath124 where @xmath125 .
the eigenvalues are not independent , but can be expressed in terms of @xmath126 : @xmath127 then it is straightforward to determine actions of all the raising and lowering superoperators on @xmath58 , @xmath128 we note that the fully symmetrical basis are also eigenstates of the quadratic casimir operator @xmath121 with common eigenvalue @xmath129 .
analogous actions for the photon part are the simple harmonic oscillator relations : @xmath130
in order to project the density operator from the _ su_(4 ) basis onto the @xmath71 representation , let us first show that @xmath86 and @xmath87 are related to the @xmath132 by @xmath72 and @xmath73 . to see this , defining @xmath133 , we could get @xmath134 and by definition , we have @xmath135 therefore , the complex coefficients from the @xmath132 basis contributing to the matrix element for @xmath71 all satisfy @xmath72 and @xmath73 . with this in mind , we now describe a systematic algorithm to obtain the density matrix elements @xmath85 from the _
su_(4 ) expansion coefficients @xmath38 .
we illustrate our method by considering in detail the elementary case of three atoms .
the density matrix in the @xmath71 representation is block diagonal in @xmath62 ; the block matrices for all @xmath62 can be arranged in the shape of a pyramid as shown in fig .
for instance , the base layer corresponds to @xmath63 , with the matrix dimension being @xmath136 .
the second layer has @xmath137 and dimension @xmath138 , and so on .
furthermore there are @xmath77 copies associated with each layer , so that @xmath78 . taking @xmath139 for example , there are two layers , @xmath140 and @xmath141 with @xmath142 and @xmath143 , so that the hilbert space dimension is @xmath144 .
the density matrix needs to be built from the bottom layer upwards . in the bottom layer , we find that the only element contributing to @xmath145 is @xmath146 .
so the top left corner is @xmath91 .
we next apply the lowering operator @xmath88 to iteratively generate @xmath147 , with @xmath148 . to do this
, we need the recursion relation @xmath149 therefore , with the actions of the raising and lowering operators [ eq . ( [ act ] ) ] , we can derive all @xmath150 , _
i.e. _ the first row of the bottom layer .
using the fact that the density matrix is hermitian and @xmath151 , we could get all the elements for the first column by @xmath152 . by repeatedly applying the recursion relation [ eq .
( [ rec ] ) ] in each row , we then construct the full base layer . as an explicit example
, we have constructed the bottom layer , _
@xmath140 for the three atom case , @xmath153 in order to illustrate the use of the recursion relation , we now show how to get @xmath154 from @xmath155 . because @xmath156 and @xmath157 , we have @xmath158 . to construct the next layer
, we thus find out the top left matrix element first , and then apply the same procedure as before to determine the rest of the matrix elements .
let us first examine the three atom case .
the @xmath141 layer has two copies , each of which is a @xmath159 matrix . to find the top left element @xmath160 ,
noticing the constraint imposed by the trace of the density matrix , we derive @xmath161 so that @xmath162 . by applying the same method as in the bottom layer ,
we construct the block matrix for @xmath141 layer @xmath163 therefore in general , if we suppose that we have constructed the block matrix for @xmath164 , the formula to find the top left matrix element @xmath165 for layer @xmath62 is @xmath166 having the top left matrix element for each layer @xmath62 , we can easily construct the @xmath167 block matrix by applying the recursion relation based on the angular momentum lowering operator .
repeated iteration of these steps systematically fills in all sites of the pyramid . | we show that open quantum systems of two - level atoms symmetrically coupled to a single - mode photon field can be efficiently simulated by applying a _
su_(4 ) group theory to quantum master equations .
this is important since many foundational examples in quantum optics fall into this class .
we demonstrate the method by finding exact solutions for many - atom open quantum systems such as lasing and steady state superradiance .
although quantum mechanics actually describes the behavior of isolated and closed quantum systems , in practice most physical situations to which it is applied are open .
the open nature is necessary to treat basic irreversible processes such as the energy transfer with a heat bath , the particle or charge exchange with a reservoir , and quantum measurements .
open quantum systems can be treated under the born and markov approximations by the quantum master equation in the lindblad form @xcite , which has been applied across many fields of physics , including quantum optics and quantum information science @xcite , atomic and molecular physics @xcite , solid state physics @xcite , and optomechanics @xcite .
here we focus on a novel group - theoretic approach to find an efficient solution of the quantum master equation for an important class of quantum optical systems .
even though we focus on these systems , the methods we present could be more generally applied to other fields .
we consider specifically the symmetric coupling of a single - mode cavity field to an ensemble of @xmath0 two - level atoms ( analogous to pseudo - spin-1/2 systems or qubits ) .
the hamiltonian that describes this situation in the interaction picture is given by @xmath1 where the first term is the free energy , with @xmath2 being the detuning of the light field from the atomic transition , and the second term is the reversible atom - field coupling with strength @xmath3 .
the photon annihilation operator is @xmath4 , and @xmath5 and @xmath6 are pauli operators for the @xmath7th spin - component . in the presence of decoherence
, the full quantum evolution is described by the quantum master equation for the reduced density operator @xmath8 : @xmath9+\kappa\mathcal{d}[a]\rho\nonumber\\ & & + \sum_{j=1}^n\left(\gamma\mathcal{d}[\sigma_j^- ] + w\mathcal{d}[\sigma_j^+]+\frac{1}{2t_2 } \mathcal{d}[\sigma_j^3]\right)\rho\,,\end{aligned}\ ] ] where @xmath10\rho=(2\hat{o}\rho \hat{o}^\dagger-\hat{o}^\dagger \hat{o}\rho-\rho \hat{o}^\dagger \hat{o})/2 $ ] denotes the lindblad superoperator .
we have introduced the decay rate @xmath11 for the cavity , and population relaxation rates for the spin components @xmath12 ( for decay and pumping respectively ) and dephasing rate @xmath13 . in general , for all but smallest values of @xmath0 , exact analytic solutions to eq .
( [ eq1 ] ) are intractable , and it is necessary to resort to numerical simulation approaches such as the quantum trajectory method @xcite .
even so , treating more than about ten spins is difficult due to the exponentially increasing dimensionality of the underlying hilbert space ( scaling as @xmath14 ) .
it should be emphasized that the reduced basis of fully - symmetrical dicke states do not suffice to solve the quantum master equation even though the lindblad operator treats the spin - components symmetrically .
as will be shown below , all state vectors with mixed symmetry are in principle required .
recently , it was pointed out that this is not true in liouville space since the lindblad operators are invariant under _
su_(4 ) transformations @xcite .
this observation allows one to express all of the lindblad operators in terms of generators of the _
su_(4 ) group . for this purpose , 18 superoperators @xmath15 , @xmath16 and @xmath17 where
@xmath18 are defined and can be shown to be linear combinations of the 15 gell - mann matrices of the _
su_(4 ) lie algebra ( see supplementary material ) . as a consequence , it is possible to construct a reduced basis for the density operator using a multiplet of the _
su_(4 ) group . transcribing notation from the four - flavor quark model
a model that has the same symmetry structure the fundamental representation is given by @xmath19 , @xmath20 , @xmath21 , and @xmath22 ( up , down , strange , and charm ) . since the symmetry type of the basis is preserved under the action of the _
su_(4 ) generators , this leads to a tremendous reduction of the number of required basis states needed to provide an exact solution of the master equation .
for the fully symmetric case , the basis is : @xmath23 where @xmath24 denotes the symmetrizer and @xmath25 .
note that only basis states with @xmath26 have non - vanishing trace .
the three quantum numbers @xmath27 and @xmath28 have ranges @xmath29 , @xmath30 and @xmath31 , resulting in the dimensionality of the basis @xmath32 , _
i.e. _ of order @xmath33 . this tremendous reduction should be compared with the case in which one does not take advantage of the accessible subspace and instead uses the full dimensionality of the liouville space given by @xmath34 .
note that all the superoperators commute with three associated casimir operators ( analagous to the @xmath35 total spin operator for _
su_(2 ) ) , and this makes it possible to uniquely label the symmetry of the invariant subspace of liouville space in terms of the casimir eigenvalues . in this paper
, we apply the _
su_(4 ) group theory to find exact solutions to the quantum master equation in general form .
we show how to calculate the various basic observables of interest .
we demonstrate that the density matrix in the _
su_(4 ) basis representation can be precisely mapped to the collective spin - angular - momentum representation @xmath36 in hilbert space , which enables us to efficiently diagonalize the density matrix .
this allows us to provide complete information about the system , including functional properties of the density operator such as the purity and von neumann entropy . in order to solve eq .
( [ eq1 ] ) , we expand the density matrix as @xmath37 where @xmath38 are complex coefficients , and @xmath39 is the photon fock state .
the lindblad operators can be written compactly : @xmath40&=&-\frac{n}{2}\pm \mathcal{q}_3+\mathcal{q}_{\pm}\,,\nonumber\\ \sum_{j=1}^n\mathcal{d}[\sigma_j^{(3)}]&=&4\mathcal{m}_3 - 2 \mathcal{q}_3 - 2\sigma_3-n\,.\end{aligned}\ ] ] the completeness of @xmath41 and @xmath4 implies that an arbitrary hamiltonian can be expressed by them , _
e.g. _ from eq .
( [ eq : hamiltonian ] ) , @xmath42&=&-2i\delta\sigma_3\rho - i\omega \left[a(\mathcal{m}_++\mathcal{n}_+)\rho+a^\dagger ( \mathcal{m}_-+\mathcal{n}_-)\rho\right]\nonumber\\ & & \quad{}+i\omega\left[(\mathcal{u}_++\mathcal{v}_+)\rho a^\dagger + ( \mathcal{u}_-+\mathcal{v}_-)\rho a\right]\,.\end{aligned}\ ] ] combining eqs .
( [ liv ] ) and ( [ ham ] ) with the action rules of the _ su_(4 ) and photon operators on the basis states ( see supplementary material ) gives a closed solution of eq .
( [ eq1 ] ) . in general , this can be solved analytically or numerically with standard methods .
having established the procedure for determining the time evolution of @xmath8 , it is now important to describe how to calculate physical observables .
we begin with the trace of the density operator , which is given by @xmath43=\sum_{m , q3}c_{n/2,q3,0}^{m , m}=1\ , , \label{eq : trace}\ ] ] which is an invariant during evolution to represent probability conservation .
average values @xmath44 and @xmath45 are found analogously .
for the spin - operators , we provide the following examples up to quadratic order : @xmath46/n,\\ & \langle\sigma_j^{(3)}\sigma_k^{(3)}\rangle=(4\mathrm{tr } [ ( \mathcal{q}_3 ^ 2-\sigma_3 ^ 2)\rho]-n)/[n(n-1)],\\ & \langle\sigma_j^{\pm}\rangle=\mathrm{tr}[(\mathcal{m}_{\pm } + \mathcal{n}_{\pm})\rho]/n,\\ & \langle\sigma_j^+\sigma_k^-\rangle=\mathrm{tr } [ \mathcal{v}_-(\mathcal{m}_-+\mathcal{n}_-)\rho- \mathcal{q}_-\rho]/[n(n-1 ) ] , \end{split}\ ] ] where @xmath47 .
we do not provide @xmath48 quantities since they follow easily from the basic algebra of the pauli spin - operators . for coherence properties it is necessary to calculate products of operators evaluated at different times . of particular interest
are the first - order and second - order correlations , which can be found by applying the quantum regression theorem : @xmath49\right ] , \nonumber\\ \hspace*{-1pc } \langle\hat{o}_1(t)\hat{o}_1(t\!+\!\tau)\hat{o}_2(t\!+\!\tau ) \hat{o}_2(t)\rangle & = & \mathrm{tr}\left[\hat{o}_2e^{\mathcal{l}\tau } [ \hat{o}_2\rho(t)\hat{o}_1]\hat{o}_1\right],\end{aligned}\ ] ] where @xmath50 $ ] is the time propagation from eq .
( [ eq1 ] ) starting with the initial density matrix @xmath8 .
for example , in order to obtain the first - order correlation of @xmath51 and @xmath52 , one takes @xmath53 as an initial condition , time evolves it for @xmath54 according to eq .
( [ eq1 ] ) , applies @xmath51 , and computes the trace .
a similar procedure follows for the second - order correlation . in this way ,
field quantities , @xmath55 and @xmath56 are directly calculated . for spin - coherence , the required expressions are : @xmath57\right],\nonumber\\ & & \sum_{j , j',k , k'=1}^{n}\langle \sigma_j^+(t)\sigma_{j'}^+ ( t+\tau)\sigma_k^-(t+\tau)\sigma_{k'}^-(t)\rangle=\nonumber\\ & & \qquad\mathrm{tr}\left[\mathcal{v}_-(\mathcal{m}_-+\mathcal{n}_- ) e^{\mathcal{l}\tau}[\mathcal{v}_-(\mathcal{m}_-+\mathcal{n}_-)\rho]\right]\,.\end{aligned}\ ] ] although at this point we have provided a theoretical framework that is complete and provides exact and efficient solutions to the general quantum master equation , it is often inconvenient to work in the @xmath58 representation of the density operator .
for example , it can be a nontrivial procedure to characterize the many - body spin - state in this representation by quantifying the degree of entanglement , which is derived from a functional ( _ i.e. _ @xmath59 $ ] ) .
for this reason , we illustrate now the procedure for efficiently projecting the density operator from the _
su_(4 ) basis representation onto the usual representation of density matrices formed from the hilbert space basis vectors .
these hilbert space basis vectors are specified by the angular momentum eigenket @xmath36 , where @xmath60 is the total spin and @xmath61 is the spin - projection .
note that @xmath62 also labels the symmetry of the states , e.g. @xmath63 corresponds to the fully symmetrical dicke states . in order to illustrate how this projection is done ,
it is instructive for us to first examine explicitly the @xmath64 case where the hilbert space is 4 dimensional .
two spins form a symmetric triplet state and an antisymmetric singlet state , corresponding to total spin @xmath65 and @xmath66 respectively . in this case , the complete density matrix from eq .
( [ ex ] ) for given @xmath67 is @xmath68 notice that the resulting matrix is block diagonal in the @xmath65 and @xmath66 subspaces ( a @xmath69 block and a @xmath70 block ) .
in addition , the complex coefficients contributing to the matrix element for @xmath71 all satisfy @xmath72 and @xmath73 . finally , the trace is simply @xmath74 .
these results can be systematically extended to higher @xmath0 . for any @xmath0 ,
the density matrix is block diagonal in @xmath62 , with each block given by @xmath75 where @xmath76 are density matrix elements for the symmetry type @xmath62 .
there are @xmath77 ways for @xmath0 spins to construct the basis for each @xmath62 , so that @xmath78 , _
i.e. _ the hilbert space dimension . to find @xmath77 , we note that @xmath36 forms a basis of the @xmath79-dimensional irreducible representation of the _
su_(2 ) group .
determining @xmath77 is accomplished with the help of the young tableau of the _
su_(2 ) group , where one can obtain the number of equivalent representations iteratively .
fig .
[ fig1](a ) shows the young tableau for the @xmath80 case . a corresponding tabular method for evaluating @xmath77 for any @xmath0
is shown in fig .
[ fig1](b ) , which contains about one half of the well - known pascal s triangle .
( a ) young tableau for determining the irreducible representations contained in the direct product representation of the _
su_(2 ) group for @xmath80 .
the dimension for @xmath81 is @xmath82 respectively , and @xmath83 , so the total hilbert space dimension is @xmath84 as expected .
( b )
pascal s triangle " to evaluate @xmath77 in an iterative way for any @xmath0 ( the case considered in ( a ) is the fourth row down from the top ) .
( c ) pyramid representation of the density operator in the @xmath36 representation for @xmath80 .
each layer of the pyramid represents the block matrix for each @xmath62 . ] with this in mind , one can now derive a systematic algorithm for obtaining density matrix elements @xmath85 given _
su_(4 ) expansion coefficients @xmath38 . the procedure is outlined as follows . for each layer of the pyramid [ cf .
fig .
[ fig1](c ) ] , one may start with a corner element ( @xmath86 and @xmath87 maximal ) and fill out the matrix by successive application of the angular momentum lowering operator @xmath88 ( noting that @xmath89 ) to recursively fill out each row , and @xmath90 ( or hermiticity of @xmath8 ) to fill out each column .
the layers are filled upwards from the base , starting with @xmath91 as the corner element of the lowest layer , and finding the corner element of higher layers by gaussian elimination from the trace constraint eq .
( [ eq : trace ] ) . in the supplementary materials ,
we demonstrate explicit application to 3 atoms , with extrapolation to higher @xmath0 straightforward .
being able to express the density operator in the @xmath36 representation makes easy the calculation of functionals , such as the purity @xmath92 $ ] , or the von neumann entropy @xmath93 where @xmath94 are eigenvalues of @xmath8 .
the point is that , because the density matrix is block diagonal in the @xmath36 representation , we do not need to diagonalize the whole density matrix , which would be a daunting task .
instead , we only need to diagonalize a series of @xmath95 blocks of dimension @xmath96 . in the following ,
we demonstrate the method by solving many - atom open quantum systems such as lasing and steady state superradiance .
we show the capability for finding exact solutions of large systems and are able to obtain full information about both the transient and steady - state density matrix .
first , let us consider a single - mode laser consisting of an ensemble of two - level atoms coupled to an optical cavity , which can be modeled by the general quantum master equation eq .
( [ eq1 ] ) @xcite . in this model
@xmath3 is the atom - cavity coupling , @xmath11 is the laser output coupling loss , @xmath97 is the incoherent laser pumping , and @xmath98 is the atom decay rate ( we will ignore @xmath99 dephasing in this example for simplicity ) .
the laser system is difficult to solve without approximation since it involves both many atoms and large numbers of photons when above threshold .
therefore , it constitutes an interesting test - case to illustrate the capability of the _
su_(4 ) approach . [ cols="^,^ " , ] fig .
[ fig3](a ) shows the average intracavity photon number of the laser as a function of the repumping rate , where the threshold is evident .
this result confirms the conventional laser theory prediction @xcite .
interestingly , the spin - spin correlation @xmath100 above the threshold is directly proportional to the photon number , which shows that the collective photon emission plays an essential role for the laser . in fig .
[ fig3](b ) , we show that the photon statistics of the laser changes from thermal below threshold to poisson above threshold . in fig .
[ fig3](c ) , we demonstrate that the laser linewidth narrows considerably as one goes above threshold . finally , in fig .
[ fig3](d ) , the laser threshold behavior is characterized by the intensity correlation @xmath101 and the entropy of the whole system .
it can be seen that @xmath101 jumps from two below threshold to one above threshold with the entropy increasing and saturating .
it is remarkable to have an exact solution to this fundamental system that rigorously confirms the standard laser theory results .
those results are based on various kinds of analytic approximations necessary to make the problem tractable .
( color online ) .
comparison of the second order intensity correlation @xmath102 as a function of the repump rate in the steady state superradiance .
the green symbols show the monte carlo results including the statistical errors for @xmath103 atoms from ref .
@xcite .
the red dots show the present calculation using the _
su_(4 ) theory . and the blue solid line shows the semiclassical results from ref .
@xcite .
inset : atom statistics for @xmath104 .
the length of the bars represents populations of the @xmath36 states .
] as a second example , we apply our approach to steady - state superradiance as previously proposed @xcite and demonstrated in a recent experiment @xcite .
the steady - state superradiance represents a novel regime of cavity quantum electrodynamics , where the highly coherent collective atomic dipole induces an extremely narrow linewidth for the generated light .
the bad - cavity mode only plays a role as the source of collective coupling for the atoms and the definition of the spatial mode for the output light @xcite .
the behavior of this system is also described by a master equation eq .
( [ eq1 ] ) , but in a completely different parameter regime to the conventional laser . for steady - state superradiance ,
the vacuum rabi splitting is much less than the cavity linewidth , @xmath105 and equivalently the photon number per atom in the cavity is much less than unity .
we present here calculations of the second order intensity correlation @xmath101 in steady - state as a function of the repump rate . as shown in fig .
[ fig4](a ) , the agreement of the present calculation and the quantum monte carlo result from ref .
@xcite is within error bars .
the quantum monte carlo simulations were of course significantly more numerically intensive . in the weak pumping limit ,
the light exhibits strongly super - poissonian fluctuations and deviates remarkably from the semiclassical prediction ( blue line in fig .
[ fig4](a ) ) .
the failure of the semiclassical prediction in the weak pumping limit indicates that the atoms are in a highly - correlated state . to reveal the atomic states in this case , we apply the techniques of projecting the density operator in the @xmath58 representation onto the @xmath36 representation and obtain the populations of the atoms on @xmath36 states .
the inset of fig .
[ fig4 ] shows explicitly that the atoms are mainly pumped into long - lived collective subradiant states @xcite @xmath106 and @xmath107 . from @xmath106 ,
the atoms can only be repumped to @xmath108 , from which they rapidly emit two photons and relax to @xmath107 . therefore
, our methods enable us to extract detailed information about the atomic states and has been essential to reveal the underlying quantum dynamics . in conclusion ,
we have formulated and applied a _
su_(4 ) theory to numerically solve the quantum master equation , which has reduced the exponential scaling of the problem to cubic in @xmath0 .
we have developed powerful methods to transform the density operator in the _
su_(4 ) basis representation to the @xmath36 representation .
this has enabled us to efficiently diagonalize the whole density matrix and thus provided complete information about the system , including state information and functional properties of the density operator .
we have included lasing and steady - state superradiance as examples in order to illustrate the potential for this method .
the method described here will find numerous applications for simulating open quantum systems with large system size .
we acknowledge stimulating discussions with j. cooper and d. meiser . this work has been supported by the darpa quasar program and the nsf .
99 g. lindblad , commun .
math .
phys . * 48 * , 119 ( 1976 ) . c. w. gardiner and p. zoller , `` quantum noise '' , springer , berlin ( 2004 ) .
j. carmichael , `` statistical methods in quantum optics 1 '' , springer - verlag ( 1998 ) .
h. uys , m. j. biercuk , a. p. vandevender , c. ospelkaus , d. meiser , r. ozeri , and j. j. bollinger , phys .
rev .
lett . * 105 * , 200401 ( 2010 ) .
a. blais , j. gambetta , a. wallraff , d. i. schuster , s. m. girvin , m. h. devoret , and r. j. schoelkopf , phys .
rev .
a * 75 * , 032329 ( 2007 ) .
j. d. teufel _ et .
al . _
nature * 475 * , 359 ( 2011 ) .
m. b. plenio and p. l. knight , rev .
mod .
phys .
* 70 * , 101 ( 1998 ) .
s. hartmann , arxiv:1201.1732v1 .
d. meiser , j. ye , d. r. carlson , and m. j. holland , phys .
rev .
lett . *
102 * , 163601 ( 2009 ) .
j. g. bohnet , z. chen , j. m. weiner , d. meiser , m. j. holland , and j. k. thompson , nature * 484 * , 78 ( 2012 ) .
d. meiser and m. j. holland , phys .
rev .
a * 81 * , 063827 ( 2010 ) .
r. h. dicke , phys . rev . * 93 * , 99 ( 1954 ) .
* supplementary material for + simulating open quantum systems using the simple lie group _
su_(4 ) * |
recent calculations in quenched qcd at light valence quark mass have been refined to sufficient accuracy to allow detailed comparison with the predictions of quenched chiral perturbation theory @xcite .
the identification of quenched chiral loop effects in lattice data serves several purposes .
it allows one to perform sensible chiral extrapolations of quenched data and to extract the parameters of the qcd chiral lagrangian in the quenched approximation .
it also provides a standard of comparison for future studies of chiral behavior in full and partially quenched qcd , which will be crucial for obtaining complete control over chiral extrapolations in full qcd .
in particular , the study of quenched chiral loop ( qcl ) effects has identified several quantities for which the effects of quenching are clearly observable in the lattice data and in detailed agreeement with quenched chiral perturbation theory .
these quantities should be particularly useful in studying the transition from quenched to full qcd via partially quenched calculations .
the most striking of the observed qcl effects appears in the scalar , isovector ( valence or `` connected '' ) meson propagator which i will discuss in this talk .
the spectroscopy of scalar mesons is somewhat complicated phenomenologically . in a nonrelativistic quark - model framework ,
the lowest lying scalars are p - wave triplet states and would be expected to be substantially heavier than the lowest vector and pseudoscalar mesons , which are s - wave .
however , the experimental situation is somewhat unclear .
there is an @xmath2 state at 980 mev , but this is very close to the @xmath3 threshold , and may be a 4-quark state ( @xmath3 `` molecule '' ) .
the next @xmath2 meson is at 1474 mev .
there is also a strange scalar @xmath4 at 1412 mev . our data for the scalar isovector propagator exhibits not only the negative @xmath0-@xmath1 qcl effect , but also clear evidence of a positive short - range component corresponding to a heavy @xmath2 state .
fitting the data to a chiral lagrangian which includes a heavy scalar field , as discussed in section 3 , we obtain a chirally extrapolated scalar meson mass of @xmath5 mev ( statistical errors only ) .
further studies are required to estimate lattice - spacing and quenching effects , but the result appears to favor the 4-quark interpretation of the @xmath6 , with the states in the 1400 - 1500 mev range being the lowest - lying scalar @xmath7 states .
while most other qcl effects amount to relatively small modifications of full qcd behavior even at the lightest quark masses studied , the effect of quenching on the scalar isovector propagator is striking .
this effect arises from the @xmath0-@xmath1 intermediate state via the chiral loop graph depicted in fig .
1 . not only
does this graph dominate the entire propagator at small quark mass and large time separations , but the overall sign of the effect is _ negative _ i.e. opposite to that required by spectral positivity .
( this arises from a two ghost - meson state in the ghost - quark formulation of quenched @xmath8 . )
most of the results presented here were obtained from an ensemble of 300 gauge configurations on a @xmath9 lattice at @xmath10 , using clover - improved fermions with @xmath11 .
the mqa pole - shifting ansatz was used to resolve the exceptional configuration problem .
nine quark masses were used , corresponding to pion masses ranging from about 280 @xmath12 to 710 @xmath12 .
the qcl effect in the scalar isovector channel is clearly visible in the bizarre mass dependence of the raw lattice propagator . in fig .
2 we show this propagator for the heaviest and lightest quark masses studied . for the heavier quarks ,
the correlator is positive and exponentially falling , as would be expected for a heavy scalar meson state of mass @xmath13-@xmath14 gev
. the correlator completely changes character as the quark mass becomes small , developing a negative long - range component .
this component is convincingly explained as the effect of the @xmath0-@xmath1 chiral loop diagram in fig .
1 . the solid curve in fig .
2 is the _ zero parameter _ prediction of one - loop chiral perturbation theory , which uses only parameters obtained from previous chiral analysis of the pseudoscalar propagator .
define the one - loop bubble integral , fig . 1
, in momentum space @xmath15 where @xmath16 is the @xmath0 mass insertion , which has been determined @xcite by studying the pseudoscalar hairpin correlator ( @xmath17 in lattice units at @xmath10 ) .
the quenched scalar propagator is dominated by the @xmath0-@xmath1 intermediated state and given by @xmath18 where @xmath19 is the @xmath20 to @xmath21 coupling constant . in a chiral lagrangian framework ,
this coupling is not independently adjustable , but is determined by the slope parameter@xcite @xmath22 the constant @xmath19 is related to @xmath23 by a soft pion theorem : @xmath24 the excellent agreement between the long - range correlator and the @xmath8 prediction exhibited in fig .
2 shows that this soft pion theorem is quite well satisfied .
it is interesting to note that , with @xmath19 fixed by current algebra , the overall size of the one - loop qcl effect in the scalar propagator is determined by the @xmath0 mass insertion @xmath25 .
if we take this as a fit parameter , we obtain @xmath26 .
this is nearly as good a determination of the @xmath0 mass parameter as the one obtained directly from the hairpin correlator .
a full chiral lagrangian description of the lattice data for the scalar isovector propagator requires the incorporation of a heavy scalar field into the lagrangian .
the formalism of nonlinear chiral lagrangians @xcite allows the incorporation of heavy fields which only have specified transformation properties under the unbroken vector subgroup of the chiral group . to first order in symmetry breaking and ignoring derivative coupling terms , the relevant chiral lagrangian terms are @xmath27 where the last term is the anomaly - induced hairpin mass insertion , @xmath28
^ 2\ ] ] the values of @xmath29 and @xmath16 have been determined by analysis of the pseudoscalar valence and hairpin correlators .
we are interested in the correlator for a flavor nonsinglet quark bilinear @xmath30 .
this operator is related to the chiral lagrangian fields via the dependence of l on the spurion field @xmath31 .
this implies that the quark bilinear consists of two terms , which describe its coupling to the @xmath0-@xmath1 and scalar meson states , respectively , @xmath32 using this chiral lagrangian analysis , a resummed - bubble expression for the @xmath33 correlator was derived and used to fit the lattice correlator @xcite .
the scalar meson parameters obtained for @xmath10 are , in lattice units , in the chiral limit @xmath34 fits of the data to the resummed bubble expression for several quark masses are shown in fig .
3 . it is particularly significant that , over the entire range of quark masses , the fit parameters @xmath35 and @xmath36 show very little mass dependence , indicating that the dramatic mass dependence of the data is almost entirely explained by the change of the pion mass in the chiral loop integral .
9 w. bardeen , a. duncan , e. eichten , and h. thacker , phys .
d62:114505 ( 2000 ) .
w. bardeen , a. duncan , e. eichten , n. isgur , and h. thacker , phys .
d ( to be published ) s. weinberg , phys .
166:1568 ( 1968 ) . | the scalar isovector meson propagator is studied in quenched qcd . for the lightest quark masses
used , this propagator is dominated by a quenched chiral loop effect associated with the @xmath0-@xmath1 two - meson intermediate state . both the time dependence and the pion mass dependence of the effect are well - described by quenched chiral perturbation theory . |
the @xmath75 tridiagonal matrix @xmath71 has the following non - zero matrix elements : @xmath83 , @xmath73 for @xmath84 .
@xmath74 is tunable and @xmath85 is fixed .
the eigenvalues and eigenvectors of @xmath71 have the following properties .
+ let @xmath86 be all the eigenvalues of matrix @xmath71 , then @xmath87 .
it is easy to verify that @xmath88 , @xmath89 , and the relation @xmath90 .
therefore , one has @xmath91 and @xmath92 ( @xmath93 ) .
when @xmath1 is odd , @xmath94 , which means that at least one eigenvalue equals to zero regardless the values of @xmath74 and @xmath10 .
for the zero eigenvalue , the eigen - equation is @xmath95 , where @xmath96 . when expanded , the equation is turned into the following equations : @xmath97 there is only one non - trivial solution . for @xmath98 ,
it is given by @xmath99 with @xmath100 , @xmath101 , and @xmath102 where @xmath103 and @xmath104 is the normalization factor .
for @xmath105 , the solution is @xmath106 .
this shows matrix @xmath71 has one and only one eigenvalue equal to zero . + if @xmath107 , when @xmath1 is even , then @xmath108 .
thus all the eigenvalues of the matrix @xmath71 are nonzero .
when @xmath76 , it is obvious that @xmath109 .
there are zero eigenvalues . with @xmath76 , the tridiagonal matrix of @xmath71
is divided into two uncoupled subspaces , i.e. , @xmath110 , where @xmath111 is a tridiagonal matrix with nonzero elements @xmath112 .
it is clear that @xmath111 possesses property 1 and has only one zero eigenvalue .
@xmath71 thus has two zero eigenvalues .
when @xmath1 is odd , for the eigenvector @xmath78 of @xmath71 belonging to @xmath124 , the inequality @xmath125 holds for a finite range of parameters ; for an eigenvector @xmath78 of @xmath71 belonging to @xmath126 , one has that @xmath127 , whether @xmath1 is odd or even . according to eq.([ev ] ) , it is clear that the inequality @xmath79 is valid only when @xmath128 .
+ when @xmath126 , the two eigenvalues @xmath113 and @xmath114 are distinct and the corresponding eigenvectors are orthogonal to each other . with property 3 ,
one has @xmath129 when @xmath1 is odd ; @xmath130 when @xmath1 is even . with the normalization condition
@xmath131 , we immediately obtain that @xmath132 . c. brif , r. chakrabarti1 , and h. rabitz , new j. phys .
* 12 * , 075008(2010 ) .
t. salger , s. kling , t. king , c. geckeler , l. m. molina , and m. weitz , science * 326 * , 1241 ( 2009 ) .
m. grifoni , and p.hnggi , phys . rep . *
304 * , 229(1998 ) .
f. grossmann , t. dittrich , p. jung , and p. hanggi , phys .
lett . * 67 * , 516 ( 1991 ) ; z. phys .
b * 84 * , 315 ( 1991 ) .
d. h. dunlap and v. m. kenkre , phys .
b * 34 * , 3625 ( 1986 ) .
m. holthaus , phys .
lett . * 69 * , 351 ( 1992 ) ; m. holthaus and d. hone , phys .
b * 47 * , 6499 ( 1993 ) . c. e. creffield , phys . rev .
99 * , 110501 ( 2007 ) .
j. gong , d. poletti , and p. hanggi , phys .
a * 75 * , 033602(2007 ) .
x. luo , j. huang and c. lee , phys .
a * 84 * , 053847(2011 ) .
s. longhi , phys .
a * 71 * , 065801(2005 ) ; s. longhi and g. della valle , phys . rev .
a * 86 * , 042104(2012 )
. j. m. villas - bas , s. e. ulloa , and n. studart , phys .
b * 70 * , 041302(r ) ( 2004 ) .
j. t. stockburger , phys .
e * 59 * , r4709 ( 1999 ) .
x. luo , q. xie , and b. wu , phys .
a * 76 * , 051802(r)(2007 ) .
j. gong , l. morales - molina , and p. hnggi , phys .
* 103 * , 133002 ( 2009 ) .
s. longhi , phys .
a * 83 * , 034102 ( 2011 ) ; s. longhi , phys . rev .
a * 86 * , 044102(2012 ) . c. e. creffield and t. s. monteiro , phys
lett . * 96 * , 210403 ( 2006 ) ; c. e. creffield , phys . rev .
a * 75 * , 031607(r ) ( 2007 ) .
a. eckardt , c. weiss , and m. holthaus , phys .
lett . * 95 * , 260404 ( 2005 ) ; a. eckardt and m. holthaus , phys .
* 101 * , 245302 ( 2008 ) .
y. kayanuma and k. saito , phys .
a * 77 * , 010101(r)(2008 ) .
g. della valle , m. ornigotti , e. cianci , v. foglietti , p. laporta and s. longhi , phys .
lett . * 98 * , 263601 ( 2007 ) .
e. kierig , u. schnorrberger , a. schietinger , j. tomkovic , and m. k. oberthaler , phys .
lett . * 100 * , 190405 ( 2008 ) .
j. zhou , p. huang , q. zhang , z.wang , t. tan , x. xu , f. shi , x. rong , s. ashhab , j. du , arxiv:1305.0157 .
h. lignier , c. sias , d. ciampini , y. singh , a. zenesini , o. morsch , and e. arimondo , phys .
rev . lett . * 99 * , 220403 ( 2007 ) .
a. eckardt , m. holthaus , h. lignier , a. zenesini , d. ciampini , o. morsch , and e. arimondo , phys .
rev . a * 79 * , 013611 ( 2009 ) .
k. bergmann , h. theuer , and b. w. shore , rev .
mod . phys . * 70 * , 1003 ( 1998 ) .
i. l. garanovich , s. longhi , a. a. sukhorukov , and y. s. kivshar , phys . rep .
* 518 * , 1 ( 2012 )
. s. longhi , laser and photon . rev . * 3 * , 243 ( 2008 ) .
a. szameit , y. v. kartashov , m. heinrich , f. dreisow , r. keil , s. nolte a. tnnermann , v. a. vysloukh , f. lederer , and l. torner , opt lett . * 34 * , 2700 ( 2009 ) .
a. szameit , y. v. kartashov , f. dreisow , m. heinrich , t. pertsch , s. nolte , a. tnnermann , v. a. vysloukh , f. lederer , and l. torner , phys .
lett . * 102 * , 153901 ( 2009 ) . | we study a system of three coherently coupled states , where one state is shifted periodically against the other two .
we discover such a system possesses a dark floquet state at zero quasi - energy and always with negligible population at the intermediate state .
this dark floquet state manifests itself dynamically in terms of the suppression of inter - state tunneling , a phenomenon known as coherent destruction of tunneling .
we suggest to call it dark coherent destruction of tunneling ( dcdt ) . at high frequency limit for the periodic driving
, this floquet state reduces to the well - known dark state widely used for stirap .
our results can be generalized to systems with more states and can be verified with easily implemented experiments within current technologies .
two - state and three - state models are the simplest quantum systems . despite their simplicity
, they often provide very good approximations to describe realistic physical systems and are capable of revealing a variety of fascinating quantum effects .
the understanding of their ubiquitous features are nowadays being exploited for the manipulation and control of quantum states of small systems involving single atoms , photons , or nano - devices @xcite .
coherent destruction of tunneling ( two - state models ) and dark state ( three - state models ) are two of the elegant prototype examples where deep understanding gained from quantum coherent effects in these simple systems are impacting the development of quantum technology in communication and computation
. coherent destruction of tunneling ( cdt ) was discovered in a periodically - driving double well system @xcite .
it describes a fascinating phenomenon whereby coherent tunneling between two wells ( or the rabi oscillation between two states ) is turned off by an externally enforced periodic level shift .
its understanding is related to dynamical localization @xcite , which occurs at isolated degenerate points of the quasienergies @xcite .
cdt has thus far generated significant interest , and has been theoretically extended into various forms @xcite-@xcite .
it has also been observed experimentally in many physical systems : including modulated optical coupler @xcite , driven double - well potentials for single - particle tunneling @xcite , and a single electron spin in diamond @xcite .
more recently , it has also found application in tuning the tunneling parameter of a bose - einstein condensate @xcite .
dark state is often discussed in terms of a three - state system where two of them are coupled coherently to the intermediate state , as in the model system we study here .
when all coupling fields are on resonance with their respective coupled pair of states , we can adopt the rotating wave approximation and change into a suitable interaction picture with all coupling coefficients becoming time independent . in this case
, there always exists a dark state , whose eigenenergy becomes uniformly zero , and the corresponding eigenvector contains no projection onto the intermediate state .
it is called dark as the intermediate state is an excited state capable of emitting photons .
this type of dark state is also known as coherent population trapping @xcite , widely used in efficient population transfer through the stimulated raman adiabatic passage ( stirap ) protocol .
it has become the theoretical basis for several well - established implementations of quantum control and rudimentary quantum information processing gates . in this letter
we report our surprising finding of an intimate relationship between dark state and coherent destruction of tunneling by studying a three - state system . in this system ,
two states are coherently coupled to an intermediate state and one of the two states shifts periodically against the other two .
we find that cdt also exists in this three - state system , where the dynamical tunneling from one state to the other two is suppressed by the periodic driving over a range of parameters .
however , this cdt for the three - state system has its own distinct feature : it is related to a dark floquet state , which has zero quasi - energy and negligible population at the the intermediate state . quite interestingly
, this dark floquet state reduces to the well - known dark state in a non - driving three - state @xmath0-system@xcite at high - frequency limit .
therefore , we call this cdt _ dark coherent destruction of tunneling_(dcdt )
. these results can be generalized to @xmath1-state system .
we also discuss a feasible experimental scheme where the visualization of the dcdt can be achieved readily .
_ three - state system .
_ the driving three - state system is described by the schrdinger equation ( @xmath2 ) @xmath3 where @xmath4 , @xmath5 , and @xmath6 are the amplitudes at three states @xmath7 , @xmath8 , and @xmath9 , respectively .
@xmath10 is the coupling constant between the neighboring states .
energy state @xmath7 is shifted periodically against the other two with driving strength @xmath11 and frequency @xmath12 .
the normalization condition @xmath13 is assumed . to investigate the tunneling dynamics , we solve the time - dependent schrdinger equation ( [ coupled ] ) numerically with initial state @xmath14 .
the evolution of the probability distribution @xmath15 is presented in fig . [ fig1 ] for three typical driving conditions .
for @xmath16 ( fig .
[ fig1 ] ( a ) ) , we see that @xmath17 oscillates between zero and one , demonstrating no suppression of tunneling . for @xmath18 ( fig .
[ fig1 ] ( b ) ) , the oscillations of @xmath17 are seen limited between 0.8 and 1 , showing suppression of tunneling . at @xmath19 ( fig . [ fig1 ] ( c ) ) , @xmath17 remains near unity , signaling a complete suppression of tunneling between energy states .
this is the quantum phenomenon well known as cdt @xcite .
we emphasize that what we find here is not a simple re - discovery of cdt in a three - state system .
the cdt in this three - state model has its own distinct feature : the results shown in fig .
[ fig1 ] ( b , c ) indicate that the suppression of tunneling occurs over a wide range of system parameters .
this is in stark contrast to the cdt in a two - state system @xcite , which occurs only at isolated points of parameters .
the widening of the suppression regime found in the driving three - state system is more clearly demonstrated in fig .
[ fig1 ] ( d ) , where the minimum value of @xmath17 is used to measure the suppression of tunneling .
when ( @xmath17 ) is not zero , the tunneling is suppressed as the population is not allowed to be fully transferred from state @xmath7 to the other two states .
it is clear from fig .
[ fig1 ] ( d ) that the suppression occurs as long as @xmath20 . for comparison , the results for the standard driven two - state system is plotted as dash dotted line in fig . [ fig1 ] ( d ) , where the extremely narrow peak width indicates that cdt occurs only at isolated points of parameters .
@xmath15 for the system ( [ coupled ] ) for various driving conditions : ( a ) @xmath16 ; ( b ) @xmath18 ; ( c ) @xmath19 .
( d ) the minimum value of @xmath17 ( solid line ) as a function of driving parameter @xmath21 .
the two - state results are plotted as a dash dotted line for comparison .
the initial condition is @xmath22 .
the other parameters are @xmath23.,width=302 ] there exists a fundamental reason why the cdt occurs at isolated system parameters in a two - state model , where the cdt is related to the degeneracy of quasi - energy levels @xcite and the degeneracy usually happens only at isolated points .
therefore , the significant widening of the suppression parameter range that we see in fig . [ fig1 ] indicates that the cdt found here should have a different origin . to investigate this origin
, we turn to the floquet theory for a periodically - driving system .
similar to bloch states for systems with spatially periodic potentials , the modulated system ( [ coupled ] ) has floquet states , @xmath24 , where @xmath25 is the quasi - energy and the amplitudes @xmath26 are periodic with modulation period @xmath27 . our numerical results of the quasi - energies and floquet states for the modulated system ( [ coupled ] )
are plotted in fig .
[ fig2 ] .
there are three floquet states with quasi - energies @xmath28 , @xmath29 , and @xmath30 .
we immediately notice from fig .
[ fig2](a ) that the quasi - energy @xmath29 for the second floquet state is always _ zero _ for all values of @xmath21 .
we call this state _ dark floquet state _ in analogy to the well - known dark state .
this dark floquet state stands out not only for its zero quasi - energy but also for its unique population distribution among energy states .
we display the time - averaged population probability @xmath31 for a given floquet state @xmath32 in fig .
[ fig2](b - d ) .
the floquet state with @xmath33-th energy state . as seen in fig .
[ fig2](c ) , the dark floquet state has almost zero population at energy state @xmath8 while the population at @xmath7 @xmath34 .
in other words , the dark floquet state is localized at @xmath7 .
the other two floquet states have identical population distribution . since all their populations @xmath35 , these two floquet states are _ not _ localized . .
solid lines are for numerical results obtained from the original model ( [ coupled ] ) and circles are for the approximation results given by the effective model ( [ eq : ceff ] ) .
time - averaged populations for the floquet state in the quasi - energy level ( b ) @xmath28 , ( c ) @xmath29 , and ( d ) @xmath30 .
the other parameters are @xmath36.,width=302 ] it is not difficult to see the suppression of tunneling seen in fig .
[ fig1 ] is linked to the existence of the dark floquet state .
we expand the initial state in terms of the floquet states @xmath37 during the dynamical evolution , the expansion coefficient @xmath38 evolve as @xmath39 .
in other words , @xmath40s are time independent .
we look at the case @xmath19 , where @xmath41 has population one at state @xmath7 while the other two states have zero population at @xmath7 . in this case
, we have @xmath42 and @xmath43 , which corresponds to a complete suppression of tunneling from @xmath7 to @xmath8 and @xmath9 . for other values of @xmath21 ,
similar arguments can be made .
this shows that the cdt observed in fig .
[ fig1 ] has a different origin : it is the consequence of dark floquet states .
therefore , we call it _ dark coherent destruction of tunneling _ ( dcdt ) .
interestingly , this dark floquet state can be reduced to the well known dark state in a non - driven three - state @xmath0-system at high frequency limit . introducing the transformation
@xmath44 $ ] ( @xmath45 for @xmath46 and @xmath47 for @xmath48 ) and averaging out high frequency terms , one can obtain a non - driven three - state system @xmath49 where @xmath50 is the zeroth order bessel function . the famous dark state ( also known as coherent trapped state ) for eq .
( [ eq : ceff ] ) is given by @xmath51 , where @xmath52 ^ 2 $ ] .
this dark state corresponds to the dark floquet state .
similarly , this dark state is always localized at state @xmath7 as @xmath53 and has zero population at state @xmath8 .
this state is completely localized at state @xmath7 when @xmath54 .
we have computed the the eigenvalues of model ( [ eq : ceff ] ) and compared them ( circles ) with the quasi - energies ( black solid lines ) in fig .
[ fig2 ] ( a ) .
the agreement is almost perfect .
_ generalization to @xmath1-state system .
_ our analysis above is given for a three - state system and the original cdt was found in a two - state system .
these results can be generalized to an @xmath1-state system , where one state is shifted periodically against all the other states .
the equations of motion are @xmath55 where @xmath56 . as a function of @xmath21 for @xmath57 ( dash dotted line ) and @xmath58 ( solid line ) .
the initial conditions are @xmath59 .
quasi - energies versus @xmath21 for ( b ) @xmath57 and ( c ) @xmath58 .
solid lines are for numerical results obtained from the model ( [ coupledn ] ) and circles are for the approximation results given by the effective model ( [ effective ] ) .
( d ) the time - averaged probability distribution of the floquet state corresponding to @xmath60 in fig .
[ fig3 ] ( c ) .
the other parameters are @xmath36.,width=302 ] the quantum dynamics of the driven @xmath1-state systems is investigated by direct integration of the time - dependent schrdinger equation ( [ coupledn ] ) with the state initially prepared on the state @xmath7 .
the cdt is found to exist .
the minimum value of @xmath15 as a function of @xmath21 is presented in fig .
[ fig3 ] ( a ) for @xmath57 and @xmath58 .
when @xmath57 , the cdt occurs at an isolated point of parameters ( dash dotted line in fig .
[ fig3 ] ( a ) ) , where two of the four quasi - energy levels become degenerate ( fig .
[ fig3 ] ( b ) ) .
this is exactly the same as in the two - state system . when @xmath58 , the parameter range where cdt occurs is extended substantially ( solid line in fig .
[ fig3 ] ( a ) ) as in the three - state model .
furthermore , this five - state system also has a dark floquet state : as seen in fig .
[ fig3 ] ( c ) , one of the quasi - energies always equals to zero .
this dark floquet state has negligible population at all of even @xmath61-th states ( fig .
[ fig3 ] ( d ) ) .
these numerical results with @xmath62 , together with the known results for @xmath63 , clearly suggest that ( _ i _ ) the dark state and the associated dcdt exist in odd @xmath1-state systems ; ( _ ii _ ) the original cdt , which occurs at isolated parameter points , exists in all even-@xmath1-state system .
this general conclusion can be proved analytically at high frequency limit . following the procedure used in the three - state system , we introduce the transformation @xmath64 $ ] , @xmath65 $ ] , where @xmath66 are slowly varying functions . using the expansion @xmath67=\sum_k(\pm
i)^k j_k ( a/\omega)\exp(\pm ik \omega t)$ ] in terms of bessel functions and neglecting all orders except @xmath68 for high frequency limit , we can reduce the coupled equations ( [ coupledn ] ) to a non - driven model @xmath69 where @xmath70 .
the matrix @xmath71 is tridiagonal with @xmath72 , @xmath73 .
the effective coupling constant @xmath74 between state @xmath7 and state @xmath8 is tunable with the driving parameters .
the eigenvalues and eigenvectors of the tridiagonal @xmath75 matrix @xmath71 enjoy some very interesting properties , whose rigorous proofs can be found in supplemental material .
\(a ) _ when @xmath1 is even , for any nonzero @xmath74 and @xmath10 , all the eigenvalues of the matrix @xmath71 are nonzero while two of the eigenvalues are zero for @xmath76 .
_ _ remark _ : this means that when @xmath1 is even , two quasi - energy levels of the driven model ( [ coupledn ] ) are degenerate at isolated points where @xmath77 .
the cdt occurs at these isolated points .
\(b ) _ when @xmath1 is odd , one and only one eigenvalue of @xmath71 always equals to zero and , for the corresponding eigenvector @xmath78 of @xmath71 , the inequality @xmath79 holds for a finite range of parameters ; for any other eigenvector @xmath78 of @xmath71 , one has @xmath80 .
_ _ remark _ : when @xmath1 is odd , the system always has one and only one dark floquet state , which is localized over a finite range of parameters . correspondingly , dcdt occurs over a finite range of parameters . _
experimental observation .
_ by mapping the temporal evolution of quantum systems into the spatial propagations of light waves , the engineered waveguides have provided an ideal platform to investigate a wide variety of coherent quantum effects@xcite .
the phenomenon of dcdt can also be observed with this kind of waveguide system .
the discrete model ( [ coupledn ] ) can be simulated by the light propagation in an array of @xmath1 waveguides placed closely and with equal spacing .
periodic driving is realized by the harmonic modulation of the refractive index of the waveguides along the propagation direction@xcite . for our system ,
the periodic modulation of the first waveguide has a phase difference of @xmath81 against the modulations for all other @xmath82 waveguides .
when @xmath1 is odd , the dcdt can be readily observed with current experimental capacity@xcite . in summary , we find that the cdt also happens in a three - state quantum system , where one energy state is shifted periodically against the other two states .
we call this type of cdt dark coherent destruction of tunneling ( dcdt ) as it is related to the existence of a dark floquet state in the three - state system
. the dark floquet state has zero quasi - energy and negligible population at the intermediate state .
it reduces to the well known dark state of a non - driven three - state system .
these results can be generalized to a periodically driven @xmath1-state system .
we have also pointed out that observation of dcdt is well within the capacity of current experiments .
this work is funded by the nsf of china ( 10965001 , 11165009 ) , the nsf of jiangxi province ( 2010gqw0033 ) , the jiangxi young scientists training plan ( 20112bcb23024 ) , the financial support provided by the key subject of atomic and molecular physics in jiangxi province and zhengzhou mbost ( 20120409 ) .
b. w. is supported by the nbrp of china ( 2012cb921300,2013cb921900 ) , the nsf of china ( 11274024 ) , the rfdp of china ( 20110001110091 )
. l. y. is supported by the nsf of china ( 11004116 ) and by most 2013cb922000 of the national key basic research program of china . |
heavy fermion ( hf ) compounds with elements from the lanthanide or actinide series share some rather general features in the fermi liquid phase , namely a strong enhancement of the effective carrier mass and a similarly enhanced pauli susceptibility with a wilson ratio typically of the order , but larger than one @xcite .
in addition to this well - understood fermi liquid phase @xcite , hf systems also exhibit a variety of phase transitions , among them magnetic and superconducting phases .
this aroused the strong interest of both experimentalists and theorists , as @xmath0-electrons conventionally tend to suppress superconductivity .
the discovery of quantum critical phenomena @xcite eventually showed the intimate link between the latter two . in spite of the rather large collection of experimental results ,
an accepted theoretical description of superconductivity has not yet been established . moreover ,
the role of phonons on the low - energy properties of hf compounds and in particular their relevance for a microscopic theory of superconductivity in hf systems has not yet been addressed in detail @xcite .
we present the first results of a study of the kondo lattice model with an effective attractive interaction among the conduction electrons .
the latter can be thought to be obtained from an optical phonon mode treated in the antiadiabatic limit ( a more realistic description employing a true optical phonon in the calculation is the subject of ongoing investigations ) .
our model is thus @xmath1 where @xmath2 annihilates ( creates ) a conduction electron at lattice site @xmath3 with spin @xmath4 , @xmath5 is the effective interaction between conduction electrons , and @xmath6 the kondo exchange .
note that in our notation antiferromagnetic coupling means @xmath7 .
finally , @xmath8 denotes the vector of pauli spin matrices .
we solve the model with dynamical mean - field theory ( dmft ) @xcite and wilson s numerical renormalization group ( nrg ) @xcite .
calculations were performed for a bethe lattice with infinite coordination number . in order to study superconductivity we allow for a corresponding symmetry broken phase @xcite .
note that we can not include unconventional order parameters here , as dmft only allows for @xmath9-wave phases @xcite .
) at half filling with @xmath10 at @xmath11 .
right : low - energy scale obtained from the width of the gap in the attractive case @xmath12 for @xmath10 .
the inset shows the different gaps for small repulsive and attractive @xmath5 . ,
title="fig:",scaledwidth=65.0% ] ) at half filling with @xmath10 at @xmath11 .
right : low - energy scale obtained from the width of the gap in the attractive case @xmath12 for @xmath10 .
the inset shows the different gaps for small repulsive and attractive @xmath5 .
, title="fig:",scaledwidth=33.0% ] it is necessary to stress that the model ( [ eq:1 ] ) does not show the usual symmetry @xmath13 under simultaneous exchange of spin and charge , i.e. its physics can not be inferred from the corresponding magnetic properties of the model with repulsive interaction . in fig .
[ fig:1 ] we compare the two cases @xmath14 and @xmath12 .
superficially , for weak interaction @xmath15 , both seem to be rather similar
. however , as is evident from the inset to the right part and the behavior for larger interaction the insulator is much stronger for repulsive @xmath5 .
it here originates from the formation of a local spin singlet rather than being of mott - hubbard type @xcite . for attractive @xmath12 ,
on the other hand , we find that kondo screening is strongly suppressed and the system eventually recovers mott - hubbard physics in the charge sector for large @xmath16 .
this difference can be easily understood . for attractive @xmath5 the conduction system
namely experiences strong correlations in the charge sector , while the kondo exchange tries to develop such feature in the spin sector . obviously , when @xmath17 , where @xmath18 is the kondo scale for @xmath19 , spin fluctuations will efficiently be suppressed , leading to the observed behaviour .
the suppression of the kondo scale is actually stronger than exponential , as shown in the right part of fig .
[ fig:1 ] . from these results
we draw two conclusions : 1 ) phonons are clearly extremely important even to the paramagnetic phase of the kondo model and thus to properly account for the low - energy scale of hf systems ; 2 ) as the low - energy scale is efficiently reduced by an attractive interaction among the conduction electrons , we expect that @xmath9-wave superconductivity will actually prevail in a large part of the phase diagram , in particular for small kondo coupling @xmath6 . in order to allow the system to show superconductivity
, we have to reformulate the dmft equations in nambu space and extend the nrg accordingly .
the latter has been accomplished some time ago already ( for a review see and references therein ; the actual way to combine dmft and nrg has been extensively discussed by bauer @xcite ) . for ( a ) @xmath20 , ( b ) @xmath21 and ( c ) @xmath22 .
, scaledwidth=65.0% ] for a very small kondo exchange interaction @xmath23 , the ground state of the model is dominated by superconductivity .
this becomes apparent from fig .
[ fig:3 ] , where the dos ( upper panels ) and the real part of the anomalous green s function ( lower panels ) is shown at half filling ( full curves ) as well as at finite filling @xmath24 ( dashed curves ) . as the low - energy scale of the model with @xmath19 is always largest at half filling @xcite , we can expect that this result remains stable for all fillings @xmath25 .
note that in none of the cases one does observe a significant dependence of the gap on the fillings , i.e. local correlations due to kondo screening are frozen out here since @xmath26 .
furthermore , @xmath27 and consequently one expects and observes a bcs like gap structure , only weakly smeared out by self - energy broadening . and
( a ) @xmath28 , ( b ) @xmath29 and ( c ) @xmath30.,scaledwidth=65.0% ] increasing @xmath31 has two effects .
first , there appears a finite , critical @xmath32 below which no superconducting solution exists .
this can be seen in fig .
[ fig:4]a , where dos and real part of the anomalous green s function are shown for @xmath33 and a small @xmath28 .
note that at half filling we find a kondo insulator , which has a gap in the dos . from that perspective
the result is actually indistinguishable from the superconducting phase .
the anomalous part , however , vanishes here , i.e. we have indeed a normal state and thus an insulator . for larger interactions
, the superconducting phase reappears .
compared to the case with small @xmath6 , we observe here visible reduction of the gap and also a broadening of the singularities at the gap edges .
we attribute this behavior to the correlations induced by the kondo exchange .
we have studied the kondo lattice model with an attractive interaction between the conduction electrons , which may arise in the presence of phonons , notably optical modes like breathing modes .
we found a tremendous effect of an attractive interaction on the low - energy scale , drastically reducing it already for comparatively modest @xmath16 .
this behavior can be understood in terms of a competition between a spin kondo effect and the charge fluctuations introduced by the attractive @xmath5 .
as the latter also favour superconductivity we can expect , and indeed do find , that for experimentally relevant values of the kondo coupling and interaction parameters the model shows an @xmath9-wave type superconducting ground state . for real systems
this underlines the importance of elastic degrees of freedom for a proper description of the physics of hf materials . | we study the kondo lattice model with additional attractive interaction between the conduction electrons within the dynamical mean - field theory using the numerical renormalization group to solve the effective quantum impurity problem .
in addition to normal - state and magnetic phases we also allow for the occurrence of a superconducting phase . in the normal phase we observe a very sensitive dependence of the low - energy scale on the conduction - electron interaction .
we discuss the dependence of the superconducting transition on the interplay between attractive interaction and kondo exchange . |
the equation of motion for a supernova remnant ( snr ) can be modeled by a single law of motion or multiple laws of motion when the appropriate boundary conditions are provided .
examples of a single law of motion are : the sedov expansion in the presence of a circumstellar medium ( csm ) with constant density where the radius , @xmath2 , scales as @xmath3 , see @xcite , and the momentum conservation in the framework of the thin layer approximation with csm at constant density where @xmath4 , see @xcite .
examples of piece - wise solutions for an snr can be found in @xcite : a first energy conserving phase , @xmath3 followed by a second adiabatic phase where @xmath5 . at the same time
it has been shown that in the first ten years of 1993j @xmath6 , which means an observed exponent larger than the previously suggested exponents , see @xcite .
the previous analysis allows posing a basic question : ` is it possible to find an analytical solution for snrs given the three observable astronomical parameters , age , radius and velocity ? ' . in order to answer the above question ,
section [ secprofiles ] introduces three profiles for the csm , section [ secmotion ] derives three pad approximated laws of motion for snrs , and section [ secastro ] closes the derived equations of motion for four snrs .
this section introduces three density profiles for the csm : an exponential profile , a gaussian profile , and a self - gravitating profile of lane emden type .
[ secprofiles ] this density is assumed to have the following exponential dependence on @xmath2 in spherical coordinates : @xmath7 where @xmath8 represents the scale .
the piece - wise density is @xmath9 the total mass swept , @xmath10 , in the interval @xmath11 $ ] is @xmath12 this density has the gaussian dependence @xmath13 and the piece - wise density is @xmath14 the total mass swept , @xmath10 , in the interval @xmath11 $ ] is @xmath15 where @xmath16 is the error function , see @xcite . the lane
emden profile when @xmath0 , after @xcite , is @xmath17 @xmath18 the total mass swept , @xmath10 , in the interval @xmath11 $ ] is @xmath19
the conservation of the momentum in spherical coordinates in the framework of the thin layer approximation states that @xmath20 where @xmath21 and @xmath22 are the masses swept at @xmath23 and @xmath2 , and @xmath24 and @xmath25 are the velocities of the thin layer at @xmath23 and @xmath2 . assuming an exponential profile as given by eq .
( [ profile_exponential ] ) the velocity is @xmath26 where @xmath27 and @xmath28 in the above differential equation of the first order in @xmath2 , the variables can be separated and integration gives the following non - linear equation : @xmath29 in this case is not possible to find an analytical solution for the radius , @xmath2 , as a function of time .
we therefore apply the pad rational polynomial approximation of degree 2 in the numerator and degree 1 in the denominator about the point @xmath30 to the left - hand side of eq .
( [ eqn_nl_exp ] ) : @xmath31 the resulting pad approximant for the radius @xmath32 is @xmath33 and the velocity is @xmath34 @xmath35 and @xmath36 assuming a gaussian profile as given by eq .
( [ prof_gaussian ] ) the velocity is @xmath37 where @xmath38 and @xmath39 the appropriate non - linear equation is @xmath40 the pad rational polynomial approximation of degree 2 in the numerator and degree 1 in the denominator about @xmath30 for the left - hand side of the above equation gives @xmath41 the resulting pad approximant for the radius @xmath32 is @xmath42^{\frac{1}{2 } } \bigg \ } \label{rmotiongauss } \ , , \end{aligned}\ ] ] and the velocity is @xmath43 @xmath44 and @xmath45 assuming a lane
emden profile , @xmath0 , as given by eq .
( [ profile_lane ] ) , the velocity is @xmath46 where @xmath47 and @xmath48 the connected non - linear equation is @xmath49 the pad rational polynomial approximation of degree 2 in the numerator and degree 1 in the denominator for the left - hand side of the above equation gives @xmath50 where @xmath51 the pad approximant for the radius is @xmath52 where @xmath53 and @xmath54 and the velocity is @xmath55 where @xmath56 and @xmath57
in the previous section , we derived three equations of motion in the form of non - linear equations and three pad approximated equations of motion .
we now check the reliability of the numerical and approximated solutions on four snrs : tycho , see @xcite , cas a , see @xcite , cygnus loop , see @xcite , and sn 1006 , see @xcite .
the three astronomical measurable parameters are the time since the explosion in years , @xmath58 , the actual observed radius in pc , @xmath2 , and the present velocity of expansion in kms@xmath59 , see table [ tablesnrs ] . . observed astronomical parameters of snrs [ cols="^,^,^,^,^",options="header " , ] the goodness of the approximation
is evaluated through the percentage error , @xmath60 , which is @xmath61 where @xmath32 is the pad approximated radius and @xmath62 is the exact solution which is obtained by solving numerically the non - linear equation of motion , as an example eq .
( [ eqn_nl_exp ] ) in the exponential case .
the numerical values of @xmath60 are reported in column 6 of tables [ tablesnrsexp ] , [ tablesnrsgauss ] and [ tablesnrslaneemden ] .
another useful astrophysical variable is the predicted decrease in velocity on the basis of the pad approximated velocity , @xmath63 , in 10 years , see column 7 of tables [ tablesnrsexp ] , [ tablesnrsgauss ] and [ tablesnrslaneemden ] .
the expansion of an snr can be modeled by the conservation of momentum in the presence of a decreasing density : here we analysed an exponential , a gaussian and a lane
emden profile .
the three equations of motion have complicated left - hand sides but simple left - hand sides , viz . , @xmath64 .
the application of the pad approximant to the left - hand side of the complicated equation of motion allows finding three approximate laws of motion , see eqs ( [ rmotionexp ] , [ rmotiongauss ] , [ rmotionlaneemden ] ) , and three approximate velocities , see eqs ( [ vmotionexp ] , [ vmotiongauss ] , [ vmotionlaneemden ] ) .
the astrophysical test is performed on four spherical snrs assumed to be spherical and the four sets of parameters are reported in tables [ tablesnrsexp ] , [ tablesnrsgauss ] and [ tablesnrslaneemden ] . the percentage of error of the pad approximated solutions for the radius is always less than @xmath1 with respect to the numerical exact solution , see column 6 of the three last tables . in order to produce an astrophysical prediction , the theoretical decrease in velocity for the four snrs here analysed
is evaluated , see column 7 of tables [ tablesnrsexp ] , [ tablesnrsgauss ] and [ tablesnrslaneemden ] .
h j 1870 on the theoretical temperature of the sun , under the hypothesis of a gaseous mass maintaining its volume by its internal heat , and depending on the laws of gases as known to terrestrial experiment _ american journal of science _ * 148 * , 57 b j , chomiuk l , hewitt j w , blondin j m , borkowski k j , ghavamian p , petre r and reynolds s p 2016 an x - ray and radio study of the varying expansion velocities in tycho supernova remnant _ _ * 823 * l32 ( _ preprint _ ) | in this paper we derive three equations of motion for a supernova remnant ( snr ) in the framework of the thin layer approximation using the pad approximant .
the circumstellar medium is assumed to follow a density profile of either an exponential type , a gaussian type , or a lane
emden ( @xmath0 ) type .
the three equations of motion are applied to four snrs : tycho , cas a , cygnus loop , and sn 1006 .
the percentage error of the pad approximated solution is always less than @xmath1 .
the theoretical decrease of the velocity over ten years for snrs is evaluated .
_ keywords _ : supernovae : general ism : supernova remnants supernovae : individual ( tycho ) supernovae : individual ( cas a ) supernovae : individual ( cygnus loop ) supernovae : individual ( sn 1006 ) |
the unification of the electromagnetic and weak interactions in 1968 @xcite , the discoveries of the neutral currents in 1973 @xcite , of the charm quark in 1974 @xcite , of the and bosons in 1983 @xcite were very successful steps for the theory of the electroweak ( ew ) interactions , the standard model ( sm ) @xcite .
after the discoveries of the top quark in 1995 @xcite and the tau neutrino in 2000 @xcite the electroweak sm became the commonly accepted theory of the fundamental electroweak interactions .
it is a gauge invariant quantum field theory based on the symmetry group @xmath0 , which is spontaneously broken by the higgs mechanism .
the renormalizability of the sm @xcite allows us to make precise predictions for measurable quantities at higher orders of the perturbative expansion , in terms of a few input parameters .
the higher - order terms , radiative corrections ( rc ) or quantum corrections , contain the self - coupling of the vector bosons as well their interactions with the higgs field and the top quark .
their calculation provides the theoretical basis for the ew precision tests . in the last thirty five years in high energy physics
two distinct and complementary strategies have been used for gaining new understanding of the nature : * the direct discovery of the new phenomena at high energy accelerators * the precision measurements of the known phenomena at existing accelerators with high luminosity the excellent example is the ratio ( fig .
1 ) r_e^+e^- . @xcite . ]
both strategies have worked very well for the studies of the ew interactions first at sps and lep1/slc , and later at lep2/sld and the tevatron , and in the future such interplay of the proton and electron colliders will be applied for the lhc and ilc / clic .
the second strategy has always demanded from the theory the prediction of physical quantities with high precision , @xmath1 at the level of quantum corrections . for the interpretation of the precision experiments
the rc play the crucial role .
in the context of the sm any electroweak process can be computed at tree level from ( the fine structure constant measured at values of @xmath2 close to zero ) , ( the w - boson mass ) , ( the z - boson mass ) , and ( the cabbibo - kobayashi - maskawa flavor mixing matrix elements ) @xcite . when higher order corrections are included , any observable can be predicted using the on - shell renormalization scheme @xcite as a function of : & = & ( , _ , _ , _ , _ , _ , v_jk ) , where the effects of heavy particles do not decouple , and there is the sensitivity to the top mass @xcite and to less extend to the higgs mass @xcite .
vertex , involving a virtual top quark @xcite.,width=377 ] since the discovery of the presence of hard @xmath3 corrections to the @xmath4 vertex ( see fig .
2 ) @xcite the calculation of the ew rc has been theoretically well established and many higher - order contributions of the radiative corrections have become available over past decades to improve and stabilize the sm predictions .
the experimental data for testing of the ew theory have achieved an impressive accuracy . after taking the measured mass , besides and ( the fermi constant measured in the muon decay ) , for completion of the input , & = & ( 91.18750.0021 ) , + _ & = & ( 1.166 371 0.000 006 ) 10 ^ -5 ^ -2 , + ^-1 & = & 137.035 999 7100.000 000 096 each other precision observable provides a test of the electroweak theory ( fig .
the predictions are calculated with computer programs zfitter @xcite and topaz0 @xcite , which incorporate state - of - the - art calculations of the ew , qed and qcd radiative corrections .
theoretical predictions of the sm depend on the mass of the top quark and of the as yet experimentally unknown higgs boson through the virtual presence of these particles in the loops . as a consequence
, precision data can be used to pin down the allowed range of the mass parameters .
this is shown in fig .
4 , which compares the information on and obtained at lep1 and sld , with the direct measurements performed at lep2 and the tevatron .
the measured at tevatron mass @xmath5 @xcite agrees better than 10 % with the value predicted within the sm on the basis of the precision ew measurements . taking all direct and indirect data into account , one obtains the pillar of the precision electroweak physics @xcite : the best constraints on the possible mass of unseen higgs . the global electroweak fit results in the @xmath6 curve shown in fig .
the lower limit on obtained from direct searches is close to the point of minimum @xmath7 . at 95% c.l .
, one gets @xcite 114.4 < < 160 . versus , from the global fit to the ew data .
the vertical band indicates the 95% exclusion limit from direct searches @xcite.,width=226 ]
in the on - shell scheme @xcite the three - level formula @xmath8 is a definition of the renormalized @xmath9 to all orders in perturbation theory , @xmath1 , ^2_w^ ^2 = 1 - _ ^2_^2 .
a precise determination of the on - shell ew mixing angle has been performed by the nutev collaboration @xcite for the first time through the measurements of the pashos - wolfenstein ratio @xcite : r^- & & from deep inelastic neutrino scattering on isoscalar targets .
the nutev collaboration finds @xmath10 which is 3.0 @xmath11 higher than the sm predictions . from this experimental value one obtains the mass of boson @xcite = 80.14 0.08 which is smaller than other measurements of at lep / sld and the tevatron ( see fig .
6 ) .
the nutev result should be considered as preliminary until a reanalysis of data will be completed including all experimental and theoretical information .
apart from the still missing higgs boson , the sm provides an elegant theoretical framework for the description of the known experimental facts in particle physics .
the sm has been impressively confirmed by successful collider experiments at the particle accelerators lep , slc and tevatron during the last fifteen years .
future colliders like the upcoming lhc or an ilc / clic offer great prospects , and in turn represent a great challenge for theory to provide even more precise calculations .
accurate predictions are necessary not only to increase the level of precision of sm tests , but also to study the indirect effects of possible new particles .
i would like to thank the organizers of the uae - cern workshop for kind invitation to give a plenary talk and for the hospitality at al - ain .
i am grateful to j. vidal for support and to d. hertzog , z. hioki and a. shiekh for remarks and comments . | the status of the precision tests of the electroweak interactions is reviewed in this paper .
an emphasis is put on the standard model analysis based on measurements at lep / slc and the tevatron .
the results of the measurements of the electroweak mixing angle in the nutev experiment and the future prospects are discussed .
= 18pt |
in hadron colliders the dominant mode of top quark production is via quark - antiquark annihilation or gluon - gluon fusion , @xmath1 however there are other modes , @xmath2 in this list i have not included processes which pick a @xmath3-quark out of the hadron .
these processes are approximately ordered according to their rates in hadron colliders .
1(a ) has the rates for the first three processes at the tevatron assuming that the dominant decay model for the top quark is @xmath4 .
the channel , positron plus jets , was chosen so that the final state for all three processes is positron , @xmath5 plus jets .
the qcd , @xmath6-gluon and @xmath7 processes have two , one and zero non-@xmath3-quark jets , respectively .
( a)(b ) fig .
1(b ) contains the qcd cross section for @xmath8 verses @xmath9 for both proton - proton colliders and for proton - antiproton colliders . at @xmath10
the gluon - gluon fusion is only 10% of the cross section for a proton - antiproton collider , the tavatron , whereas at a @xmath11 proton - proton collider , the lhc , gluon - gluon fusion is 90% of the cross section . for an accurate determination of the qcd top cross section , we need to consider the next to leading order calculations and the soft gluon resummation of the next to leading order calculations@xcite . in fig .
2 , the results of these calculations using the same structure functions are shown . at high
top quark masses the difference between these two calculations is at the 20% level .
the standard model decays of the top are @xmath12 for @xmath13 , the total width of the top quark is approximately @xmath14 .
the ckm suppressed decays are expected to be less than 0.1% of the non - suppressed decays . whereas the decays including a @xmath15 or higgs will be extremely small unless the on - mass shell decay is kinematically allowed .
flavor changing neutral currents , @xmath16 have branching ratios less than @xmath17 in the standard model .
both cdf@xcite and d0@xcite presented detailed results on the search for top at the tevatron .
the data presented included both the dilepton and the lepton plus jets mode for the decay of the @xmath0 pair .
however , neither collaboration presented data on the six jet mode .
theoretical calculations suggest that with an efficient @xmath3-quark tag , that this mode will be accessible at the tevatron .
a detailed summary of the experimental results present can be found in the review of hadron collider physics by shochet@xcite .
cdf observes a @xmath18 ( 0.26% ) effect which is not sufficient to firmly establish the existence of top but which , if interpreted as top , yields @xmath19 and @xmath20 .
d0 does not observe a significant excess of events due to @xmath0 production .
the probability for the background to fluctuate to give greater than or equal to the observed number of events is 7.2% ( @xmath21 ) . if @xmath22 then @xmath23 .
orr@xcite presented the results of a study on the effects of soft gluon radiation in the determination of the top quark momentum .
the results of this study will be important for precision measurements of the top quark mass at hadron colliders .
in the standard model the couplings of the top quark to each of the gauge bosons , @xmath24 and @xmath25 are determined , including radiative corrections .
therefore potential new physics could show up as deviations of these vertices from standard model expectations .
kao@xcite and rizzo@xcite discussed corrections to the qcd coupling , @xmath26 . kao s paper concentrated on the one - loop weak corrections in both the standard model and the minimal supersymmetric standard model .
whereas rizzo considered the effects of an anomalous chromomagnetic moment to this coupling .
schmidt@xcite summarized top quark physics at @xmath27 colliders and in particular discussed the signatures of deviations to the @xmath28 and @xmath29 vertices at such machines . of course the top quark could present more dramatic surprises such as charged higgs decays , @xmath30 , large flavor changing neutral current decays , + @xmath31 or enhanced production through a new resonance .
this latest possibility could occur either through the quark - antiquark production mode@xcite , as expected in top - color models of electroweak symmetry breaking or via the gluon - gluon fusion@xcite as suggested by some technicolor models . in both cases
the @xmath0 pair is produced by the decay of a heavy new particle , top - color boson or techni - eta , which distorts the @xmath32 , @xmath33 and @xmath34 distributions from the standard model expectation .
3 is the change in the shape of the @xmath34 distribution in the top - color model discussed by hill and parke@xcite .
we should think of top quark production as a new drell - yan process probing extremely high mass scales , greater than 500 gev .
the top quark is an exciting new window on very high mass scale physics . while exploring the vista from this window we should be on the lookout for any deviation from the standard model which will provide us with information about that elusive beast , the mechanism of electro - weak symmetry breaking . because the mass of the top quark is very heavy , this quark is the particle most strongly coupled to the electro - weak symmetry breaking sector
. therefore the deviations could be seen at zeroth order or may require more subtle measurements .
\99 . # 1#2#3 nucl . phys . *
b#1 * # 3 , ( # 2 ) # 1#2#3 phys
b#1 * # 3 , ( # 2 ) # 1#2#3 phys .
* # 1 * # 3 , ( # 2 ) # 1#2#3 phys . rev . *
# 1 * # 3 , ( # 2 ) # 1#2#3 phys . rev .
* d#1 * # 3 , ( # 2 ) # 1#2#3 phys . rep . *
# 1 * # 3 , ( # 2 ) # 1#2#3 rev .
phys . * # 1 * # 3 , ( # 2 ) # 1#2#3 z. phys .
* c#1 * # 3 , ( # 2 ) # 1#2#3 comm .
phys . * # 1 * # 3 , ( # 2 ) # 1#2#3_ibid . _ * # 1 * # 3 , ( # 2 ) # 1#2#3 jetp lett .
* # 1 * # 3 , ( # 2 ) # 1#2#3 sov .
# 1 * # 3 , ( # 2 ) j. benlloch , _ ` results from the cdf top search in the dilepton channel , ' _
+ g. watts , _ ` cdf top results in the lepton plus jets channel , ' _ + j. konigsberg , _ ` discussion of results of the cdf top searches , ' _
+ b. harral , _ ` kinematics properties of lepton plus multijet events at cdf , ' _ + these proceedings .
k. genser , _ ` search for top with d0 detector in the dilepton channel , ' _
+ d. chakraborty , _ ` search for top in the lepton plus jets channel at d0 , ' _
+ w. cobau , _ ` search for the top quark in electron plus jets plus b - quark tag using the d0 detector , '
_ + p. bhat , _ ` search for the top quark using multi - variate analysis techniques , ' _ + these proceedings . | i briefly review standard top quark physics at hadron colliders and summarize the contributions to this conference .
the possibility of new mechanisms for @xmath0 production are also discussed .
fermilab - conf-94/322-t + hep - ph/9409312 + september 13 , 1994 + |
the large n limit of four dimensional non - abelian gauge theories is interesting from the view point of qcd phenomenology @xcite and string theory @xcite .
lattice qcd is a useful technique for extracting fundamental results in the large n limit of qcd .
fermions are naturally quenched in the t hooft limit of large n qcd and this significantly reduces the computational cost in a lattice calculation .
in addition , there is a concept of continuum reduction @xcite , namely , physics does not depend on the size of box @xmath0 for @xmath1 and @xmath2 is a physical critical size .
these two observations have been used to extract physical results in the large n limit of qcd using numerical techniques on the lattice .
large n qcd on a continuum torus @xmath0 has several phases @xcite depending upon the size of the torus as shown in fig .
[ fourd ] .
the continuum action has @xmath3 symmetries associated with the polyakov loops in the four directions and the various phases correspond to the number of directions in which this symmetry is broken .
the continuum limit is obtained by going to the top - right corner of fig .
[ fourd ] and different approaches to this corner will result in one of the five continuum phases .
the @xmath4h - phase present for @xmath5 for all @xmath6 is an unphysical phase that does not survive the continuum limit .
the @xmath4h to @xmath4c transition is associated with the single plaquette operator opening up a gap around @xmath7 in its eigenvalue distribution .
gauge fields come in disconnected pieces in all the @xmath8c - phases due to the presence of the gap in the single plaquette operator @xcite .
the @xmath4c - phase is the confined phase of large n qcd and the @xmath9c - phase is the deconfined phase and @xmath10 .
an immediate consequence of continuum reduction is that large n qcd does not feel temperatures below @xmath11 @xcite .
numerical analysis has shown that lattice spacing effects are small in the @xmath4c - phase and it is sufficient to work at @xmath12 and @xmath13 to extract continuum results .
therefore , numerical computations can be performed on a serial computer and a cluster of computers can be efficiently used to generate statistics in a monte - carlo calculation .
since physics does not depend on the box size in @xmath4c - phase , one should show that chiral symmetry is spontaneously broken in finite volume in order to properly reproduce physics in this phase @xcite .
the order of limits are important and one has to take the large n limit before taking the quark mass to zero at finite phsyical volume . the low lying spectrum of the massless dirac operator shows evidence for spontaneous chiral breaking since the eigenvalues , @xmath14 , scales like @xmath15 with @xmath16 obeying a universal distribution .
the chiral condesate , @xmath17 , is independent of @xmath18 .
results of a calculation of the chiral condensate on the lattice is shown in fig .
[ sigma ] .
results from chiral random matrix theory @xcite were used to extract the chiral condensate at a fixed @xmath19 , @xmath6 and lattice coupling .
two lowest non - zero eigenvalues in the @xmath20 and @xmath21 topological sectors were used to show consistency .
the plot shows that there is a limit as @xmath22 and this limit is independent of @xmath6 .
results obtained at different lattice couplings yield @xmath23
since chiral symmetry is broken in large n qcd even in finite volume , one should be able to observe massless pions in finite volume .
this result emerges in the following manner @xcite .
properties of a single quark in a background gauge field @xmath24 can not depend on a shift of @xmath25 for arbitrary @xmath26 since the @xmath3 symmetries associated with the polyakov loops are not broken in the @xmath4c - phase .
but the propagator of a non - singlet meson will depend on @xmath26 , if one quark sees @xmath27 and the other sees @xmath28 as their respective gauge fields .
this is referred to as the quenched momentum prescription @xcite for the computation of meson propagators in the large n limit of qcd .
one can use the results for the chiral condensate , @xmath29 , and critical lattice size , @xmath30 , to plot the pion mass as a function of @xmath31 .
the results fall on a single universal curve as shown in fig .
[ pion ] and @xmath32 .
the @xmath4c to @xmath9c phase transition is the confinement - deconfinement phase transition since the @xmath33 symmetry associated with one of the polyakov loops is broken .
this transition is first order since there is a latent heat associated with the single plaquette @xcite .
the fermion determinant does matter in the @xmath9c - phase and it picks the correct boundary conditions for fermions in the broken direction , namely , anti - periodic with respect to the polyakov loop @xcite .
the lowest eigenvalue of the dirac operator with the correct boundary conditions can be used to study the gap in the @xmath9c - phase and one finds that chiral symmetry is restored in the @xmath9c - phase @xcite .
furthermore , the chiral transition is first order as shown in fig .
if one were to super - cool the @xmath9c - phase into the @xmath4c - phase , a second order transition with a square root singularity would be observed at @xmath34 .
non - abelian gauge theories in the confined phase are strongly interacting at large distances and weakly interacting at short distances .
if this is seen as a phase transition in some observable , one could use the universal behavior of this transition to connect the low energy physics of qcd to the high energy physics of qcd .
the wilson loop operator as a function of its size is the most likely candidate to study this transition within the @xmath4c - phase of large n qcd @xcite .
such a transition exists in two dimensional large n qcd @xcite and it is claimed that the transition in four dimensional qcd is in the same universality class . this transition is referred to as the durhuus - olesen phase transition in fig [ fourd ] .
wilson loop operators suffer from a perimeter divergence in four dimensions and one has to eliminate it when defining this operator if one were to study its eigenvalue distribution .
one possible way to suppress the perimeter divergence is to use smeared operators on the lattice .
numerical studies of the eigenvalue distribution of the smeared wilson loop operator on the lattice shows clear evidence for a phase transition as a function of the size of the wilson loop @xcite .
the universality class is the same as the one found in two dimensional large n qcd as shown in fig .
[ wilson ] and the critical loop size is roughly @xmath35 .
r. n. would like to thank the organizers of caqcd-06 for a stimulating atmosphere .
r. n. acknowledges partial support by the nsf under grant number phy-0300065 and partial support from jefferson lab . the thomas jefferson national accelerator facility ( jefferson lab )
is operated by the southeastern universities research association ( sura ) under doe contract de - ac05 - 84er40150 .
h. n. acknowledges partial support by the doe under grant number de - fg02 - 01er41165 at rutgers university .
a. v. manohar , arxiv : hep - ph/9802419 .
o. aharony , s. s. gubser , j. m. maldacena , h. ooguri and y. oz , phys . rept .
* 323 * , 183 ( 2000 ) [ arxiv : hep - th/9905111 ] .
j. kiskis , r. narayanan and h. neuberger , does the crossover from perturbative to nonperturbative physics in qcd phys .
b * 574 * , 65 ( 2003 ) [ arxiv : hep - lat/0308033 ] .
r. narayanan and h. neuberger , pos * lat2005 * , 005 ( 2006 ) [ arxiv : hep - lat/0509014 ] .
j. kiskis , r. narayanan and h. neuberger , phys .
d * 66 * , 025019 ( 2002 ) [ arxiv : hep - lat/0203005 ] .
t. d. cohen , phys .
* 93 * , 201601 ( 2004 ) [ arxiv : hep - ph/0407306 ] .
r. narayanan and h. neuberger , nucl .
b * 696 * , 107 ( 2004 ) [ arxiv : hep - lat/0405025 ] .
j. j. m. verbaarschot and t. wettig , ann .
nucl . part .
sci . * 50 * , 343 ( 2000 ) [ arxiv : hep - ph/0003017 ] .
r. narayanan and h. neuberger , phys .
b * 616 * , 76 ( 2005 ) [ arxiv : hep - lat/0503033 ] .
d. j. gross and y. kitazawa , nucl .
b * 206 * , 440 ( 1982 ) .
j. kiskis , arxiv : hep - lat/0507003 .
r. narayanan and h. neuberger , phys .
b * 638 * , 546 ( 2006 ) [ arxiv : hep - th/0605173 ] .
r. narayanan and h. neuberger , jhep * 0603 * , 064 ( 2006 ) [ arxiv : hep - th/0601210 ] . b. durhuus and p. olesen , nucl
. phys .
b * 184 * , 461 ( 1981 ) . | some physical results in four dimensional large n gauge theories on a periodic torus are summarized . |
the action of the auxiliary impurity problem that we minize in our calculations is @xmath74 where @xmath75 is the imaginary time , @xmath76 is the annihilation operator for the impurity electrons , @xmath77 and @xmath78 are the orbital and spin indices , and @xmath49 is the impurity hybridization function .
the on site electron - electron coulomb interaction between the d electrons is represented by the slater form : @xmath79 and @xmath80 here , @xmath81 are the radial part of the spherical harmonics , the index @xmath77 denotes @xmath82 , and @xmath83 are the slater integrals .
the explicit form of the frequency dependent hybridization @xmath84 can be written in terms of the projector @xmath85 , the kohn - sham hamiltonian ( without the spin - orbit coupling ) @xmath86 , the spin - orbit coupling hamiltonian @xmath87 , the self - energy @xmath88 , the local green s function @xmath89 and the double counting energy @xmath90
as@xcite @xmath91 the small latin indices @xmath92 enumerate the kohn - sham bands and include the spin as well .
@xmath93 is the crystal momentum .
the form of the spin - orbit coupling hamiltonian is @xmath94 .
forms of different projectors ( @xmath85 ) and double counting ( @xmath90 ) have been previously discussed in , for example , [ ] and [ ] .
@xmath95 , @xmath96 , @xmath86 , and @xmath87 are determined self consistently by extremizing the action ( [ equ : action ] ) , hence @xmath95 and @xmath96 obey the dmft self consistency condition and @xmath86 , and @xmath87 are determined from the self consistent electronic charge .
the impurity model is solved with the continous time quantum monte carlo ( ctqmc ) solver . in order to reduce the sign problem ,
we employ orbital and spin rotations ( @xmath97 ) that cast the hybridizaton @xmath49 in a diagonal form in the relevant low energy limit @xmath98 the hybridization is strongly frequency dependent , however , its eigenvectors do not change much with frequency . in other words , it is possible to obtain an _ almost diagonal hybridization _ by using a _ frequency independent _ rotation @xmath97 .
we ignore the off diagonal @xmath99 and as a result our ctqmc impurity solver suffers very little sign problem , even in the presence of spin - orbit coupling and low crystal symmetry .
unlike sr@xmath7iro@xmath8 , where spin - orbit coupling ( soc ) is necessary for the insulating behaviour , the compounds with the kgf structure that we consider can be mott insulators even in the absence of soc , because they have narrow bands in dft even without soc . in order to verify this point , we performed dft+dmft calculations without soc on rb@xmath7rhf@xmath23 and rb@xmath7irf@xmath23 .
the dos from these calculations , along with the dos with soc for comparison , are presented in figure 1 . as expected from a crystal structure with unconnected polyhedra , both of these compounds are mott insulators with wide charge gaps .
rb@xmath7irf@xmath23 has a smaller gap when soc is not taken into account , but the width of the gap of rb@xmath7rhf@xmath23 does not change much , in line with the small energy scale of the soc in this compound . as a result , we conclude that the soc in the tm - fluorides with the kgf structure is not responsible of the insulating behaviour , but it only changes the character of the insulating state . in the absence of soc , these compounds would be spin-1/2 mott insulators , whereas , due to soc , they become j@xmath34=1/2 mott insulators .
this difference is clear considering the character of the low energy degrees of freedom , and would be visible in magnetic properties , such as the stength of the magnetocrystalline anisotropy or the magnon dispersion .
irf@xmath23 and rb@xmath7rhf@xmath23 with and without spin orbit coupling . ]
in the main text , we generalized the @xmath53 states as @xmath59 + \big[-|e_-\downarrow\rangle+(\alpha - i\alpha^2)|e_-\uparrow\rangle\big ] \big)\ ] ] @xmath60 + \big[|e_-\uparrow\rangle+(\alpha+i\alpha^2)|e_-\downarrow\rangle\big ] \big)\ ] ] where @xmath100 @xmath101 @xmath102 and @xmath58 .
these states are the eigenstates of the soc hamiltonian under a trigonal distortion , which breaks the degeneracy of @xmath103 with @xmath104 .
the ideal j@xmath34=1/2 states @xmath53 are su(2 ) invariant : the ratio of orbital to spin angular momenta is @xmath105 and is independent of direction .
however , the generalized states @xmath106 do not satisfy these conditions .
for example , for @xmath17 being the axis of trigonal distortion , and @xmath107 , one gets @xmath108 . in this respect
, @xmath61 is a natural parameter to quantify the deviation of the system from an ideal j@xmath34=1/2 insulator .
the fact that the magnetic moment is anisotropic , and that the system is not in a heisenberg regime , has important consequences in the magnetic excitation spectrum .
for example , sr@xmath14ir@xmath7o@xmath21 , which has a @xmath64 that is much larger than sr@xmath7iro@xmath8 , has a large ( 92 mev ) magnon gap that is even wider than the magnon bandwidth in this compound.@xcite 4ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ]
+ 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1103/physrevb.81.195107 [ * * , ( ) ] link:\doibase 10.1103/physrevb.90.075136 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.111.246402 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.109.157402 [ * * , ( ) ] | discovery of new transition metal compounds with large spin orbit coupling ( soc ) coexisting with strong electron - electron correlation among the @xmath0 electrons is essential for understanding the physics that emerges from the interplay of these two effects . in this study , we predict a novel class of @xmath1 mott insulators in a family of fluoride compounds that are previously synthesized , but not characterized extensively .
first principles calculations in the level of all electron density functional theory + dynamical mean field theory ( dft+dmft ) indicate that these compounds have large mott gaps and some of them exhibit unprecedented proximity to the ideal , @xmath2 symmetric @xmath1 limit .
interest in @xmath3 compounds has been blossoming in the recent years in response to the scientific advances and applications in the areas of topological insulators , multiferroics , and thermoelectrics . at the forefront of this activity
are the ir compounds , because of the interesting interplay between itinerancy , the electronic correlations and strong spin - orbit coupling ( soc).@xcite this strong coupling between the spin and orbital degrees of freedom gives rise to various interesting phases , such as the exotic spin - liquid phase predicted in honeycomb iridates , or the recently observed fermi arcs and the spin - orbit induced mott insulating phase in the perovskite - related ir - oxides.@xcite in these latter systems , the soc splits the six - fold degenerate ir t@xmath4 states into 4 occupied @xmath5 and 2 half - occupied @xmath1 states .
the bands formed by the @xmath1 states are much narrower than the width of the whole @xmath6 manifold in the absence of soc , and as a result , the system can be easily drawn to a mott - insulating phase with even a modest amount of correlations on the 5d ir atom . @xcite
the most widely studied soc induced correlated insulator is sr@xmath7iro@xmath8 , which is an antiferromagnetic insulator below 240 k.@xcite there are numerous studies that involve strain , and pressure on this material ; and various related compounds are also extensively studied.@xcite however , despite being the prototypical system , sr@xmath7iro@xmath8 is far from being the ideal @xmath1 mott insulator : the existence of the insulating state above the neel temperature is due to short range order , which is around 100 lattice constants even 20k above the neel temperature,@xcite hence sr@xmath7iro@xmath8 was termed a _ `
marginal mott insulator'_. this marginal nature of the insulating state was confirmed theoretically , as the first - principles calculations , which neglect short range order , predict bad metallic state in the paramagnetic phase.@xcite also , the crystal structure of sr@xmath7iro@xmath8 is far from cubic : it has the tetragonal spacegroup i4@xmath9/acd . the tetragonal symmetry breaks the degeneracy of the t@xmath4 orbitals , and thus the @xmath1 orbitals mix , moving the system away from the ideal limit where the moments are @xmath2 invariant . since @xmath2 symmetric @xmath1 insulators
are proposed to exhibit superconductivity when doped,@xcite it is important to identify new compounds that are true @xmath1 mott insulators with sizeable gaps . in this study
, we predict a novel class of @xmath1 mott insulator compounds that are both very close to the @xmath2 limit and have large charge gaps in the paramagnetic state .
we achieve this by considering crystal structures that are not commonly studied in the context of correlated electron physics .
we focus on a group of already synthesized iridium and rhodium fluoride compounds and use first - principles calculations at the level of fully charge self - consistent dft+dmft to show the presence of the @xmath1 insulating state in these compounds .
we thus expand the search for new @xmath1 insulators to the family of fluorides , and for the first time show that the @xmath1 state can exist in a rhodium compound .
we begin our search for new @xmath1 insulators by the well known observation that lower bandwidth favours the mott insulating phase . the sr@xmath10v@xmath11o@xmath12 ruddlesden - popper ( rp ) series nicely demonstrates this point:@xcite the @xmath13 srvo@xmath14 is a correlated metal . in this compound , the oxygen octahedra are corner sharing , and the number of nearest neighbour transition metal ions is @xmath15 . with decreasing @xmath16
, @xmath17 decreases monotonically from @xmath15 to @xmath18 for sr@xmath7vo@xmath8 ( @xmath19 ) .
this leads to a decrease of the bandwidth as @xmath16 decreases , and as a result there is a metal - insulator transition as a function of @xmath16 , and sr@xmath7vo@xmath8 is a mott insulator.@xcite the sr@xmath10ir@xmath11o@xmath12 compounds also behave similarly : the perovskite sriro@xmath14 ( @xmath15 ) is a correlated metal , the @xmath20 sr@xmath14ir@xmath7o@xmath21 ( @xmath22 ) is barely an insulator , and the @xmath19 sr@xmath7iro@xmath8 ( @xmath18 ) is the well - known @xmath1 insulator.@xcite a strategy to obtain a small bandwidth and hence a possible @xmath1 mott insulator in an iridate compound is to look for crystal structures where the connectivity of anion octahedra is low .
the extreme case is a structure that consists of isolated iro@xmath23 octahedra that are not corner- , edge- , or face- sharing with any other octahedra .
but , to the best of our knowledge , there exists no structure with isolated mo@xmath23 units in transition metal oxides .
however , isolated hexafluoro- transition metal complexes ( mf@xmath23 ) are known to exist and are very common in fluoride compounds.@xcite the ir ion in many of these compounds have the d@xmath24 electronic configuration , and hence can lead to the @xmath1 mott insulating phase .
gef@xmath23 ( kgf ) crystal structure . ( b ) the mf@xmath23 octahedra are aligned parallel and form triangular layers .
the alkali metals are both above and below these layers , shown by green and red .
( c ) coordination environment of the transition metals in the kgf and ( d ) the @xmath19 rp structure .
chemically inequivalent f ions in the rp structure are shown by blue and red . ] as an example of this group of compounds , we consider the alkali metal hexafluoro - iridates and rhodates with the chemical formula a@xmath7mf@xmath23 and the so called k@xmath7gef@xmath23 ( kgf ) crystal structure@xcite shown in fig .
[ fig : structure ] . here
, a is the alkali metal ion and m is the transition metal ion .
each m ion ( in our case either ir or rh ) is in the center of an f@xmath23 octahedron .
the space group is trigonal p@xmath25m1 .
while there is no symmetry element that imposes the octahedra to be regular , all six m - f bondlengths are equal and the f - m - f angles are close to 90@xmath26 .
the site symmetry of the m ion is @xmath25 m , and the threefold degenerate @xmath6 states are split into 2 + 1 .
however , unlike in the rp compound sr@xmath7iro@xmath8 , all ligands are symmetry equivalent ( fig . [
fig : structure]c - d ) , and as a result an equally distorted octahedron is expected to cause a smaller splitting of the @xmath6 states in the a@xmath7mf@xmath23 compounds than in the rp compounds .
the m ions form regular triangular layers ( fig .
[ fig : structure]b ) .
the octahedra and the local coordinate axes of all m ions are aligned in a parallel fashion .
the out - of - plane lattice constant @xmath27 is smaller than the in - plane lattice constant @xmath28 , and as a result , the band structure is of 3-dimensional character .
the ir and rh cations we consider have 4 + formal valence and 5 electrons in their @xmath6 orbitals in this structure .
since the mf@xmath23 octahedra are isolated in the sense that there are no f ligands that are coordinated to two different m ions , the effective hopping between the m ions is small and hence the @xmath0 bands at the fermi level are expected to be extremely narrow - rendering the system a strong mott insulator .
irf@xmath23 and rb@xmath7rhf@xmath23 within density functional theory , with and without spin - orbit coupling . ] in fig .
[ fig : wiendos ] , we show the densities of states ( dos ) of rb@xmath7irf@xmath23 and rb@xmath7rhf@xmath23 , obtained from density functional theory in the generalized gradient approximation@xcite using the full - potential linear augmented wave formalism as implemented in wien2k@xcite , and using the experimental crystal structures.@xcite when the soc is not taken into account , both compounds have very similar dos ( fig . [
fig : wiendos]a - b ) : there is a narrow ( @xmath29400 mev ) band that consists of the transition metal @xmath6 states , which is partially occupied .
the @xmath6-@xmath30 splitting is @xmath293 ev , and the @xmath30 states are well above the fermi level .
there is no other state than the @xmath6 states around the fermi level for a 4 - 5 ev interval .
the strong spin orbit coupling due to the heavy ir ion in rb@xmath7irf@xmath23 dramatically alters the band structure of this compound ( fig .
[ fig : wiendos]c ) . the partially filled @xmath6 band near the fermi level is split into two bands , a lower lying @xmath5 band with 4 electrons , and a half filled @xmath1 band that crosses the fermi level .
the latter is extremely narrow ( @xmath29100 mev ) but since the mott physics is beyond dft , this theory predicts metallic state .
the rh ion in rb@xmath7rhf@xmath23 , which is above ir in the periodic table , introduces a much weaker soc than ir . as a result , even when soc is taken into account , the @xmath5 states are not energetically separated from the @xmath1 ones . however , it is still possible to identify the two overlapping peaks corresponding to these two groups of states in the dos .
both of these compounds have narrow , half filled @xmath1 bands near the fermi level , indicating that a small amount of on - site correlations can drive them into a mott - insulating state . while this state is beyond dft at the gga level , it is possible to capture the mott insulating phase using dynamical mean field theory ( dmft ) . which contains all feynman diagrams local to the ir ion is added to the kohn - sham hamiltonian .
the self energy is obtained by solving the local impurity problem using continuous time quantum monte carlo@xcite and full charge self - consistency is obtained by repeating dft and dmft steps .
] dft+dmft has been successfully applied to reproduce the properties of various mott insulators and it has been recently used to study the @xmath1 insulating phase in sr@xmath7iro@xmath8.@xcite as a result , it is the natural method of choice to study the possibly mott insulating electronic structure of the hexafluoro - iridates and -rhodates .
we chose the same on - site coulomb repulsion in these compounds as estimated for iridates in ref .
, i.e. , @xmath31ev and @xmath32ev .
we note that these values are the lower bound for more localized fluorides , hence we are possibly underestimating the size of the mott gap . ) and dos of ( a ) rb@xmath7irf@xmath23 , and ( b ) rb@xmath7rhf@xmath23 ( bottom ) . ] in fig .
[ fig : akw_rb ] , we present the result of our dmft calculations : the spectral functions a(k,@xmath33 ) of rb@xmath7irf@xmath23 and rb@xmath7rhf@xmath23 from dft+dmft . both compounds are mott insulators , with wide gaps close to @xmath292 ev . in rb@xmath7irf@xmath23 , the upper and lower hubbard bands are clearly separated and have @xmath1 character , indicating that rb@xmath7irf@xmath23 is a @xmath1 mott insulator . in rb@xmath7rhf@xmath23 ,
the lower hubbard band overlaps with the fully occupied , uncorrelated @xmath5 bands and so can not be clearly seen in the a(k,@xmath33 ) plot .
however , the upper hubbard band has a clear @xmath1 character and therefore this compound is a @xmath1 insulator as well . to the best of our knowledge ,
this is the first report of a @xmath1 insulator in a compound that does not contain iridium .
furthermore , both of these compounds have the largest gaps ever reported for a @xmath1 insulator .
both the large gaps , and the possibility of the @xmath1 state in a rhodate compound are thanks to the non - connectivity of the mf@xmath23 octahedra in the kgf structure , and the resulting very narrow @xmath1 bands . in passing , we note that replacing ir with rh in sr@xmath7iro@xmath8 leads to a metallic phase both because of the much weaker soc@xcite but also possibly because of the slightly larger electronegativity of the rh ion . in the kgf fluorides ,
the charge gap is large , which makes the electronegativity difference negligable , and also the soc is not necessary for the mott insulating phase ( it is essential only for the j@xmath34=1/2 character ) . as a result ,
even the rhodates in this structure are j@xmath34=1/2 mott insulators .
( see the supplamental material . ) encouraged by the success of our strategy to look for @xmath1 mott insulators in this class of coumpounds , we also performed dft+dmft calculations in three other compounds with the same crystal structure , cs@xmath7irf@xmath23 , k@xmath7irf@xmath23 , and k@xmath7rhf@xmath23 . while these compounds have significantly different lattice constants due to the different alkali metals they contain , we find all of them to be @xmath1 insulators with large gaps as well .
all of these compounds were synthesized and their crystal structures were studied before@xcite but there is very little information on their magnetic properties or conductivities .
our predictions call for more experiments to characterize these materials better .
we predict a fluctuating magnetic moment of 1.6 @xmath35 in both rb@xmath7irf@xmath23 and rb@xmath7rhf@xmath23 , which is smaller than the value expected for an ideal spin-1/2 mott insulator ( 1.73 @xmath36 ) because of the charge fluctuations ( there is a @xmath37 probability that there are 6 electrons in the @xmath6 orbitals ) .
these values are @xmath38 larger than what is measured in cs@xmath7irf@xmath23 in ref . , but @xmath39 smaller than the value measured in the rh compounds in ref . at room temperature .
the ideal @xmath1 state is @xmath2 invariant , and so it has no magnetic anisotropy .
however , systems such as sr@xmath7iro@xmath8 are observed not to be exactly at this limit due to deviations of the wave function from the ideal @xmath1.@xcite the reason is that sr@xmath7iro@xmath8 lacks cubic symmetry : it has the space group i4@xmath9/acd , which is tetragonal , and hence the three @xmath6 orbitals of the ir ion are split into a degenerate doublet and a singlet .
the deviation from ideal @xmath1 state is small but not negligible , and it depends strongly on biaxial strain and pressure.@xcite in the kgf structure , the space group is trigonal , and the @xmath6 irreducible representation is split into two , a singlet @xmath40 and a doublet @xmath41 , similar to sr@xmath7iro@xmath8 .
this also introduces a deviation from the @xmath1 state and a resultant magnetic anisotropy . in order to see how much the wavefunction is different from the ideal @xmath1 state
, we study the hybridization function @xmath42 used in the dmft calculation.@xcite it is given by @xmath43 where @xmath44 is the dmft self energy , @xmath45 are the dft kohn - sham eigenvalues , and @xmath46 and @xmath47 are the projector and the embedder on the transition metal site . in the high frequency limit @xmath48 , the eigenvalues of the @xmath49 matrix give the atomic energy levels ( including both the crystal field and the spin - orbit coupling ) and it is related to the single ion anisotropy . in the @xmath50 limit , it is related to the low energy electronic excitations .
the two eigenvectors of @xmath49 with the largest eigenvalues are the @xmath1-like states @xmath51 and @xmath52 .
the inner products of these with the ideal @xmath1 states @xmath53 can be used as a measure of how close the system to the @xmath2 limit is . however , this product is second order in the mixing , and a better measure is the coefficients in the expansions of @xmath54 .
this measure is used in ref . [ ] to study the effect of tetragonal symmetry breaking in sr@xmath7iro@xmath8 . under a trigonal perturbation ,
the @xmath6 orbitals are split into a singlet and a doublet as@xcite @xmath55 , @xmath56 , and @xmath57 , where @xmath58 .
a generalization of the @xmath1 states that takes into account this splitting is @xmath59 + \big[-|e_-\downarrow\rangle+(\alpha - i\alpha^2)|e_-\uparrow\rangle\big ] \big)\ ] ] @xmath60 + \big[|e_-\uparrow\rangle+(\alpha+i\alpha^2)|e_-\downarrow\rangle\big ] \big)\ ] ] here , @xmath61 quantifies the deviation from the ideal limit , and @xmath62 gives @xmath63 .
a large @xmath64 indicates strong deviation from the heisenberg regime , and leads to large magnon gaps , even larger than the spin wave bandwidth in sr@xmath14ir@xmath7o@xmath21.@xcite since hybridization is frequency dependent , so is @xmath61 . in rb@xmath7irf@xmath23 , the low frequency @xmath65 and the high frequency @xmath66 .
compared to sr@xmath7iro@xmath8,@xcite which has @xmath67 and @xmath68 ; the electronic state in rb@xmath7irf@xmath23 is much more isotropic , and closer to the ideal @xmath2 limit .
the rhodate compound rb@xmath7rhf@xmath23 , which has weaker soc , shows a more significant deviation from the ideal limit : it has @xmath69 and @xmath70 .
this very isotropic behaviour despite the noncubic spacegroup of rb@xmath7irf@xmath23 can be better understood considering the local coordination geometry of the transition metal ion .
the site symmetry of ir is @xmath71 .
the elements of the point group include various rotations , such as a threefold rotation around [ 001 ] and a twofold rotation around [ 100 ] ( fig .
[ fig : structure]c ) . as a result , all six f - ligands around a m ion are symmetry equivalent : they are chemically identical , and their f - m bond lengths are the same .
the deviation from the ideal cubic symmetry on the m site is only due to the presence of further neighbours that reduce the symmetry , and the deviation of the f - octahedra from a regular octahedron .
this latter effect is quite small ( the largest f - m - f bond angle variance in the compounds we consider is less than 6 degrees ) , and as a result , the ir ion is in an almost cubic environment . in the rp family of iridate compounds , the site symmetry of the ir ion
can be as high as @xmath72 .
however , despite a 4-fold rotation and various 2-fold rotation axes that pass through the ir ion ( fig .
[ fig : structure]d ) , there is no 3-fold rotation in the point group , and there are two _ chemically _ distinct ligands around each ir ion .
the apical oxygens , shown by red in fig .
[ fig : structure]d , are bonded to only one ir ion , whereas the other oxygens are bonded to two ir each .
this necessarily results in very a noncubic _ local _ environment of the ir ion , which leads to deviations from the ideal @xmath1 state even when the ir - o bondlengths are artificially set to be equal . in conclusion
, we identified a new class of @xmath1 mott insulators , which includes the first two examples of such compounds without iridium .
these materials are wide gap mott insulators , with no visible tendency towards magnetic ordering , and some of them are also closer to the isotropic @xmath2 limit than the well studied sr@xmath7iro@xmath8 .
this work extends the search for new materials which display an interplay of correlations with spin - orbit coupling to flouride compounds .
we posit that the @xmath1 mott insulating phase is very common in transition metal fluorides with isolated ir@xmath73f@xmath23 and rh@xmath73f@xmath23 complexes .
studying other structure types that satisfy this property would lead not only to the discovery of new @xmath1 mott insulators but also many other strongly correlated complex fluorides with interesting physical properties .
_ note : _ while this manuscript was under review , we became aware of a study on rucl@xmath14 which also reports a relativistic mott insulating phase in a 4d transition metal halide.@xcite we acknowledge fruitful discussions with n.a .
benedek and o. erten .
t. b. was supported by the rutgers center for materials theory , and k. h. was supported by nsf dmr-1405303 and nsf dmref-1233349 .
41ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1146/annurev - conmatphys-020911 - 125138 [ * * , ( ) ] link:\doibase 10.1103/physrevb.83.205101 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.101.226402 [ * * , ( ) ] link:\doibase 10.1126/science.1251151 [ ( ) , 10.1126/science.1251151 ] link:\doibase 10.1103/physrevlett.111.246402 [ * * , ( ) ] @noop * * , ( ) link:\doibase 10.1103/physrevlett.105.216407 [ * * , ( ) ] link:\doibase 10.1103/physrevb.87.075112 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.101.076402 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.112.016405 [ * * , ( ) ] @noop ( ) link:\doibase 10.1103/physrevlett.109.027204 [ * * , ( ) ] link:\doibase 10.1103/physrevb.85.035101 [ * * , ( ) ] @noop ( ) link:\doibase 10.1103/physrevlett.107.266404 [ * * , ( ) ] @noop ( ) link:\doibase 10.1103/physrevlett.108.247212 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.108.086403 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.106.136402 [ * * , ( ) ] link:\doibase 10.1103/physrevb.43.181 [ * * , ( ) ] http://books.google.com.tr/books?id=ur77aaaaqbaj[__ ] , oxford classic texts in the physical sciences ( , ) @noop _ _ ( , ) @noop * * , ( ) @noop * * , ( ) @noop _ _ , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1103/physrevb.86.125105 [ * * , ( ) ] @noop ( ) @noop * * , ( ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1103/physrevb.81.195107 [ * * , ( ) ] link:\doibase 10.1103/physrevb.82.085111 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.109.157402 [ * * , ( ) ] link:\doibase 10.1103/physrevb.90.041112 [ * * , ( ) ] link:\doibase 10.1103/physrevb.75.155113 [ * * , ( ) ] link:\doibase 10.1103/revmodphys.83.349 [ * * , ( ) ] link:\doibase 10.1103/physrevb.90.075136 [ * * , ( ) ] * supplemental information for + the @xmath1 mott insulating state in rh and ir fluorides " * |
the type - i susy seesaw model can be described by the superpotential : @xmath8 where @xmath9 is the superpotential for the minimal supersymmetric standard model ( mssm ) , @xmath10 are the lepton flavour indices , @xmath11 are the majorana masses of the right - handed singlet neutrinos with generation indices @xmath12 , and @xmath13 , @xmath14 , @xmath15 are the chiral superfields for the right - handed singlet neutrinos , the left - handed lepton doublets and the higgs doublets , with @xmath16 and @xmath17 .
the relevant soft susy - breaking terms are given by @xmath18 the singlet sneutrino and anti - sneutrino states mix , giving rise to the mass eigenstates : @xmath19 where @xmath20 , that correspond to the mass eigenvalues @xmath21
for simplicity , we will concentrate on sl arising from a single sneutrino generation @xmath22 and in what follows we will drop that index .
after superfield phase rotations , we have three independent physical phases , they are @xmath23 eq . ( [ eq : soft_terms ] ) leads to cp asymmetries @xmath24 arising from self - energy diagrams induced by the bilinear @xmath7 term , @xmath25 where @xmath26 is the thermal factor associated to the difference between the phase - space , bose - enhancement and fermi - blocking factors for the scalar and fermionic channels , that vanishes in the zero temperature limit @xmath27@xcite .
regarding the flavour structure of the soft terms relevant for flavoured sl , we can distinguish two general possibilities : \1 . _
universal soft susy - breaking terms_. this case is realized in supergravity and gauge mediated susy - breaking models ( neglecting the renormalization group running of the parameters ) , in our notations corresponds to @xmath28 in this case the only flavour structure arises from the yukawa couplings and both the cp asymmetries @xmath29 and the corresponding washout terms are proportional to the same @xmath30 , resulting in mild enhancement of @xmath31 in efficiency from one - flavour approximation @xcite .
we refer to this case as _ universal trilinear scenario _ ( uts ) .
_ general soft susy - breaking terms_. the most general form for the soft - susy breaking terms is allowed , only subject to the phenomenological constraints from limits on flavour changing neutral currents ( fcnc ) and from lepton flavour violating ( lfv ) processes . to simplify the analysis
while still capture some of the main features of the general case , we choose @xmath32 such that the cp asymmetries become flavour independent , @xmath33 for each flavour . in what follows we will refer to this case as the _ simplified misaligned scenario _ ( sms ) . with this choice , since it is possible to reduce the washout in a particular flavour direction while keeping the corresponding cp asymmetry fixed , a much greater enhancement than the uts becomes possible . in both the uts and sms , from ( [ eq : cpphase1 ] )
, we see that we only have one unique phase @xmath34 .
we numerically solved the relevant boltzmann equations to obtain the final amount of @xmath35 asymmetry generated in the decay of the singlet sneutrinos ( assuming no pre - existing asymmetry ) which can be parametrized as : @xmath36 after conversion by the sphaleron transitions , the final baryon asymmetry is related to the @xmath35 asymmetry by @xmath37 we also define the @xmath38 decay parameter , @xmath39 which is related to the washout parameter @xmath40 as @xmath41 where @xmath42 is the total singlet sneutrino decay width , @xmath43 ( with @xmath44 gev ) , @xmath45 with @xmath46 the total number of relativistic degrees of freedom ( @xmath47 in the mssm ) and @xmath48 the planck mass . in the left panel of fig .
( [ fig : efficiency ] ) , we plot the efficiencies as a function of @xmath49 for both the scenarios uts and sms . deviating from the flavour equipartition case @xmath50 , in the sms
, we can obtain an enhancement up to @xmath6 compared to the one - flavoured approximation . with this enhancement , it is possible to push the values of @xmath7 up to natural values at tev scale for successful leptogenesis as shown in the right panel of fig .
( [ fig : efficiency ] ) . .
right : maximum values of @xmath7 which can lead to successful leptogenesis as a function of @xmath51 and @xmath52 .
the figures correspond to @xmath53=1 tev and @xmath54.,title="fig : " ] .
right : maximum values of @xmath7 which can lead to successful leptogenesis as a function of @xmath51 and @xmath52 .
the figures correspond to @xmath53=1 tev and @xmath54.,title="fig : " ]
as has been highlighted in ref .
@xcite , at sufficiently low temperatures the off - diagonal soft - susy breaking slepton masses can give rise to lepton flavour equilibration ( lfe ) , effectively damping all dynamical flavour effects . in the left panel of fig .
( [ fig : lfe ] ) , we show the dependence of the efficiencies ( normalized to the flavour equipartition case ) on the off - diagonal soft slepton mass parameter @xmath55 which for simplicity , we assume to be flavour independent .
we see that there is a cut - off value of @xmath56 for each @xmath57 such that the enhancement is totally damped out . in the right panel of fig .
( [ fig : lfe ] ) , we show that in most part of the susy parameter space that is relevant for sl , subjecting to low energy constraints , the large flavour enhancements can survive the lfe effects . .
right : excluded region ( shaded in yellow ) of @xmath56 versus @xmath58 arising from the present bound of @xmath59 , together with the minimum value of @xmath56 for which lfe effects start damping out flavour effects . three lines shown corresponds to @xmath60gev , @xmath61gev and @xmath62gev .
the vertical dashed line represents the value of @xmath63 required to explain the discrepancy between the standard model ( sm ) prediction and the measured value of muon anomalous magectic moment @xmath64 @xcite . in the plots , we assume @xmath54.,title="fig : " ] .
right : excluded region ( shaded in yellow ) of @xmath56 versus @xmath58 arising from the present bound of @xmath59 , together with the minimum value of @xmath56 for which lfe effects start damping out flavour effects . three lines shown corresponds to @xmath60gev , @xmath61gev and @xmath62gev .
the vertical dashed line represents the value of @xmath63 required to explain the discrepancy between the standard model ( sm ) prediction and the measured value of muon anomalous magectic moment @xmath64 @xcite . in the plots , we assume @xmath54.,title="fig : " ]
the speaker thanks concha gonzalez - garcia , enrico nardi and juan racker with whom he collaborated with in this work .
he is also grateful to the 2^nd^ young researchers workshop ( in conjuction with xv frascati spring school `` bruno touschek '' ) organizing committee for the hospitality during his stay in beautiful frascati .
y. grossman , t. kashti , y. nir and e. roulet , phys .
* 91 * ( 2003 ) 251801 [ arxiv : hep - ph/0307081 ] .
g. dambrosio , g. f. giudice and m. raidal , phys .
b * 575 * , 75 ( 2003 ) [ arxiv : hep - ph/0308031 ] . c. s. fong and m. c. gonzalez - garcia , jhep
* 0806 * ( 2008 ) 076 [ arxiv:0804.4471 [ hep - ph ] ] .
d. aristizabal sierra , m. losada and e. nardi , jcap * 0912 * , 015 ( 2009 ) [ arxiv:0905.0662 [ hep - ph ] ] . s. davidson , j. garayoa , f. palorini and n. rius , jhep * 0809 * , 053 ( 2008 ) [ arxiv:0806.2832 [ hep - ph ] ] . | successful soft leptogenesis ( sl ) requires a relatively low mass scale for the su(2 ) singlet neutrinos of @xmath0 gev .
however , conventional sl ( unflavoured ) requires an unnaturally small soft supersymmetry(susy)-breaking bilinear @xmath1 coupling for successful leptogenesis . on the other hand ,
in this regime , the interactions mediated by @xmath2 , @xmath3 ( and even @xmath4 ) charged lepton yukawa interactions are in equilibrium , making the lepton number asymmetries and the washouts flavour dependent .
hence , it is crucial to take into account the flavour effects . considering a general soft susy - breaking trilinear @xmath5 couplings
, it is possible to enhance the efficiency up to @xmath6 compared to the unflavoured case . with the enhanced efficiency
, we can raise the @xmath7 up to tev scale for successful leptogenesis .
taking into account the low energy constraints , we verify that the fast lepton flavour violation processes induced by the soft susy - breaking slepton masses would not destroy the enhancement .
= 11.6pt |
it is well - known that the ( co - moving ) space densities of the rarest , most powerful quasars and radio galaxies were much higher at epochs corresponding to @xmath1 than they are now ( longair 1966 ) .
the behaviour of the space density beyond these redshifts is the subject of this paper .
dunlop & peacock ( 1990 ) found evidence for a ` redshift cut - off ' ( a decline in the co - moving space density ) in the distribution of flat - spectrum radio sources over the redshift range @xmath2 . through failing to find any flat - spectrum radio quasars at @xmath3 in a large ( @xmath440 per cent of the sky ) survey ,
shaver et al ( 1996 , hereafter sh96 ) argued for an order - of - magnitude drop in space density between @xmath5 and @xmath6 , for this class of object .
as emphasised by sh96 , the crucial advantage of any radio - selected survey is that with sufficient optical follow - up , it can be made free of optical selection effects , such as increasing dust obscuration at high redshift .
it is chiefly for this reason that the work of sh96 provides the most convincing evidence to date for the existence of an intrinsic decline in the co - moving space density of any galaxy class at very high redshift .
we adopt a parameterisation of the rlf which is separable in 151-mhz luminosity @xmath7 and redshift @xmath8 with a single power - law in @xmath7 of the form @xmath9 .
we consider two cosmologies @xmath10 , @xmath11 ( cosmology i ) and @xmath12 , @xmath13 ( cosmology ii ) .
model a parameterises the redshift distribution as a single power - law of the form @xmath14 . for model
b the redshift distribution is parameterised as a gaussian , giving an overall expression for the co - moving space density of @xmath15 where @xmath16 and @xmath17 are the normalising term and power - law exponent respectively , @xmath18 is the gaussian peak redshift and @xmath19 is the characteristic width of the gaussian .
model c is described by the same model up to @xmath18 beyond which it becomes constant .
for sources in the top - decade in luminosity of the @xmath20 plane ( fig.1 ) our parametric fitting and likelihood analysis of model radio luminosity functions ( table 1 ) show that the data are inconsistent with a @xmath21 power - law in redshift ( model a ) , but are well fitted by both models b and c. these models are shown in fig.@xmath22 in the form of a log@xmath23 / log@xmath24 plot .
we conclude that although the relative likelihood for model b is @xmath25 times larger than for model c , this is not statistically significant enough to distinguish between the two models with any confidence .
this uncertainty is further compounded by the effects of assuming a mean spectral index in the model fitting .
this result is in very close agreement with the rlfs for radio loud quasars modelled by willott et al ( 1998 ) and various studies of agn at optical ( irwin et al 1991 ) and x - ray ( hasinger et al 1998 ) wavelengths .
this is in apparent contradiction to the findings of sh96 for flat - spectrum quasars .
if the relationship between the flat- and steep - spectrum populations is as described by unification models of agn then we might expect to see similar evolution in the two populations .
thus to determine the co - moving space density of radio sources at high - redshift , an understanding of the spectral index trends , @xmath26corrections and associated selection effects must first be achieved .
fig.@xmath22 also illustrates the contribution of powerful sources at high redshift to the total source count in a low - frequency survey .
we see that even for the no cut - off model ( model c ) the fractional contribution is very small .
this may render the location of the redshift cut - off virtually impossible to determine until the selection effects associated with radio surveys are fully understood .
blundell k.m . , rawlings s. , eales s.a . , taylor g.b .
, bradley a.d . , 1998 , mnras , 295 , 265 dunlop , j.s .
& peacock , j.a .
, 1990 , mnras , 247 , 19 eales s.a . , rawlings , s. , law - green , d. , cotter , g. , lacy , m. , 1997 , mnras , 291 , 593 hales , s.e.g . , baldwin , j.e . & warner , p.j .
, 1988 , mnras , 234 , 919 hasinger , g. , 1998 , astron . nachr . , 319 , 37 irwin , m. , mcmahon , r. & hazard , c. , 1991 , in the space distribution of quasars , ed .
crampton , aspcs 21 , 117 laing , r.a .
, riley , j.m .
& longair , m.s . , 1983 ,
mnras , 204,151 longair , m.s . , 1966 , mnras , 133 , 421 mcgilchrist m.m . ,
baldwin , j.e . , riley , j.m . ,
titterington , d.j . ,
waldram , e.m . ,
warner , p.j .
, 1990 , mnras , 246 , 110 shaver , p.a . , wall , j.v . ,
kellermann , k.i . ,
jackson , c.a . , hawkins , m.r.s . , 1996 , nature , 384 , 439 willott , c.j . , rawlings , s. , blundell , k.m . ,
lacy m. , 1998 , mnras , 300 , 625 | we use three samples ( 3crr , 6ce and 6c * ) to investigate the radio luminosity function ( rlf ) for the ` most powerful ' low - frequency selected radio sources .
we find that the data are well fitted by a model with a constant co - moving space density at high redshift as well as by one with a declining co - moving space density above some particular redshift .
this behaviour is very similar to that inferred for steep - spectrum radio quasars by willott et al(1998 ) in line with the expectations of unified schemes .
we conclude that there is as yet no evidence for a ` redshift cut - off ' in the co - moving space densities of powerful classical double radio sources , and rule out a cut - off at @xmath0 . |
our purpose is to provide a description of the semileptonic decays of the tau lepton that incorporates as many theoretical restrictions derived from the fundamental interaction , @xmath0 @xcite , as possible .
this is a very convenient scenario to investigate the hadronization of @xmath0 because one fermionic current is purely leptonic and thus calculable unambiguously so that we can concentrate our efforts on the other one , involving light quarks coupled to a @xmath3 current .
+ the decay amplitude for the considered decays may be written as : @xmath4 where the strong interacting part is encoded in the hadronic vector , @xmath5 : @xmath6 symmetries let us decompose @xmath5 depending on the number of final - state pseudoscalar ( @xmath7 ) mesons , @xmath8 .
+ one meson tau decays can be predicted in terms of the measured processes @xmath9 , since the matrix elements are related .
this provides a precise test of charged current universality @xcite . on the other side
, it can not tell anything new on hadronization . + the two - pion tau decay is conventionally parameterized -in the isospin limit , that we always assume- just in terms of the vector ( @xmath10 ) form factor of the pion , @xmath11 : @xmath12 where @xmath13 .
+ because @xmath14 is broken appreciably by the difference between @xmath15 and @xmath16 , two form factors are needed to describe the decays involving one pion and one kaon : @xmath17 where @xmath18 .
@xmath19 carries quantum numbers @xmath20 , while @xmath21 is the pseudoscalar form factor ( @xmath22 ) .
other two meson decays can be treated similarly and one should take advantage of the fact that chiral symmetry relates some of their matrix elements .
+ for three mesons in the final state , the most general decomposition reads : @xmath23 and @xmath24 @xmath25 , @xmath26 , correspond to the axial - vector current ( @xmath27 ) while @xmath28 drives the vector current ( @xmath29 ) . the form factors @xmath30 and @xmath31 have a transverse structure in the total hadron momenta , @xmath32 , and drive a @xmath33 transition . the pseudoscalar form factor , @xmath34 , vanishes as @xmath35 and , accordingly , gives a tiny contribution .
higher - multiplicity modes can be described proceeding similarly @xcite .
this is as far as we can go without model assumptions , that is , it is not yet known how to obtain the @xmath25 from @xmath0 .
however , one can derive some of their properties from the underlying theory , as we will explain in the following .
we use a phenomenological lagrangian @xcite written in terms of the relevant degrees of freedom that become active through the energy interval spanned by hadronic tau decays .
the chiral symmetry of massless @xmath0 determines @xcite the chiral invariant operators that can be written including the lightest mesons in the spectrum , the pseudoscalar ones belonging to the pion multiplet .
it was carefully checked @xcite that -as one expects- chiral perturbation theory , @xmath36 , can only describe a little very - low - energy part of semileptonic tau decays .
+ then one may attempt to extend the range of applicability of @xmath36 to higher energies while keeping its predictions for the form factors at low momentum : this is the purpose of resonance chiral theory , @xmath37 , @xcite that includes the light - flavoured resonances as explicit fields in the action .
+ at @xmath38 in the @xmath39 limit of @xmath0 @xcite one has as infinite tower of stable mesons that experience local effective interactions at tree level .
we depart from this picture in two ways : * we incorporate the widths of the resonances worked out consistently within @xmath40 @xcite . *
we attempt a description including the least possible number of resonance fields reducing -ideally- to the single resonance approximation , @xmath41 @xcite .
we take vector meson dominance into account when writing our lagrangian .
thus , it will consist of terms accounting for the following interactions ( @xmath42 , @xmath43 stand for the axial(-vector ) currents and @xmath44 and @xmath45 for the axial(-vector ) resonances ) : * those in @xmath36 at @xmath38 and @xmath36-like : @xmath46 , @xmath47 , @xmath48 with even - intrinsic parity ; and @xmath49 in the odd - intrinsic parity sector . * those relevant in @xmath40 -@xmath50 @xmath36 operators are not included to avoid double counting , since they are recovered and their couplings are saturated upon integration of the resonance contributions @xcite- .
they include : @xmath51 , @xmath52 , @xmath53 , @xmath54 and @xmath55 in the even - intrinsic parity sector and @xmath56 , @xmath57 and @xmath58 in the odd - parity one .
the explicit form of the operators and the naming for the couplings can be read from @xcite , @xcite , @xcite , @xcite , @xcite and @xcite .
+ the @xmath40 just determined by symmetries does not share the @xmath59 @xmath0 behaviour yet . for this , and for our purposes , we need to impose appropriate brodsky - lepage conditions @xcite on the relevant form factors .
explicit computation and these short - distance restrictions reduce appreciably the number of independent couplings entering the amplitudes which enables us to end up with a useful -that is , predictive- theory .
our framework describes pretty well the two - meson decays of the @xmath2 , as shown in the @xmath60 @xcite and @xmath61 @xcite cases .
two - meson modes including @xmath62 can be worked analogously .
the data in these modes are so precise that although the @xmath41 describes the gross features of the data , one needs to include the first excitations of the @xmath45 resonances to achieve an accurate description .
although @xmath19 is much more important than @xmath21 , one needs an appropriate pseudoscalar form factor to fit well the data , specially close to threshold @xcite .
+ the three meson modes are much more involved .
however , a good description of the data has been achieved through a careful study @xcite taking into account all theory constrains and experimental data on the @xmath63 and @xmath64 channels .
we predict the @xmath64 spectral function and conclude that the vector current contribution can not be neglected in these modes .
we will study the other three meson modes along the same lines .
in particular , our study of the @xmath65 channels might help improve the simultaneous extraction of @xmath15 and @xmath66 @xcite .
our expressions for the vector and axial - vector widths and the hadronic matrix elements have been implemented successfully in the tauola library @xcite .
this way , the experimental comunity will have as its disposal a way of analysing hadronic decays of the tau that includes as much as possible information from the fundamental theory
. we also plan to study @xmath67 at low energies what can eventually be used by @xcite .
i congratulate the local organizing committee for this first edition of the young researchers workshop as well as for the xiv lnf spring school bruno touschek held in parallel .
i am grateful to jorge portols for a careful revision and useful suggestions on the draft .
i acknowledge useful discussions with olga shekhovtsova . this work has been supported in part by the eu mrtn - ct-2006 - 035482 ( flavianet ) and by the dfg cluster of excellence origin and structure of the universe .
99 h. fritzsch , m. gell - mann and h. leutwyler , phys .
b * 47 * ( 1973 ) 365 .
d. j. gross and f. wilczek , phys .
* 30 * ( 1973 ) 1343 .
h. d. politzer , phys .
lett . * 30 * ( 1973 ) 1346 .
a. pich , nucl .
phys . proc
. suppl .
* 98 * ( 2001 ) 385 .
suppl . *
181 - 182 * ( 2008 ) 300 .
r. fischer , j. wess and f. wagner , z. phys .
c * 3 * ( 1979 ) 313 .
s. weinberg , physica a * 96 * ( 1979 ) 327 .
j. gasser and h. leutwyler , annals phys .
* 158 * ( 1984 ) 142 .
b * 250 * ( 1985 ) 465 .
g. colangelo , m. finkemeier and r. urech , phys .
d * 54 * ( 1996 ) 4403 .
g. ecker , j. gasser , a. pich and e. de rafael , nucl .
b * 321 * ( 1989 ) 311 .
g. ecker , j. gasser , h. leutwyler , a. pich and e. de rafael , phys .
b * 223 * ( 1989 ) 425 .
g. t hooft , nucl .
b * 72 * ( 1974 ) 461 , * 75 * ( 1974 ) 461 .
e. witten , nucl .
b * 160 * ( 1979 ) 57 .
d. gmez dumm , a. pich and j. portols , phys .
d * 62 * ( 2000 ) 054014 .
m. knecht , s. peris , m. perrottet and e. de rafael , phys .
lett . * 83 * ( 1999 ) 5230 .
d. ruiz - femena , a. pich and j. portols , jhep * 0307 * ( 2003 ) 003 .
d. gmez dumm , a. pich and j. portols , phys .
d * 69 * ( 2004 ) 073002 . v. cirigliano , g. ecker , m. eidemller , a. pich and j. portols , phys .
b * 596 * ( 2004 ) 96 .
p. roig , aip conf .
* 964 * ( 2007 ) 40 .
d. gmez - dumm , p. roig , a. pich , j. portols , to appear .
s. j. brodsky and g. r. farrar , phys .
* 31 * ( 1973 ) 1153 .
g. p. lepage and s. j. brodsky , phys .
d * 22 * ( 1980 ) 2157 .
f. guerrero and a. pich , phys .
b * 412 * ( 1997 ) 382 .
a. pich and j. portols , phys .
d * 63 * ( 2001 ) 093005 .
* 121 * ( 2003 ) 179 .
m. jamin , a. pich and j. portols , phys .
b * 640 * ( 2006 ) 176 phys .
b * 664 * ( 2008 ) 78 .
e. gmiz , m. jamin , a. pich , j. prades and f. schwab , phys .
* 94 * ( 2005 ) 011803 .
o.shekhovtsova , private communication . | we study two and three meson decays of the tau lepton within the framework of the resonance chiral theory , that is based on the following properties of @xmath0 : its chiral symmetry in the massless case , its large-@xmath1 limit , and the asymptotic behaviour it demands to the relevant form factors .
+ most of the couplings in the lagrangian are determined this way rendering the theory predictive .
our outcomes can be tested thanks to the combination of a very good experimental effort ( current and forthcoming , at b- and tau - charm - factories ) and the very accurate devoted monte carlo generators .
= 11.6pt |
the authors acknowledge financial support from the agence nationale de la recherche ( anr ) through the @xmath32 ( anr-14-ce32 - 0019 ) and @xmath33 ( anr-2011-emma-0002 ) projects .
a. z. acknowledges financial support from the universit nice sophia antipolis .
f. k. acknolewdges financial support from the foundation simone et cino del duca ( institut de france).the authors would like to thank laurent labont , philippe bouyer , and baptiste battelier for technical support .
0 j. laurat , g. keller , j. a. oliveira - huguenin , c. fabre , t. coudreau , a. serafini , g. adesso , f. illuminati , j. opt .
b * 7 * , s577 ( 2005 ) .
m. bellini and a. zavatta , progr .
optics * 55 * , 41 ( 2010 ) .
u. l. andersen , g. leuchs , and c. silberhorn , laser & photon . rev . * 4 * , 337354 ( 2010 ) .
s. l. braunstein , p. van loock , rev .
phys . * 77 * , 513 ( 2005 ) . n. j. cerf , g. leuchs , e. s. polzik , quantum information with continuous variables of atoms and light , imperial college press ( 2010 ) .
d. gottesman and j. preskill , phys .
a * 63 * , 022309 ( 2001 ) . v. c. usenko and r. filip , new j. phys . * 13 * , 113007 ( 2011 ) .
t. eberle , v. handchen , j. duhme , t. franz , f. furrer , r. schnabel and r. f. werner , new j. phys .
* 15 * , 053049 ( 2013 ) .
l. s. madsen , v. c. usenko , m. lassen , r. filip , and u. l. andersen , nat .
commun . * 3 * , 1083 ( 2012 ) .
p. jouguet , s. kunz - jacques , a. leverrier , p. grangier , and e. diamanti , nat . photon . * 7 * , 378381 ( 2013 )
. h. takahashi , j. s. neergaard - nielsen , m. takeuchi , m. takeoka , k. hayasaka , a. furusawa , and m. sasaki , nat .
photon . * 4 * , 178 181 ( 2010 ) .
d. buono , g. nocerino , a. porzio , and s. solimeno , phys .
a * 86 * , 042308 ( 2012 ) .
s. n. filippov and m. ziman , phys .
rev . a * 90 * , 010301(r ) ( 2014 ) .
m. mehmet , s. ast , t. eberle , s. steinlechner , h. vahlbruch , and r. schnabel , opt .
express * 19 * , 25763 ( 2011 ) .
f. y. hou , l. yu , x. j. jiaa , y. h. zheng , c. d. xie , and k. c. peng , eur .
j. d * 62 * , 433437 ( 2011 ) .
j. zhao , x. m. guo , x.y .
wang , n. wang , y. m. li , k. c. peng , chin .
. lett . * 30 * , 060302 ( 2013 ) . c. baune , j. gniesmer , s. kocsis , c. e. vollmer , p. zell , j. fiurasek , and r. schnabel , e - print arxiv : 1510.00603 ( 2015 ) b. gouraud , d. maxein , a. nicolas , o. morin , and j. laurat , phys .
lett . * 114 * , 180503 ( 2015 ) .
s. tanzilli , a. martin , f. kaiser , m. p. de micheli , o. alibart , and d. b. ostrowsky , laser & photon . rev .
* 6 * , 115 ( 2012 ) .
g. s. kanter , p. kumar , r. v. roussev , j. kurz , k. r. parameswaran , and m. m. fejer , opt .
express * 10 * , 177 ( 2002 ) .
k. yoshino , t. aoki , and a. furusawa , appl .
lett . * 90 * , 041111 ( 2007 ) .
y. eto , t. tajima , y. zhang , and t. hirano , opt .
express * 16 * , 10650 ( 2008 ) .
l. a. ngah , o. alibart , l. labont , v. dauria , s. tanzilli , laser & photon . rev .
* 9 * , l1 ( 2015 ) .
c. weedbrook , s. pirandola , r. garcia - patron , n. j. cerf , t. c. ralph , j. h. shapiro , and s. lloyd , rev .
phys . * 84 * , 621 ( 2012 ) .
g. masada , k. miyata , a. politi , t. hashimoto , j. l. obrien and a. furusawa , nat .
* 9 * , 316 ( 2015 ) .
t. umeki , o. tadanaga , and m. asobe , ieee j. quantum electron .
* 46 * , 1206 ( 2010 ) .
f. kaiser , l. a. ngah , a. issautier , t. delord , d. aktas , v. dauria , m. p. de micheli , a. kastberg , l. labont , o. alibart , a. martin , s. tanzilli , opt .
comm . * 327 * , 716 ( 2014 )
. j. appel , d. hoffman , e. figueroa , and a. i. lvovsky , phys .
a * 75 * , 035802 ( 2007 ) .
s. ast , a. samblowski , m. mehmet , s. steinlechner , t. eberle , and r. schnabel , opt . lett .
* 37 * , 2367 ( 2012 ) .
j. roslund , r. m. de araujo , s. jiang , c. fabre , and n. treps , nat .
* 8 * , 109 ( 2013 ) .
t. hirano , k. kotani , t. ishibashi , s. okude , and t. kuwamoto , opt .
lett * 30 * , 1722 ( 2005 ) .
a. gerthoffer , c. guyot , w. qiu , a. ndao , m .-
bernal , n. courjal , opt . mater . * 38 * , 3741 ( 2014 ) . | we demonstrate , for the first time , the realization of an entirely guided - wave squeezing experiment at a telecom wavelength .
the state generation relies on waveguide non - linear optics technology while squeezing collection and transmission are implemented by using only telecom fibre components .
we observe up to @xmath0db of squeezing emitted at 1542 nm in cw pumping regime .
the compactness and stability of the experiment , compared to free - space configurations , represent a significant step towards achieving out - of - the - lab cv quantum communication , fully compatible with existing telecom fibre networks .
we believe that this work stands as a promising approach for real applications as well as for `` do - it - yourself '' experiments .
generation and manipulation of continuous variable ( cv ) non - classical states of light are the object of intense research due to their importance in both fundamental and applied physics @xcite . among others , a valuable feature of cv quantum resources is that they can be generated in a deterministic way at the output of non - linear optical media @xcite . moreover , cv entanglement is affected but never vanishes completely for any level of external loss @xcite . on these bases
, cv quantum optics has experienced an increasing interest for its application to quantum key distribution ( qkd ) @xcite , with many proposals based on both single - mode @xcite and two - mode squeezed light @xcite .
entanglement distillation and entanglement swapping schemes for long distance quantum communication have been demonstrated @xcite and systematic studies have been performed on the robustness of non - classicality against the communication channel losses @xcite .
+ a further step towards real - world applications of cv quantum communication has been done by generating squeezed light in the telecom c - band of wavelengths , where low - loss optical fibres and high performance standard components are available @xcite . in the perspective of implementing quantum networks that exploit optical fibres to connect distant atomic quantum memories ,
a quantum interface has recently been developed , converting squeezed light from telecom to visible wavelengths compatible with suitable atomic transitions @xcite . in the same spirit , a light - matter interface , coupling light guided in a tapered nanofibre to cold atoms , has been demonstrated @xcite .
+ in this framework , and in order to comply with further out - of - the - lab realizations of cv quantum optics , we demonstrate , for the first time , the feasibility of a full guided - wave approach for both the generation and measurement of squeezed light at a telecom wavelength .
+ in our scheme , single - mode squeezing at 1542 nm is generated by spontaneous parametric down conversion ( spdc ) in a periodically poled lithium niobate ridge - waveguide ( ppln / rw ) . at the output of the ppln / rw
, the non - classical beam is measured with a fibre homodyne detector .
this configuration allows implementing an extremely easy setup , entirely based on commercially available components , and fully compatible with existing fibre networks . on one hand ,
non - linear optics based on waveguide technology offers , compared to bulk implementations , better compactness and stability @xcite , as well as the possibility of efficient spdc in a single pass arrangement @xcite . on the other hand
, the use of off - the - shelf telecom fibre components permits the realization of a simple and plug - and - play setup that requires no alignment effort for spatial mode matching and that can be straightforwardly modified by connecting additional fibre components @xcite .
our approach , by first combining these two technologies and cv quantum optics , paves the way towards the realization of accessible and versatile experiments for cv quantum communication @xcite .
+ eventually , we note that the possibility of miniaturizing cv quantum technologies is at the center of recent investigations , in particular with the demonstration of a photonic chip for _ in situ _ operations on squeezing @xcite . compared to this work
, our paper follows a complementary vision by fully exploiting guided - wave optics for networking between remote quantum sources and nodes .
+ the experimental setup is presented in fig.[setup]-a .
a telecom continuous wave ( cw ) laser at 1542 nm ( _ toptica _ , dl pro , fibre coupled ) is amplified using an erbium doped fibre amplifier ( edfa , keopsys , cefa - c - hg ) and directed towards a 70:30 fibre beam splitter .
the less intense beam is used as the local oscillator ( lo ) for the homodyne detector .
the brighter beam is frequency doubled to 771 nm via second harmonic generation ( shg ) to be subsequently employed as pump field for the spdc process for the squeezing generation .
the shg stage is implemented employing a commercial periodically poled lithium niobate waveguide ( ppln / w , _ hc - photonics _ , efficiency of @xmath1 ) . at its output , frequency doubled light
is directly collected using a single mode fibre .
the beam at 771 nm then passes thought an in - line variable fibre attenuator and is directed towards the spdc stage .
type-0 spdc is obtained in a 4 cm - long commercial ppln / rw working at frequency degeneracy around 1542 nm ( _ nel _ , wh-0770 - 000-f - b - c ) .
we stress that this is , to our knowledge , the first time a ppln / rw is employed for a cv experiment .
the ridge waveguide structure offers a strong light confinement owing to a step index profile and guarantees high conversion efficiency over a large operation bandwidth of operation @xcite . by means of single - photon regime characterization , we estimate an spdc conversion efficiency of @xmath2 photon pairs / mw / ghz / s .
the spdc emission covers a continuous spectral bandwidth of 80 nm fwhm ( see fig.[setup]-b ) , corresponding to 10thz in the frequency domain .
we stress that , as no optical cavity is required to enhance the spdc process , this value represents directly the squeezing bandwidth @xcite .
the ppln / rw input and output facets are connected to polarization maintaining fibres ( pmfs ) , whose coupling with the ridge is optimized by the manufacturer thanks to micro - lenses .
for the input pump beam at 771 nm , we measured a fibre - to - waveguide transmission of @xmath3 . at the output of the ridge waveguide , single - mode squeezed light at 1542 nm
is collected with a measured coupling efficiency @xmath4 and it is directly available at the output of the pmf . to detect it , we send it to a fibre homodyne detector based on a 50:50 fibre beam splitter ( 50:50 f - bs ) followed by two ingaas photodiodes . in order to minimize fresnel reflection losses ,
the outputs of the 50:50 f - bs are spliced to ar - coated fibre optic patchcords .
the measured transmission of the signal path from the pmf output to the homodyne optical outputs is @xmath5 .
+ in addition to the compactness and stability of the setup , a major advantage of guided - wave optics lies in the achievement of a high degree of spatial mode matching between the lo and the signal without optical adjustment at the 50:50 f - bs inputs @xcite .
this huge benefit extremely simplifies the homodyne detector implementation ( see fig . [
setup]-a ) .
moreover , compared to the pulsed regime , cw pumping bypasses the difficulties of obtaining a lo matched with squeezed light in the temporal domain @xcite .
polarization matching is simply obtained by inserting a fibre polarization controller on the lo path .
a home - made fibre stretcher implements the lo phase scanning @xcite . at the 50:50 f - bs outputs , light
is directly sent to two ingaas photodiodes ( _ thorlabs _ , fga10 , without cap ) showing each @xmath6 quantum efficiency at 1542 nm .
the difference photocurrent , obtained by connecting the photodiodes to each other , is amplified by a low - noise home - made transimpedence amplifier with bandwidth of @xmath75mhz .
the noise power is measured for each quadrature phase by an electronic spectrum analyzer ( esa , _ hp _ , esa - l1500a ) set at zero - span around the analyzing frequency . as discussed in @xcite , the observed bandwidth of squeezed states produced by ppln / ws
is ultimately limited by that of the homodyne detection . in our experiment , we chose to work at 2mhz , where for a lo of 6.3mw , we observe a signal - to - noise ratio ( snr ) of 15.6db .
residual electronic noise associated with the detectors affects the measurement as an additional loss and can be taken into account by a factor @xmath8 @xcite .
note that squeezing at the telecommunication wavelength of 1550 nm can be detected over bandwidths of more than 2ghz , by means of ultra - fast detectors and electronics @xcite . in this context
, we recall that the exploitation of broadband squeezing is a key element for quantum channel multiplexing and high - speed quantum communication @xcite .
+ in the presence of losses , the variance of measured squeezed state quadratures , @xmath9 , can be written as @xcite : @xmath10 + 1-\eta , \label{quad}\ ] ] where @xmath11 is the overall detection efficiency . here , the values @xmath12=0 and @xmath12=@xmath13/2 correspond to anti - squeezing and squeezing , respectively . in equation ( [ quad ] ) , the squeezing parameter @xmath14 depends on the spdc pump power as @xmath15 , where @xmath16 is proportional to the crystal length and to the non - linear interaction strength .
+ fig.[sqvspower ] shows squeezing and anti - squeezing ( both in db ) as functions of the pump power at 771 nm .
each point corresponds to an average over several acquisitions with an error of @xmath17db .
data include the effect of imperfect ridge waveguide - to - fibre coupling , propagation losses in the waveguide and in the fibre components , non - unitary detection efficiency , and residual electronics noise .
pump powers reported on the graph are estimated with an error of @xmath18 and refer to inferred values at the ppln / rw input , taking into account the coupling and propagation losses at 771 nm .
different power levels are obtained with the variable attenuator at the shg output . as it can be seen , experimental data for both squeezing and anti - squeezing correctly follow the quadratic behavior predicted by the theory .
this shows , in particular , the absence of unwanted excess noise on anti - squeezed quadratures . by fitting the entire ensemble of data with equation ( [ quad ] ) , we obtain @xmath19mw@xmath20 and an overall detection efficiency @xmath21 .
a comparison of @xmath22 with our estimated detection efficiency , @xmath23 , gives for the propagation losses inside the ridge waveguide @xmath240.4db / cm , in agreement with typical reported values @xcite .
fig.[squeezing ] shows a typical squeezing curve obtained by scanning the phase of the local oscillator overtime .
it corresponds to the highest pump power ( 28mw ) coupled inside the ppln / rw and to a measured squeezing value of @xmath0db , with an anti squeezing of @xmath25db .
we stress that , by correcting the measured values for @xmath26 , we can infer the squeezing at the output of the waveguide to be @xmath7 - 3.3db , which is among the best values reported to date for cw - pumped squeezing @xcite .
a further improvement could be obtained by reducing the propagation losses inside the ppln / rw and by employing detectors with a higher @xmath27 at @xmath71550 nm .
the fabrication of low loss ridge waveguides is at the center of intense investigations with encouraging results leading to propagation losses lower than @xmath28db / cm @xcite . in parallel , detection efficiencies as high as @xmath29 at 1550 nm
have already been demonstrated on custom detectors @xcite .
eventually , the setup performances could be enhanced by improved pumping conditions .
these could be achieved , for example , by implementing another ppln / rw for the shg - stage . this way , higher optical powers at 771 nm could be achieved .
additionally , an improved fibre - to - waveguide coupling at the spdc stage would lead to a greater efficiency for the squeezing generation .
+ let us emphasize that for any application relying on entanglement as a quantum ressource , our setup can be easily modified so as to generate two - mode squeezing .
this can be achieved by mixing the output of two identical ppln / rws at a 50:50 f - bs plugged just before the homodyne detector .
the use of such a fibre component would automatically guarantee the mode - matching conditions for high - visibility quantum interference between the two squeezed states @xcite and will only introduce additional propagation loss typically of @xmath30db . by considering our measured best squeezing level of @xmath0db and based on the duan criterion for cv entanglement
, this would lead to a correlation variance of @xmath31 , which is well below the classical limit and in line with recent experiments showing the on - chip detection of einstein - podolsky - rosen entanglement @xcite .
+ in conclusion , based on advanced waveguide non - linear optics and telecom technology , we have implemented for the first time an entirely guided - wave optical setup allowing both the generation and the detection of single - mode squeezed light at a telecom wavelength .
we observe squeezing levels down to of @xmath0db .
our setup emploies plug - and - play components fully compatible with existing telecom fibre networks and requiring no alignment procedures for spatial mode matching .
these advantages guarantee an extreme reliability and make our approach a valuable candidate for real - world quantum communication based on continuous variable quantum optics . |
empirically the literature reports several behaviors for the income and wealth distributions in different countries .
a century ago , the italian social economist pareto suggested a power - law @xcite distribution in the high - income range , namely , in terms of cumulative distribution : @xmath0 , with @xmath1 being the pareto index @xcite . on the other hand montroll
@xcite suggested a lognormal distribution with power law tail for the usa personal income .
more recently , wealth and income distributions in the usa and in the united kingdom have been described by an exponential distribution with power law high - end tails @xcite . whereas , the japanese personal income distribution appears to follow lognormal distributions also with power law tails @xcite . in some recent papers zipfs law
has also been proposed @xcite . in this paper
we add to the above empirical investigations an analysis of the income distribution in australia ( figure [ f.income ] ) .
> from the theoretical side , it has been shown that pure multiplicative stochastic ( msp ) processes can explain the lognormal income distribution but they fail to explain the power law tails @xcite .
power law tails can be obtained extending msp processes by including -for instance- additive noise and boundary constraints @xcite .
these models explain well the emergence of power law distributions , but they are incomplete , neglecting interactions between agents . hence , msps with interacting agents connected through a network have been developed @xcite .
these models retrieve power law tails with exponents @xmath1 which are related to the network properties . in this paper
, we show that distributions with power law tails can emerge also from additive stochastic processes with interacting agents . in this case , we show that the network of connections among agents plays a crucial role .
indeed , the resulting wealth distribution is shaped directly by the degree distribution of the network .
the original purpose of the present work was not to construct any realistic model for the wealth distribution .
our aim was simply to demonstrate the possibility to obtain ` fat ' tails also without the use of multiplicative stochastic processes .
rather surprising we find out that the results from such an additive process are in good qualitative agreement with the empirical data for the income distribution in australia . [
cols="^,^ " , ]
we have shown that a mechanism of wealth exchange with additive gaussian noise can produce distributions with power - law tails when the network which connects the agents is of a scale - free type . although the original purpose of this work was not to produce a realistic model for the wealth evolution
, we find a good qualitative agreement between the empirical data and the theoretical prediction .
more realistic models will be proposed in future works by introducing also multiplicative stochastic terms and a dynamical evolution in the network connectivity .
t. di matteo wishes to thank the research school of social sciences , anu , for providing the abs data .
this work was partially founded by the arc discovery project : dp0344004 .
we acknowledge the stac supercomputer time grant at apac national facility . | we investigate the wealth evolution in a system of agents that exchange wealth through a disordered network in presence of an additive stochastic gaussian noise .
we show that the resulting wealth distribution is shaped by the degree distribution of the underlying network and in particular we verify that scale free networks generate distributions with power - law tails in the high - income region .
numerical simulations of wealth exchanges performed on two different kind of networks show the inner relation between the wealth distribution and the network properties and confirm the agreement with a self - consistent solution .
we show that empirical data for the income distribution in australia are qualitatively well described by our theoretical predictions .
[ 1999/12/01 v1.4c il nuovo cimento ] |
the @xcite and @xcite _ chandra _ surveys of the nuclear bulgerevealed a large population of weak , hard point - like x - ray sources that could account for up to 10% of the previously observed `` diffuse '' x - ray emission from the nuclear bulge .
numerous studies have tried to characterise these newly discovered x - ray sources of the nuclear bulge surveys based on their x - ray properties .
@xcite suggest that a large fraction may be wind - accreting neutron stars with high mass companions . @xcite and
@xcite propose that they could be white dwarfs accreting from main sequence counterparts ( cataclysmic variables , polars and intermediate polars ) . @xcite and
@xcite believe them to be neutron stars with low mass companions and @xcite have speculated that they could be isolated neutron stars and black holes accreting from the interstellar medium .
however , the weak nature of the sources means that positive identification of the majority of the sources is impossible based solely on the x - ray data .
identification of the stellar counterparts to these x - ray sources we will allow the differentiation between these possibilities .
as shown in @xcite , to identify candidate counterparts to x - ray sources in the nuclear bulge , very high resolutions imaging is required to avoid issues of confusion due to the high stellar density of the region .
in addition to that , the extremely high , variable extinction towards the nuclear bulge requires these observations to be performed in the near - infrared or longer wavelengths .
previously , only the denis and 2mass surveys had observed the nuclear bulge entirely in the near - infrared , however as will be shown , their depth and resolution is insufficient for the purposes of identifying the counterparts to the majority of the nuclear bulgex - ray sources .
the ( united kingdom infrared deep sky survey - galactic plane survey ) ukidss - gps is one of the five near infrared public legacy surveys that are being undertaken by the ukidss consortium , using the wide field camera on the united kingdom infrared telescope @xcite .
surveying the northern galactic plane and the nuclear bulge in @xmath1 , @xmath2 and @xmath3 bands , integration times of 80s , 80s and 40s respectively achieve median 5-@xmath4 depths of @xmath5 , @xmath6 and @xmath7 ( vega system ) for the most recent data release 2 ( dr2 ; * ? ? ?
the resolution of the ukidss - gps observations are 0.2 , an order of magnitude better than the 2mass survey , with a similar positional accuracy of @xmath8 . in the nuclear bulge
, the crowding of this extremely dense stellar region coupled with the high level of intervening extinction reduces the completion limit of the survey to @xmath9 , @xmath10 and @xmath11 with detection limits of @xmath12 , @xmath13 and @xmath14 . despite this
, the @xmath15 region shown in figure [ f : nbimage ] contains @xmath16 point sources . as
such it is the first survey covering the entire nuclear bulge to have the resolution and depth to allow the identification of candidate counterparts to the majority of the nuclear bulge x - ray sources .
we used the topcat program to identify candidate counterparts to the x - ray sources .
we used a larger @xmath17 positional error for the ukidss - gps nuclear bulge source positions , than the stated accuracy of @xmath18 , to account for the confusion in the nuclear bulge caused by the very high stellar density .
the `` out - of - the - box '' _ chandra_positional error is @xmath19 , though this can be considerably larger ( up to @xmath20 ) in some cases due to image distortion in the outer regions of the _ chandra _ array and/or to the very low s / n of the faintest sources detected . for the purpose of this study , we discarded all x - ray sources for which the x - ray positional errors were greater than @xmath21 radius ; for error circles greater than this size , the number of candidate counterparts is sufficiently high ( 5 - 30 stars ) to render meaningless any attempt at astrometric matching between the near - infrared and x - ray catalogs .
we used the @xmath17 positional error for the ukidss - gps source positions , along with the derived positional errors from the @xcite and @xcite x - ray source catalogues to set a maximum separation of @xmath22 between and x - ray source and a star that can be considered a match .
[ cols="^ , > , > , > , > , > " , ] [ t : ncounterparts ] of the 4256 x - ray sources in the @xcite catalogues , 3963 x - ray sources have positional errors of less than @xmath21 . from these , we found 3076 candidate counterparts to 1963 of the x - ray sources .
there are 1368 x - ray sources with only one candidate counterpart , 341 with two candidate counterparts , 151 with three and 103 with 4 or more candidate counterparts .
table [ t : ncounterparts ] gives a breakdown of the numbers of counterparts for x - ray sources with error circles of @xmath23 , @xmath24 and @xmath25 .
as can be seen , for x - ray sources with positional errors of @xmath26 , the majority of these have only one candidate counterpart , whereas those with @xmath24 errors have a slightly larger proportion with 2 candidate counterparts . as might be expected , it is the sources with the larger error circles , @xmath25 , which have a much larger proportion with multiple candidate counterparts .
figure [ f : xrscolmag ] shows colour magnitude diagrams ( cmds ) of the candidate counterparts compared to a representative sample of nuclear bulge stars from the ukidss - gps dr2 catalogue . from the diagrams it can be seen that the x - ray sources follow the general trend of the overall stellar distribution but with some differences to their specific distribution .
for instance , the cmds containing @xmath1-band data reveal a high proportion of the candidate counterparts to be in the local , main - sequence arm of the cmds .
the majority of the remaining candidate counterparts in all three cmds are consistent with red giants at a galactic centre distance with variable levels of extinction ( see poster contribution by gosling et al . for details of the nuclear bulgeextinction ) .
figure [ f : xrscolmag ] also demonstrates the increase in candidate counterparts that occurs when sources with photometry in the @xmath2 and @xmath3-band is compared to those for which there is photometry in all 3 or @xmath1 and @xmath2-bands .
there is a large amount of extinction towards the nuclear bulge ( see additional poster contribution of gosling et al . for further details ) , this extinction has a greater effect on shorter wavelengths and so is most likely to obscure a source in the @xmath1 band .
this is also apparent in the increase in sources being predominately those with large values of @xmath27 indicating high levels of extinction .
identifying the candidate counterparts to the nuclear bulge x - ray sources is only the first step in understanding this population . to better understand them
, it will be necessary to identify the true companion to each of the x - ray sources where possible . in order to do this ,
we intend to search for accretion signatures in the candidate counterparts .
we are undertaking a narrow - band brackett-@xmath28 ( br-@xmath28 , a known accretion signature ) imaging survey of the nuclear bulge to identify sources with br-@xmath28excess , and will also follow - up the candidate counterparts with near - infraredmulti - object spectroscopy using the flamingos-2 instrument soon to be commissioned on gemini south .
we will also compare our catalogue of candidate counterparts to the _ spitzer _ catalogue of point sources of @xcite to increase our wavelength coverage of these sources and to identify those with spectra indicating that they are likely to be in accreting or x - ray emitting systems .
we have presented an initial matching of the source positions of the _ chandra _ nuclear bulge surveys of @xcite and @xcite to the new ukidss - gps near - infrared survey of the nuclear bulge . in doing so ,
we have identified candidate counterparts to @xmath29 of the x - ray sources in this extremely crowded and heavily extincted region .
we show that these candidate counterparts are consistent with the overall stellar distribution of observations towards the nuclear bulge although the relative proportions of the populations are different .
candidate counterparts that are observed in the @xmath1-band have a higher tendency to be foreground sources and those observed only in the @xmath2 and @xmath3-bands are more likely to be nuclear bulge sources .
this is most likely to be an effect of the high levels of extremely spatially variable extinction ( see additional poster contribution by gosling et al . for further details ) towards the nuclear bulge .
further observations including narrow - band br-@xmath28 imaging and near - infraredspectroscopy using the flamingos-2 instrument as well as comparison to other datasets such as the _ spitzer _ observations of the nuclear bulge will be used to better identify the true companions to these x - ray sources and so gain an understanding as to the nature of the nuclear bulge x - ray source population . | we present an initial matching of the source positions of the _ chandra _ nuclear bulge x - ray sources to the new ukidss - gps near - infrared survey of the nuclear bulge .
this task is made difficult by the extremely crowded nature of the region , despite this , we find candidate counterparts to @xmath0 of the x - ray sources . we show that detection in the @xmath1-band for a candidate counterpart to an x - ray source preferentially selects those candidate counterparts in the foreground whereas candidate counterparts with only detections in the @xmath2 and @xmath3-bands are more likely to be nuclear bulge sources .
we discuss the planned follow - up for these candidate counterparts . |
fmi acknowledges the support by conacyt ( mexico ) grant no . 34668-e .
w. wang , f.m . izrailev and g. casati ,
phys . rev . *
e 57 * , 323 ( 1998 ) ; f. borgonovi , i. guarneri and f.m .
izrailev , phys . rev . * e 57 * , 5291 ( 1998 ) ; l. meza - montes , f.m .
izrailev , and s.e .
ulloa , phys .
. sol . * 220 * , 721 ( 2000 ) ; g.a.luna-acosta , j.a.mndes-bermdez , and f.m.izrailev , phys .
a. , * 274 * , 192 ( 2000 ) ; l. benet , f.m .
izrailev , t.h .
seligman and a. suarez moreno , phys .
a. * 277 * , 87 ( 2000 ) . | a novel approach is suggested for the statistical description of quantum systems of interacting particles .
the key point of this approach is that a typical eigenstate in the energy representation ( shape of eigenstates , se ) has a well defined classical analog which can be easily obtained from the classical equations of motion .
therefore , the occupation numbers for single - particle states can be represented as a convolution of the classical se with the quantum occupation number operator for non - interacting particles .
the latter takes into account the wavefunctions symmetry and depends on the unperturbed energy spectrum only . as a result ,
the distribution of occupation numbers @xmath0 can be numerically found for a very large number of interacting particles . using the model of interacting spins
we demonstrate that this approach gives a correct description of @xmath0 even in a deep quantum region with few single - particle orbitals .
2 in many physical systems such as complex atoms , heavy nuclei and interacting spins , highly excited eigenstates in the unpertured many - particles basis can be treated as a chaotic superposition of a very large number of components , for a relatively strong interaction among particles ( see , e.g. @xcite ) .
this fact has been used in @xcite in order to develop a statistical description of closed systems with a finite number of fermi - particles . in particular
, it was analytically shown that for a strong enough interaction , a smooth dependence of occupation numbers on the energy occurs , which is related to global properties of chaotic eigenstates . as is known , the direct numerical computation of excited eigenstates is strongly restricted due to a very large number of many - particles states , which grows extremely fast with the number of particles . however , the mean values of occupation numbers turn out to depend on the average shape of chaotic eigenstates in the unperturbed basis , not on exact , specific values of their components @xcite . in this letter
we develop a novel approach to quantum systems with chaotic behaviour in the classical limit .
this approach takes into account both the chaotic properties of the classical system , and the specific features of the unperturbed single - particle spectrum . as a result
, one can avoid diagonalization of hamiltonian matrices of a huge size which may be practically unfeasible .
this kind of approach can be applied to generic hamiltonian systems with two - body interaction of the type : @xmath1 here @xmath2 describes @xmath3 _ non - interacting _ particles with @xmath4 as single - particle hamiltonians , and @xmath5 stands for a long - range two - body interaction between the particles . in what follows , we assume that the single - particle spectrum is determined by a finite number @xmath6 of single - particles energies @xmath7 , @xmath8 ; however , the approach is valid for more generic systems with an infinite spectrum .
the unperturbed hamiltonian @xmath2 determines the many - particle states @xmath9 ( with @xmath10 , @xmath11 as creation - annihilation operators ) , that form the basis in which the exact eigenstates of @xmath12 are represented . as usual , we assume that the basis is ordered according to increasing unperturbed energy values @xmath13 .
the distribution of occupation numbers ( don ) for single - particle states is defined by the relation , @xmath14 where @xmath15 is the occupation number operator giving the occupation numbers @xmath16 equal to @xmath17 or @xmath18 for fermi - particles , and to @xmath19 for bose - particles .
these numbers @xmath20 indicate how many particles in a many - particle _ basis _ state @xmath21 , occupy a particular single - particle state @xmath22 . correspondingly
, the occupation numbers @xmath23 give the probability that one of @xmath3 particles in a many - particle _ exact _ state with the _ total _ energy @xmath24 , occupies a particular single - particle state @xmath22 .
the total number @xmath25 of many - body states equals @xmath26 for fermi and @xmath27 for bose - particles .
one should note that while in the above expression for the don , the eigenfunctions @xmath28 depend on the total hamiltonian @xmath12 , the term @xmath20 depends on the unperturbed spectrum only .
this fact is crucial for our semiquantal approach . due to the chaotic structure of exact eigenstates
, one can make an average of the don over a small energy window @xmath29 around the fixed value @xmath24 .
this averaging procedure is similar to that used in the conventional statistical mechanics developed for systems with a finite number of particles in contact with a heat bath , or for isolated systems of an _ infinite _ number of _ non - interacting _ particles .
expression ( [ nqu ] ) for the mean values @xmath23 can be considerably simplified by introducing the so - called _ shape of eigenfunctions _ , se ,
( envelope of eigenstates in energy representation ) .
the form of the se has been studied in details both in the model with random two - body interaction @xcite , and in dynamical models of interacting particles @xcite .
the introduction of the average quantity se ( thus neglecting correlations between different components @xmath28 ) represents the key point of our approach .
we assume that the unperturbed many - body energy spectrum has an intrinsic degeneracy .
this situation is typical for spin systems , and is more complicated in comparison with those studied before @xcite .
below we show how this difficulty can be overcome .
let us redefine the state @xmath30 by means of a indexes pair @xmath31 , where @xmath32 labels the `` unperturbed energy '' @xmath33 of the many - body state , while @xmath34 labels its degeneracy @xmath35 .
if there are @xmath36 different `` unperturbed '' energies , one can write , @xmath37 , therefore , one has , @xmath38 according to standard definition@xcite , the se is given by : @xmath39 by substituting @xmath40 with @xmath41 as an average over @xmath42 , we obtain an approximate expression for the don in terms of the se , @xmath43 needless to say , if an unperturbed spectrum has no degeneracy , eq.([crus ] ) can be written in a similar way by taking an average over a small window of energy around @xmath33 .
as one can see , expression ( [ crus ] ) depends on two terms of different nature .
the first one , @xmath44 , refers to the unperturbed many - particle spectrum and reflects the specific properties of a single - particle spectrum , as well as quantum features related to fermi - dirac or bose - einstein statistics .
in contrast , the second term , @xmath45 , refers to global properties of eigenstates and describes _ interaction _ effects .
therefore , the basic idea of our semiquantal " approach is to substitute the latter term ( se ) by its classical analog which can be easily found from classical equations of motion .
classical analogs of the se have been studied in different models , see , for example , @xcite ) . in practice
, one has to derive the distribution @xmath46 for the probability to find the unperturbed energy @xmath47 for @xmath2 , given the conserved total energy @xmath24 .
this can be obtained by generating many different initial classical configurations on the energy surface @xmath48 or sampling the @xmath49 values generated by one single trajectory onto the energy surface and computing the correspondent distribution of @xmath50 @xcite .
the two procedures have been found to give the same results in the chaotic region@xcite . in order to facilitate the comparison with the quantum se , in our numerical simulations the bin size of @xmath47
equals the energy distance between neighbour values of @xmath33 . in the same way
one can define the classical distribution of occupation numbers , @xmath51 ( see also @xcite ) . for the quantum - classical comparison ,
the bin size of @xmath52 is taken to be equal to the spacing between close single - particle energy levels @xmath7 .
let us stress that in this semiquantal approach ( sa ) it is possible to study specific systems of , let us say , @xmath53 interacting particles occupying @xmath54 single - particle levels .
surely , one expect this approach to be valid for highly excited chaotic states in a deep semiclassical region .
however , by direct numerical simulations we have found that the sa gives correct results even for energy values close to the ground state .
the model that we have studied , consists of @xmath3 3-d interacting spins placed in a magnetic field @xmath55 directed along the @xmath56-axis . in order to have a proper many - body operator one should require a coupling between _ all spins _ ( not only between neighbors ) .
the hamiltonian thus reads , @xmath57 using the well known relations @xmath58 , one can write , @xmath59 + & \\
+ \frac{1}{4}(j_x - j_y ) \sum\limits_{i=1}^{n-1 } \sum\limits_{j = i+1}^{n } [ s_i^+ s_j^+ + s_i^- s_j^- ] + & \\ \frac{1}{4 } ( j_x+j_y ) \sum\limits_{i=1}^{n-1 } \sum\limits_{j = i+1}^{n } [ s_i^+ s_j^- + s_i^- s_j^+ ] \label{h00 } \end{array}\ ] ] in the mean field approximation , we put @xmath60 .
the interaction can be further simplified by the particular choice @xmath61 .
thus , our hamiltonian @xmath62 has the following form , @xmath63 .
\label{h0}\ ] ] for simplicity , the @xmath3 classical constants of motion @xmath64 have been set to 1 , therefore , the only free classical parameters are the total conserved energy @xmath24 and the interaction @xmath65 .
the classical model has been studied in @xcite and it was numerically found to be chaotic and exponentially unstable in a wide energy range .
more precisely , in order to have strong chaos , one needs the interaction @xmath65 between particles to be strong enough .
a convenient choice is to take the interaction strength @xmath66 .
one should stress that this situation is the most difficult for theoretical studies , see discussion in @xcite .
quantization follows the standard rules , which gives , @xmath67 and @xmath68 with @xmath69 .
the action of creation and annihilation operators is defined by : @xmath70 where @xmath71 are the non - symmetrized states ( first quantization states ) .
there are @xmath72 single - particle energy levels @xmath73 with @xmath74 .
therefore , the unperturbed many - particle energy spectrum consists of a number of degenerate levels with the spacing equal to @xmath75 .
note , that both the ground state @xmath76 and the upper level @xmath77 are non - degenerate .
the classical limit is recovered when spins are allowed to have any possible orientation , that is @xmath78 , and @xmath79 .
the choice we have done ( @xmath61 ) allows to reduce the dimension of the hilbert space by , approximately , one half .
this happens because the operator @xmath5 in ( [ h0 ] ) connects only those unperturbed many - body states that are separated by the spacing @xmath80 . in what follows
, we consider the subset of the many - body states containing the ground state . from these states
we construct the completely symmetrized states @xmath81 ) , in the second quantization , can be written as : @xmath82 with @xmath83 here @xmath84 , with @xmath85 and @xmath86 the creation - annihilation operators satisfying the standard relation @xmath87= \delta_{hk}$ ] .
as to the coefficients @xmath88 , @xmath89 , they have quite complicated expressions ; however , they can be easily computed numerically .
the procedure we have used in our numerical simulations consists of the following steps : a ) compute the classical values @xmath90 , and @xmath91 as described above ; b ) compute the quantum values @xmath90 and @xmath91 by diagonalization of the total hamiltonian ( [ cal0 ] ) ; c ) compute @xmath90 and @xmath91 by using the semiquantal approximation according to expression ( [ crus ] ) .
the results for the don are summarized in fig.[n4 ] . for the convenience of comparison , symbols refer to the quantum and sa results , while the classical data are presented as hystograms , .
note , that each particle can have energy within the interval @xmath92 $ ] . in order to make the quantum - classical comparison as close as possible
, we took the classical bin size equal to @xmath75 .
all distributions have been normalized in such a way that @xmath93 . in cases (
a ) and ( b ) we choose the same energy , close to the ground state and two different @xmath94 values . in ( c ) and
( d ) instead , we choose a higher energy value .
the latter case ( ( c ) and ( d ) ) should describe a situation more classical than the former ( higher energy should correspond to higher temperature ) .
one can see that , while classical and quantum data only disagree in the _ deep _ quantum region ( a ) ( energy close to the ground state and small @xmath94 ( _ big _
@xmath75 ) ) , there is a very nice correspondence between quantum and sa data in all cases ( including region ( a ) ) .
this nice correspondence is far from trivial since sa does not take into account quantum correlations inside exact eigenstates , together with possible correlations between the two terms , @xmath95 and @xmath96 in expression ( [ nquan ] ) , both expected to be strong in the deep quantum region .
it is very interesting to explore the occurence of the bose - einstein ( be ) distribution in our model .
a similar problem has been studied in detail for the model of two - body random interaction @xcite where the conditions for the appearence of fermi - dirac distribution have been found for few interacting fermi - particles . by assuming , a priori , the validity of the be - distribution @xmath97^{-1}$ ] in our closed system
, one can find the temperature " @xmath98 and the chemical potential " @xmath99 via the standard relations , @xmath100 here @xmath101 is the numerically computed energy obtained from the single - particle quantum distribution ( see details in @xcite ) , and @xmath3 is the number of particles . notice that , due to interaction , @xmath102 .
the comparison between be and sa distributions are shown in fig.2 .
as one can see , even for relatively small @xmath103 , the distribution @xmath90 can be closely approximated by be - distribution .
this confirms the expectation that a strong enough interaction between particles can play the role of an internal heat bath @xcite .
therefore , the standard quantum distributions can be used , with a corresponding renormalization of the energy @xmath101 ( see details in @xcite ) .
thus in our model there is no need to increase further the number of particles , since even for @xmath103 a remarkable agreement with be distribution has been found .
we would like to stress that an exact quantum treatment of the last example calls for a diagonalization of a huge matrix of size @xmath104 , while , with the semiquantal approach , all computations required few minutes on a standard portable pc . in conclusion , we suggest an effective semiquantal approach to closed systems of interacting particles , based on the chaotic structure of eigenstates . in this approach
, the computation of the distribution of occupation numbers can be easily performed by making use of the classical analog of the shape of eigenstates in the unperturbed many - particle basis .
we demonstrate the effectiveness of this approach using the model of 3-d spins with anisotropic ising interaction .
the data show that semiquantal computations give results which are very close to the exact ones . |
experiment e864 at brookhaven has a quite comprehensive set of measurements which addresses the topic of coalescence of multibaryon states in heavy - ion collisions at ags energies .
these include measurements of stable light nuclei from mass number @xmath4=1 ( including the first measurement of neutrons in an ags au+pb or similar system ) up to @xmath4=7 .
in addition , we have measured production of the strongly decaying states @xmath1 and @xmath2 and the hypernucleus @xmath3 . with this set of measurements we can systematically examine the dependences of production of coalesced states on kinematic variables and collision centrality as well as on the mass number , spin , isospin , and strangeness content of the state .
only for the lighter states ( @xmath5 ) do we currently have sufficient statistics to study the kinematic and centrality dependences of production . in figure [
fig : temp_vs_mass ] we display inverse slope parameters for protons , deuterons , and @xmath6 nuclei as a function of mass number .
these slope parameters are determined from boltzmann fits in transverse mass within the rapidity range from 2.2 to 2.4 and are shown both for 10% most central events and more peripheral events .
polleri et .
@xcite have demonstrated that such trends in the temperature parameters of light nuclei are sensitive to both the spatial profile of coalescing nucleons and to the flow profile of the source .
our reach in mass up to @xmath4=3 is then very useful in untangling these two profiles .
if we focus only on a narrow slice in transverse momentum at @xmath7=100 - 200 mev / c , we can examine the yields of these light nuclei as function of rapidity .
we find that the invariant yields are concave in shape ( i.e. are lowest at midrapidity and increase toward beam rapidity ) and that the relative concavity increases as we move to nuclei with higher masses .
this can be understood as an effect of longitudinal flow or incomplete stopping .
these and other trends in these lighter nuclei are explored much more fully in @xcite .
we now focus only on 10% most central events and on a kinematic region around @xmath8=1.9 , @xmath7=200 mev / c and explore the dependences of production on properties of the nuclei . to start simply , we plot in figure [ fig : adep ] the invariant yields in this narrow kinematic region as a function of mass number @xmath4 for @xmath0 .
we see that over almost ten orders of magnitude , the yields are well described by a simple exponential dependence ; implying that to add a nucleon to a cluster , one pays a penalty factor of approximately 48 .
there are small deviations from this trend , and we next move to trying to explain those . two dependences that are apparent are the spin and isospin dependences of the yields . examining the ratios of invariant yields for @xmath9 , @xmath10 and @xmath11 near this same kinematic range , we find that @xmath9 and @xmath10 are consistent with a value of approximately 1.2 while the @xmath11 ratio is nearer to 0.3 .
the neutron , proton , triton , and @xmath6 are all spin @xmath12=1/2 , while @xmath13 is @xmath12=0 and @xmath14 is @xmath12=1 .
we take this as evidence that the yields of these nuclei include a dependence of @xmath15 ( with @xmath16 ) where the first term accounts for the neutron to proton ratio at freeze - out and the second term is for the spin degeneracy of the state as is generally included in coalescence models .
we next take these measured invariant yields from figure [ fig : adep ] and divide them by @xmath17 to remove these dependences on mass number , spin , and isospin of the states .
we then look for any other trends in these corrected yields .
in fact , we do see such a trend when we plot these ratios as a function of binding energy per nucleon as shown in figure [ fig : bind ] .
this binding energy per nucleon is defined as the sum of all the masses of the constituent nucleons of a state less the nuclear mass all divided by the number of nucleons .
we note the low temperature parameter of 6 mev that we extract from this fit ( strongly decaying states were not included in determining the fit ) .
it is possible then that this represents some final freeze - out of the nucleons at a much lower temperature than kinetic freeze - out , or it is possible that this is evidence of some other trend that coincidently shows up as a correlation with this binding energy .
we are also exploring other possible correlations such as with nuclear size .
to complement these measurements of stable light nuclei , we have made measurements of strongly decaying nuclei and the hypernucleus @xmath3 .
because these analyses both involve states which decay at most centimeters from our target ( and therefore have decay products which are indistinguishable in our apparatus from particles originating from the target ) , they proceed along similar lines .
the measurements are made in each case by identifying both of the decay products in our apparatus .
when a pair of decay products is found in an event , an invariant mass for the pair is calculated and placed in a histogram of pair invariant masses . to mimic and subtract away the background , pairs consisting of one decay product from one event and the second from a separate event
are put though this same process , producing a second invariant mass histogram .
the properly normalized difference of these two histograms should then be the signal under study as shown in figure [ fig : h3l ] ( see @xcite and @xcite for details ) . with this method we measure @xmath2 ( @xmath1 ) through its decay to @xmath18 . on a gross scale ,
the invariant yields of these states sit closely along the trend shown in figure [ fig : adep ] .
but on closer inspection in figure [ fig : bind ] , the yields for these states sit lower by a factor of 2 to 4 than the trend set by the stable light nuclei . perhaps still more interesting
is the absence of any signal for the @xmath19 16.7 mev excited state from its decay to @xmath20 . from the absence of a signal
, we set the 90% confidence level upper limit on production of this state as shown in figures [ fig : adep ] and [ fig : bind ] .
note that if we assume that the ground state production sits at its most probable value from our measurement , then this upper limit implies an upper limit for an excited state temperature of 15 mev in a simple thermal picture ; this is consistent with measurements @xcite made at the lower energies of gsi and possibly indicative @xcite of the same final - state interactions that may give rise to the the trend seen in figure [ fig : bind ] . after the analysis of nearly 2/3 of the relevant data
, we observe a signal for @xmath3 at approximately the @xmath21 level .
when our analysis is complete , we expect if this is indeed a signal that with improved analysis methods and the use of the full statistics we will observe a signal at approximately the @xmath22 level .
we measure a preliminary invariant multiplicity for @xmath3 in the kinematic range @xmath23 of @xmath24 @xmath25 .
we can then extract a total penalty factor for adding a unit of strangeness in this kinematic range by taking the ratio of the @xmath3 invariant yield to that of @xmath6 in the same kinematic region .
this gives a penalty factor of @xmath26 @xmath27 .
some of this penalty is simply due to the fact that it is harder to get the all ingredients of a @xmath3 close enough in momentum space to coalesce than is the case for @xmath6 .
we can remove this part of the penalty factor by normalizing each of these yields to the product of the invariant yields of their ingredient baryons in the relevant kinematic ranges . using results from e891 for the @xmath28 yields and e864 measurements for the remaining quantities ,
we obtain @xmath29 as a preliminary result .
this then represents a penalty of approximately 6 for coalescing a strange as opposed to a non - strange state ; we note that this was predicted to be equal to 1 @xcite .
by our measurements of light nuclei with @xmath5 we can study trends in light nuclei production as a function of kinematics and centrality . in 10% central collisions in a limited kinematic range
, we can explore dependences of production on mass , spin , isospin , strangeness , and potentially binding energy of the state up to mass number @xmath30 .
an interestingly low excited state temperature of less than 15 mev is implied by our upper limit on production of @xmath19 , and our measurement of @xmath3 implies a larger than expected strangeness penalty factor .
9 a. polleri et .
al . , phys .
b. , 419 ( 1998 ) 19 .
george , proceedings of park city conference , january 1999 .
proceedings of aps heavy - ion symposium , 1999 .
world scientific .
proceedings of aps heavy - ion symposium , 1999 . world scientific . v. serfling et .
al . , phys . rev .
lett . , 80 ( 1998 ) 3928 .
a. j. baltz et .
al . , phys .
b. , 382 ( 1996 ) 35 . | we present measurements of the production of stable light nuclei for mass number @xmath0 , of strongly decaying states @xmath1 and @xmath2 and of the the hypernucleus @xmath3 .
we also examine trends in the production of these multibaryon states as a function of kinematic variables and properties of the states including strangeness content . |
ic 2554 is a southern galaxy with a peculiar optical appearance .
it is also known as se 72/1 ( srsic 1974 ) , eso 092-ig012 , and iras 100756647 .
1 shows a deep optical image of ic 2554 ( laustsen , madsen & west 1987 ) revealing many bright knots as well as a network of dust lanes intersecting the main body of the galaxy .
the optical extent of ic 2554 is 325 ( see table 1 ) .
its irregular and asymmetric appearance has prompted the division into multiple components , roughly aligned north - south .
lauberts et al .
( 1978 ) describe ic 2554 as a ` fox - shaped ' system with a complex spiral pattern .
they distinguish three components : two central condensations separated by 18 with optical velocities of 1230 and 1310 kms@xmath6 and a detached arm or satellite to the north ( 1190 kms@xmath6 ) .
corwin et al . ( 1985 ) describe ic 2554 as a colliding pair ( ic 2554a and b , 08 apart ) with plumes .
laustsen et al .
( 1987 ) describe ic 2554 as a very disturbed pair of galaxies with a large number of emission nebulae , indicating high activity of star formation .
lauberts ( 1982 ) and laustsen et al .
( 1987 ) note ic 2554 as possibly disturbed by the elliptical galaxy ngc 3136b ( eso 092-g013 ) . but
ic 2554 has also been classified as a peculiar barred spiral galaxy ( de vaucouleurs et al .
1991 ) , where the northern spiral arm appears elongated .
high - resolution hi observations ( presented here ) are needed to study the gas dynamics of this complex system and distinguish between the numerous scenarios .
close to ic 2554 ( see fig . 2 ) are three known galaxies : the elliptical galaxy ngc 3136b ( 1780 kms@xmath6 ) , the faint spiral eso 092-g009 and the galaxy rkk 1959 . for a summary of various optical properties of ic 2554 and
the neighbouring galaxies see table 1 . | atca hi and radio continuum observations of the peculiar southern galaxy ic 2554 and its surroundings reveal typical signatures of an interacting galaxy group .
we detected a large hi cloud between ic 2554 and the elliptical galaxy ngc 3136b .
the gas dynamics in ic 2554 itself , which is sometimes described as a colliding pair , are surprisingly regular , whereas ngc 3136b was not detected . the hi cloud , which emerges from ic 2554 as a large arc - shaped plume , has a size of @xmath0 kpc , larger than that of ic 2554 .
the total hi mass of the ic 2554 system is @xmath1 m@xmath2 , a third of which resides in the hi cloud .
it is possible that tidal interaction between ic 2554 and ngc 3136b caused this spectacular hi cloud , but the possibility of ic 2554 being a merger remnant is also discussed .
we also detected hi gas in the nearby galaxies eso 092-g009 and rkk 1959 as well as an associated hi cloud , atca j10066710 .
together they have an hi mass of @xmath3 m@xmath2 .
another new hi source , atca j10076659 , with an hi mass of only @xmath4 m@xmath2 was detected roughly between ic 2554 and eso 092-g009 and corresponds to a face - on low surface brightness dwarf galaxy .
star formation is evident only in the galaxy ic 2554 with a rate of @xmath54 m@xmath2yr@xmath6 .
galaxies : individual ( ic 2554 , ngc 3136b , eso 092-g009 , rkk 1959 ) galaxies : interactions |
in 1964 gell - mann and zweig independently proposed a quark model in which all known hadrons were described as bound states of only three fundamental particles @xcite .
each of these spin-1/2 particles , which gell - mann named quarks , has their corresponding antiparticles . however , a precise mechanism of the bound states and quark confinement has still not been established .
gell - mann s model requires that the valid quark states should be colorless and so a free quark is not allowed . since a free single quark has not yet been observed , the model assumes that quarks appear as bound states .
the baryons are bound states of three quarks ( or antiquarks ) and the mesons are made up of one quark and one antiquark . as a model , to describe this behavior , one can think of a hadron as a cavity in which the quark wave function is confined , and the cavity is surrounded by the qcd vacuum @xcite . therefore in a simple model quarks confined in a sphere with radius @xmath6 and the dirac equation
sould be solved within this sphere . from this point of view
, the solution of the dirac equation in a three - dimensional scalar potential , apart from its interesting theoretical aspects , provide useful tools for studying the properties of elementary particles .
for example , the mit bag model @xcite and its charily invariant versions , such as the chiral bag model @xcite and the cloudy bag model @xcite , are some models for describing the physics of the nucleon and other baryons .
a bag is a region of space in which quarks and gluons are confined , i.e. they are forced by an external constant pressure b , which can be fitted using experimentally determined hadron masses , to move only inside the bag .
historically , chodos _ et .
have considered the mit bag model through the dirac equation ( except the bag pressure b ) @xcite .
they solved bag equations for the massless dirac fields in three space dimensions .
their solutions are for the special case of static spherical boundary .
they also computed charge radius and found it to be 1.0 fm .
al . _ , in the other case of this model , calculated the masses and the static parameters of the light hadrons @xcite . in the cloudy bag model a baryon is treated as a three - quark bag that is surrounded by a cloud of pions .
thomas _ et . al .
_ investigated the static properties of the nucleon within this model @xcite .
they found the bag radius to be about 0.8 fm by a fit to pion - nucleon scattering in the ( 3,3)-resonance region .
the chiral bag model for the nucleon is a hybrid of quark and meson degrees of freedom , interpolating the two limits of the skyrme model at @xmath7 and the mit bag model at @xmath8 @xcite . in the skyrme model mesons acts as gauge particles so that baryons would interact with each other by the exchange of mesons @xcite .
skyrmions are the solutions of the field equations
. these solutions are solitons and no longer plain wave .
one may interpret these skyrmions as coherent states of baryons and excited baryons @xcite ; however , the physical interpretation is still not completely resolved . with this model ,
it is also possible to calculate nucleon masses and other particle properties @xcite .
both the mit bag and skyrme model are useful to calculate masses and other properties of hadrons . in ref .
@xcite , hosaka and toki investigated the static properties of the nucleon such as masses and magnetic moments as a function of @xmath6 , in both the original chiral bag model and models with vector mesons .
the mit bag model introduces many free parameters for energy corrections that could be helpful in understanding the physical processes inside the nucleus .
it is a curious and complex situation to solve the relativistic quantum mechanics problems in a finite potential in comparison with the equivalent problem in nonrelativistic quantum mechanics . in the dirac equation , the wave function is continuous , its first derivative is discontinuous and the second derivative has a very large jump , whereas , in the schrdinger equation the wave function and its first derivative are continuous , but the second derivative has a certain jump related to the potential jump .
the solutions of the dirac equation in a @xmath9 potential exist in the literature , see for example @xcite .
however , for a finite spherical potential well , as far as we are aware of , there is no solution in the literature . in this paper
, we consider the solution of the dirac equation in a spherically symmetric scalar potential well , which is not necessarily infinite .
the origin of this scalar potential could be a strong force that binds quarks together in clusters to make more familiar subatomic particles , such as protons and neutrons .
it also holds together the atomic nucleus and underlies interactions between all particles containing quarks @xcite .
although this model is not compatible with the quark confinement at finite potential , it could serve a dual purpose .
first , one could observe the evolution of the wave functions as @xmath10 , where one could recover the mit bag model results .
second , for finite values of @xmath11 this could serve as an effective model for the nucleus where @xmath5 is the effective single particle potential emerging from the meson exchange of the nucleons . here
we obtain eigenvalue equations for the energies and numerically calculate the energy eigenvalues for the @xmath1 and @xmath3 states .
these states are derived normally from the continuity of the wave function and imposing boundary conditions on the cavity @xcite , with different radii @xmath12 fm and the quark masses @xmath13 @xmath14 .
we then , compare the values of the energy levels in each of specific conditions and also with the energy eigenvalue obtained in the previous mit bag model .
the relation between energy eigenvalues and the radius of cavity and the mass of the quark is considered .
we also obtain the dirac wave function components for a quark particle and depict them in figures . as a result ,
when the strength of the potential is increased , the wave function components on the boundary of cavity fall down and it would have the sharper point , which are in good agreement with the mit bag model . finally , we obtain the magnitude of sharpness of the relativistic wave function component when crossing the wall . the paper is organized as follows : section [ sec2 ] is devoted to an introduction of the dirac equation with a central scalar potential . in sec
[ sec3 ] we calculate the energy eigenvalues for a dirac particle in a scalar potential with full spherical symmetry for the @xmath1 and @xmath3 states .
then we discuss about the sharpness of the wave function components on the boundary
. finally in sec [ sec4 ] we summarize our results .
in the dirac equation , the scalar potential @xmath15 and the fourth component of a vector potential , @xmath16 are accompanied by mass @xmath17 and energy @xmath18 , respectively .
although @xmath16 is not a vector potential , since it is the fourth component of a four vector , it is called a vector potential .
the general form of the equation of motion for a spin-@xmath19 particle with these two potential is ( in relativistic units , @xmath20 and @xmath21 ) @xmath22\psi ( x , t ) = i\frac{\partial } { { \partial t}}\psi ( x , t),\ ] ] where @xmath23 is the three - dimensional momentum operator . in the above equation @xmath24 and @xmath25
are the @xmath26 dirac matrices which , in the usual representation , are given by @xmath27 where @xmath28 is the @xmath29 unit matrix .
the subscript @xmath30 can take the values of 1,2,3 , and @xmath31 are the @xmath29 pauli matrices . for a dirac particle in a spherically symmetric potential field , the total angular momentum operator @xmath32 , and the spin - orbit matrix operator @xmath33 , commute with the dirac hamiltonian . here
@xmath34 is the orbital angular momentum .
the complete set of the conservative quantities with their eigenvalues can be written as follows : @xmath35 so that , @xmath36 = 0,\qquad\left [ { h,{j } } \right ] = 0,\qquad \left [ { j^2 , j_3 } \right ] = 0,\qquad\left [ { { j},k } \right ] = 0,\ ] ] @xmath37 therefor the quantum number @xmath38 is a nonzero integer number .
given stationary solutions @xmath39 , we have @xmath40 where @xmath41 and @xmath42 are real square - integrable functions , and @xmath43 and @xmath44 can be written in terms of the spherical harmonic functions with the relevant clebsch - gordan coefficients .
then the two coupled equations for the radial parts of the dirac equation with a given scalar potential turn out to be , @xmath45 the solutions of eqs .
( [ 7 ] ) and ( [ 7.1 ] ) for a scalar potential well , @xmath46 and @xmath47 , are the spherical bessel functions and modified spherical bessel functions of the first kind , for the regions @xmath48 and @xmath49 , respectively
. therefore for region i , @xmath50 with @xmath51 , and we have [ 8 ] @xmath52 and for region ii , @xmath49 with @xmath53 , [ 10 ] @xmath54 where @xmath55 and @xmath56 , and @xmath57 , and @xmath58 are the normalization factors @xcite .
in this section we compute the energy eigenvalues for a dirac particle in a full spherically symmetric scalar potential .
reported eigenvalues , for which the massless spin-@xmath19 field is confined to an infinite spherical potential well of radius @xmath59 fm , are listed in table [ table1 ] .
these values have been computed through an equation of motion and boundary conditions @xcite . | in this paper we investigate a solution of the dirac equation for a spin-@xmath0 particle in a scalar potential well with full spherical symmetry .
the energy eigenvalues for the quark particle in @xmath1 states ( with @xmath2 ) and @xmath3 states ( with @xmath4 ) are calculated .
we also study the continuous dirac wave function for a quark in such a potential , which is not necessarily infinite .
our results , at infinite limit , are in good agreement with the mit bag model .
we make some remarks about the sharpness value of the wave function on the wall .
this model , for finite values of potential , also could serve as an effective model for the nucleus where @xmath5 is the effective single particle potential . : 12.39.-x , 03.65.pm |
let @xmath0 be a qbf in _ prenex cnf ( pcnf ) _ where @xmath1 with @xmath2 is the prefix containing quantified propositional variables @xmath3 and @xmath4 is a quantifier - free cnf . given a pcnf @xmath0 , an _
unsatisfiable core ( uc ) _ of @xmath5 is an unsatisfiable pcnf @xmath6 such that @xmath7 and @xmath8 .
the prefix @xmath9 is obtained from @xmath10 by deleting the quantified variables which do not occur in @xmath11 .
a _ _ minimal unsatisfiable core ( muc ) _ _ of @xmath5 is an unsatisfiable core @xmath12 of @xmath5 where , for every @xmath13 , the pcnf @xmath14 is satisfiable . _
incremental solving _ is crucial for the computation of mucs in the context of propositional logic ( sat ) , e.g. @xcite .
modifications of a cnf by adding and deleting clauses in incremental solving are typically implemented by _ selector variables _ and _ assumptions _ @xcite .
an added clause @xmath15 is augmented by a fresh selector variable @xmath16 so that actually @xmath17 is added . via the solver api
, the user assigns these variables as assumptions under which the cnf is solved to control whether a clause is effectively present in the cnf .
different from the assumption - based approach , the sat solver zchaff @xcite provides an api to modify the cnf by adding and removing _ groups _ ( sets ) of clauses .
clauses are associated with an integer i d of the group they belong to . in assumption - based incremental
solving , clause groups may be emulated by augmenting all clauses in a group by the same selector variable .
the user must specify the necessary assumptions via the api in all forthcoming solver invocations to enable and disable the right groups .
in contrast to that , zchaff allows to delete groups by a single api function call . in terms of usability , we argue that incremental solving by a clause group api is less error - prone , more accessible to inexperienced users , and facilitates the integration of the solver in other tools .
we present a novel clause group api of our qbf solver depqbf ( version 4.0 or later ) in the style of zchaff .
different from zchaff , we implemented clause groups based on selector variables and assumptions to combine the conceptual simplicity of zchaff s api with state of the art assumption - based incremental solving . as a novel feature of our api , the handling of selector variables and assumptions
is entirely carried out by the solver and is hidden from the user .
our approach is applicable to any sat or qbf solver supporting assumptions .
based on the novel clause group api of depqbf , we implemented a tool to compute mucs of pcnfs , a problem which has not been considered so far .
results on benchmarks used in the qbf gallery 2014 illustrate the applicability of the clause group api for muc computation of pcnfs .
depqbf is a solver for pcnfs based on the qbf - specific variant of the dpll algorithm @xcite with learning @xcite . since version 3.0 @xcite
, depqbf supports incremental qbf solving via an api to add and remove clauses in a stack - based way ( cf .
fig . 3 in @xcite ) .
this api is suitable for solving incremental encodings where clauses added most recently tend to be removed again in subsequent solver calls , like reachability problems such as conformant planning @xcite or bounded model checking @xcite .
the new clause group api of depqbf , however , allows to add and delete clauses _ arbitrarily _ , which is necessary for the incremental computation of mucs of pcnfs .
we first present our novel approach to keeping selector variables invisible to the user , which is a unique feature of depqbf . to this end , we distinguish between selector variables and variables in the encoding .
let @xmath18 be a sequence of pcnfs .
we consider variables over which the pcnfs @xmath19 are defined as _ user variables _ because they are part of the problem encoding represented by @xmath20 . when solving @xmath20 incrementally , _
selector variables _ used to augment clauses in @xmath19 are not part of the original encoding .
variables @xmath21 are stored in an array @xmath22 indexed by an integer i d @xmath23 of @xmath21 such that @xmath24 = v$ ] .
user and selector variables reside in separate sections of @xmath22 : | we consider the incremental computation of minimal unsatisfiable cores ( mucs ) of qbfs . to this end , we equipped our incremental qbf solver depqbf with a novel api to allow for incremental solving based on clause groups .
a clause group is a set of clauses which is incrementally added to or removed from a previously solved qbf .
our implementation of the novel api is related to incremental sat solving based on selector variables and assumptions .
however , the api entirely hides selector variables and assumptions from the user , which facilitates the integration of depqbf in other tools .
we present implementation details and , for the first time , report on experiments related to the computation of mucs of qbfs using depqbf s novel clause group api . |
the total amount of emitted fluorescence light in a shower is a very good approximation to the total number of charged particles @xmath0(@xmath1 ) , where @xmath1 is the atmospheric depth . in this sense
the number of particles at shower maximum can serve as an estimator of the shower energy .
the total energy that goes into electromagnetic charged particles is obtained by integration of the shower longitudinal profile @xmath2 where @xmath3 is the average ionization loss rate and the integral on the right - hand side represents the total track length of all charged particles in the shower projected onto the shower axis . as an alternative proposal @xcite the electromagnetic energy
can also be calculated by using the fluorescence light intensity and the fluorescence efficiency , without the obligation to reconstruct the number of particles as a function of the atmospheric depth .
such approach is taken as a very precise measurement of the primary shower energy because it is supposed to be weakly dependent of the simulation models and the primary particle type .
however , when details of the shower development are taken into account the calorimetric measurement can lead to high systematic uncertainties .
a not less important concern is that the fluorescence efficiency as a function of air pressure , density and humidity is only known up to a certain extent .
according the approach given by equation [ eq : eem ] , the average ionization loss rate is used in the air shower reconstruction and hence the energy spectrum of the electron in the shower must be known via monte carlo simulation .
although the electrons and positrons constitute the majority of the charged particles in a shower and contribute most to the fluorescence light , an important fraction of the shower energy is carried by particles which are invisible to fluorescence telescopes .
such `` missing energy '' is estimated using monte carlo air shower simulation and contributes to the uncertainties involved in this method , being sensitive to the primary composition .
theoretical works have shown the existence of a clear relation between the primary energy and the maximum number of particles in the shower . recently , alvarez - muiz et al .
@xcite have studied the @xmath4 shower quantity as an estimator of the primary shower energy , confirming the efficiency of this technique .
however , telescopes particularities and reconstruction procedures must be considered due to the introduction of biases and fluctuations in the calculation of @xmath4 .
we explore the possibility of estimating the primary shower energy using the @xmath5 shower quantity for the hires @xcite and euso @xcite fluorescence experiments , i.e. , ground and space based experiments , respectively .
the telescopes particularities and the reconstruction procedures are included in our analysis , predicting more realistic results .
the importance of the fluorescence technique in measuring air showers has been demonstrated along the years by the fly s eye and hires collaboration and now is also being successfully used by the pierre auger observatory @xcite , all ground based experiments . at the same time , projects are under development and intend to use the fluorescence approach from space observatories . in such projects , fluorescence telescopes would be installed at the international space station or in satellites which would increase by at least a factor of 10 the aperture reached by the current ground based telescopes . in this work
we study the possibility of using the @xmath5 parameter as an estimator of the primary energy , employing hires and euso telescopes as case studies to test its quality in two different setups : ground and space based experiments . the hires telescope specifications were considered and simulated in complete accordance with @xcite .
the program explained in reference @xcite has been used again to obtain the comparisons between our simulations and the hires data and simulations .
such program scheme was adapted to mimic in details the euso telescope according to the technical configuration given in @xcite .
the longitudinal air shower profiles were generated by corsika @xcite and conex @xcite simulators . from the obtained longitudinal particle profiles
the number of fluorescence photons can be calculated and propagated to the telescopes , being in agreement to the general procedure specified in @xcite .
once the simulation of the shower and the telescopes has been done , the shower longitudinal profile is reconstructed in the standard procedure @xcite .
the number of fluorescence photons measured as a function of time is converted to the number of particles as a function of depth and then a gaisser - hillas profile is fitted .
one of the parameters fitted in the gaisser - hillas function was @xmath4 .
only showers which survived the hires - ii cuts as published in @xcite were used in the following analysis .
the euso collaboration has not defined quality cuts yet and therefore we have imposed very loose ones requiring total path length greater than @xmath6 and greater than 200 g/@xmath7 and @xmath8 in the field of view of the telescope .
we have simulated 100 showers with corsika for energies varying from @xmath9 to @xmath10 ev for the hires analysis and with conex for energies varying from @xmath11 to @xmath12 ev for the euso .
each shower was used 50 times by drawing a different geometry . for the hires calculations
we have randomly distributed the showers with zenith angle smaller than 60@xmath13 over an area with radius of 50 km . for the euso calculations we have drawn core positions in a circle with radius of 430 km and zenith angle smaller than @xmath14 .
[ fig : nmax ] illustrates on the left hand the @xmath4 distribution as simulated by the monte carlo program and the distribution of the same reconstructed quantity on the right hand .
one can easily verify how the detection and reconstruction procedures distort the distribution producing a wider distribution and a shift in the values . any reconstruction method based on @xmath4
should take these biases into account .
[ fig : en : nmax : hi ] shows the relation between the primary energy simulated by the monte carlo schemes for the hires and euso telescopes specifications with the average reconstructed @xmath4 .
the small error bars show the one sigma confidence level for the @xmath4 distribution .
the relation between @xmath4 and energy in fig .
[ fig : en : nmax : hi ] can be well fitted by a straight line @xmath15 the values of _ a _ and _ b _ parameters were determined to be @xmath16 and @xmath17 , respectively , for the hires experiment and @xmath18 and @xmath19 for the euso telescope .
using equations [ eq : en : nmax ] and [ eq : en : nmax ] ( with the a and b parameters as given above ) we simulated a second set of showers and reconstructed the energy using both procedures : a ) the standard integral of the gaisser - hillas profile ( integral ) and b ) the @xmath4 relation ( equation [ eq : en : nmax ] ) .
[ fig : en ] illustrates the error distributions related to the energy reconstruction obtained by using the @xmath4 relation and the integral procedure for the hires experiment , for proton - induced showers at @xmath20 ev . for the hires telescopes
the reconstruction error was calculated to be around 20% at @xmath20 ev reducing to 15% above @xmath21 ev . to this range of energy
the @xmath4 reconstruction showed an average reconstruction error 1.5% smaller than the integral procedure .
[ fig : erro : en ] shows the dependence of the energy reconstruction as a function of energy for the euso telescope . for energies below @xmath22
the reconstruction error related to the @xmath4 method was smaller .
however , for higher energies , the euso telescope is able to detect the entire development of the shower leading to a good fit of the gaisser - hillas at all depths and a better efficiency of the energy reconstruction .
this paper was partially supported by the brazilian agencies cnpq and fapesp .
f. sanchez thanks iag / usp for its hospitality and infn / unimi for the funding support .
most of simulations presented here were carried on a cluster linux tdi , supported by laboratrio de computao cientfica avanada at universidade de so paulo . | the fluorescence technique has been successfully used to detect ultrahigh energy cosmic rays by indirect measurements .
the underlying idea is that the number of charged particles in the atmospheric shower , i.e , its longitudinal profile , can be extracted from the amount of emitted nitrogen fluorescence light .
however the influence of shower fluctuations and the very possible presence of different nuclear species in the primary cosmic ray spectrum make the estimate of the shower energy from the fluorescence data analysis a difficult task .
we investigate the potential of shower size at maximum depth as estimator of shower energy .
the detection of the fluorescence light is simulated in detail and the reconstruction biases are carefully analyzed .
we extend our calculations to both hires and euso experiments .
this kind of approach is of particular interest for showers that are not fully contained inside the field of view of the detector . |
in the yang - mills theory ghost field lagrangian does nt possess gauge symmetry and together with a gauge fixing term breaks gauge invariance of the effective action .
it makes problems for regularization and renormalization of the theory .
the slavnov - taylor identities are more complicated then the ward identities in electrodynamics . recently a new formulation of the yang - mills theory
was proposed @xcite in which the gauge invariance is broken only by the gauge fixing term . in the paper @xcite it was shown that in the framework of perturbation theory this model is equivalent to the usual yang - mills theory . calculating the observables in this model one can pass to the lorentz - type gauge in which the renormalizability is evident .
nevertheless a proof of renormalizability directly in the gauge proposed in the paper @xcite is absent . in the present paper we calculate at one - loop the gauge field and @xmath2-vertex renormalization constants .
it is shown that a relationship between this constants is the same as in the ordinary yang - mills theory .
let introduce notations .
the lagrangian proposed in @xcite looks as follows @xmath3 the fields @xmath4 , @xmath5 are commuting complex @xmath6-doublets and @xmath7 , @xmath8 are anticommuting ones .
@xmath10 is the covariant derivative ; @xmath11 are pauli matrices .
the yang - mills lagrangian is @xmath12 , @xmath13 .
let introduce the fields @xmath14 , @xmath15 . in terms of these fields
the gauge transformation leaving the lagrangian ( [ l_origin ] ) invariant is @xmath16 being quantized in the lorentz gauge @xmath17 the model is described by the effective action which contains the gauge fixing term and non gauge invariant faddeev - popov ghost lagrangian .
however in this model the lorentz invariant condition @xmath18 is also an admissible gauge . in this case
the gauge invariance is broken by only the gauge fixing term : @xmath19 , here @xmath20 is the lagrangian ( [ l_origin ] ) .
the lagrangian ( [ l_origin ] ) at the surface @xmath18 looks as follows @xmath21 the propagators and vertices are given in the appendix .
we start with considering the gauge field renormalization constant @xmath1 and @xmath2-vertex renormalization constant @xmath0 and show that in the one - loop approximation these constants coincide with the corresponding ones in the ordinary yang - mills theory .
we also consider anticommuting fields renormalization constant @xmath22 and @xmath23-vertex renormalization constant @xmath24 and show that the relationship @xmath25 holds in one - loop approximation .
the calculations can be found in the appendix .
the dimensional regularization is used , hence all tadpole diagrams are equal to zero .
the constant @xmath1 renormalizes the transversal part of one - particle irreducible diagrams with two external gauge field lines @xmath26 .
there are three types of the contributions to the divergent part of the corresponding diagrams .
the first one is a contribution of gauge field @xmath26 loops .
this contribution is the same as in the ordinary yang - mills theory , because the vertices @xmath2 , @xmath27 and the propagators coincide with the usual ones .
the second one is the contribution of loops with commuting scalar fields @xmath28 , @xmath29 .
and the third one is the contribution of loops with anticommuting fields @xmath7 , @xmath8 .
the sum of the second and the third contributions equals to @xmath30 in the ordinary yang - mills theory divergent part of faddeev - popov ghosts loop is the following @xcite , @xcite .
@xmath31 one can see that transversal parts of ( [ z2_sumcommanticomm ] ) and ( [ z2_fpghosts ] ) coincide . as it was mentioned above the contributions of gauge field @xmath26 loops in the present theory and in the yang - mills theory
coincide and therefore constants @xmath1 coincide too . note that contrary to the standard formulation of the yang - mills theory the radiative corrections generate also renormalization of the longitudinal part of the polarization operator , that is the counterterm proportional to @xmath32 . such a counterterm does not break the gauge invariance , because it originates from the admissible gauge invariant counterterm @xmath33 after the shift @xmath34 .
the constant @xmath0 performs renormalization of @xmath2-vertex .
again there are three types of contributions .
contribution of the gauge field @xmath26 loops coincide with the corresponding one in the ordinary yang - mills theory . in one - loop approximation
the total contribution of commuting scalar fields @xmath28 , @xmath29 and anticommuting fields @xmath7 , @xmath8 is equal to @xmath35 it coincides with the contribution of faddeev - popov ghosts in the ordinary yang - mills theory and therefore the constant @xmath0 equals yang - mills constant @xmath0 .
thus in one - loop approximation the constants @xmath1 , @xmath0 are the same as in the yang - mills theory and therefore the expression @xmath36 is the same as in the yang - mills theory . @xmath37 which means that the model is asymptotically free . to find the constants @xmath22 , @xmath24 ,
it is necessary to calculate the divergent part of the diagrams represented on fig .
[ fig_z2bar ] , [ fig_z1bar ] . performing the calculations we obtain @xmath38 thus @xmath39 .
in the present paper it was shown that the theory with the gauge invariant ghost lagrangian agrees with the standard yang - mills theory in one - loop approximation . the relationship @xmath40 between renormalization constants which is one of the necessary conditions of gauge invariance of renormalized lagrangian holds
. a complete renormalization of the theory requires further investigation .
* acknowledgements * + i am grateful to a.a .
slavnov for useful discussion and remarks .
99 a.a.slavnov , a lorentz invariant formulation of the yang - mills theory with gauge invariant ghost field lagrangian , jhep 08(2008)047 l.d.faddeev,a.a.slavnov gauge fields .
introduction to quantum theory .
second edition .
addison - wesley publishing company 1991 .
chapter 4 .
m.e.peskin , d.v.schroeder an introduction to quantum field theory .
addison - wesley publishing company 1995 .
chapter 16 .
here we present the calculations of the commuting scalar fields @xmath28 , @xmath4 and anticommuting fields @xmath7 , @xmath8 loops contributions to the divergent part of the gauge field two - point green function . for calculation of commuting scalar fields contribution
it is necessary to find divergent part of two diagrams which are represented at the fig .
[ fig_z2commute ] . left diagram ( fig .
[ fig_z2commute ] ) gives the following integral .
@xmath41 it is easy to see that the right diagram at fig .
[ fig_z2commute ] coincides with the left diagram after the change @xmath42 , @xmath43 , @xmath44 and consequently it gives the same result .
therefore the total commuting scalar fields contribution is @xmath45 now let us find the anticommuting fields contribution .
we calculate divergent part of diagrams shown at fig .
[ fig_z2anticommute ] . for the first diagram ( fig .
[ fig_z2anticommute ] ) we have @xmath46 one can see that the remaining diagrams have identical divergent parts .
furthermore sum of these divergences is equal to the divergence of the first diagram .
therefore the total anticommuting fields contribution is @xmath47 summarizing ( [ app_z2_commute ] ) and ( [ app_z2_anticommute ] ) we find @xmath48
now we calculate the contribution of the commuting scalar fields @xmath28 , @xmath4 and the anticommuting fields @xmath7 , @xmath8 into divergent part of the gauge field three - point green function .
the contribution of commuting fields @xmath28 and @xmath29 loops is given by the sum of six diagrams one of which is represented at fig .
[ fig_z1commute ] and other five diagrams differ from this one by permutation of vertices .
the diagram at fig .
[ fig_z1commute ] gives @xmath49 contributions of five remaining diagrams can be obtained from formula ( [ z1_commute1of6 ] ) .
for example if we replace @xmath50 , @xmath51 , @xmath52 , @xmath53 in this formula , we obtain the divergent part of the diagram which differs by permutation of two bottom vertices . summarizing all six we obtain @xmath54
now let us consider the loops of the anticommuting fields @xmath7 and @xmath8 .
corresponding diagrams are presented at fig .
[ fig_z1anticommute ] . vertices @xmath55 ,
@xmath56 , @xmath57 differ from each other only by tensors @xmath58 , @xmath59 , @xmath60 correspondingly . for the top and bottom diagrams we obtain correspondingly @xmath61
so these diagrams give the same results .
in addition one can see that each remaining diagrams give the same result too .
so we have to calculate divergent part of the first diagram at fig . [ fig_z1anticommute ] and multiply it by eight
. @xmath62 the total contribution of the anticommuting fields loops and loops of the fields @xmath28 , @xmath29 is @xmath63
now we calculate the constants @xmath64 , @xmath65 .
let us consider the one - loop diagram at fig .
[ fig_z2bar ] .
the corresponding integral is equal to @xmath66 this divergence is canceled by the following counterterm : @xmath67 to find the constant @xmath24 one has to calculate the sum of divergent parts of diagrams which are presented at fig .
[ fig_z1bar ] .
besides the presented diagrams there are the diagrams with three vertices , but their divergent parts are equal to zero . for the left diagram at fig .
[ fig_z1bar ] we obtain the following integral .
@xmath68 for the right diagram on fig . [ fig_z1bar ]
we obtain @xmath69 summarizing the results ( [ z1bar_left ] ) and ( [ z1bar_right ] ) one gets @xmath70 this divergencies are canceled by counterterm @xmath71 . | one - loop calculations of renormalization constants @xmath0 , @xmath1 in the model , proposed in the paper @xcite with gauge invariant ghost field lagrangian are performed .
it is shown that the model is asymptotically free and the renormalization constants satisfy the same equation as in the ordinary yang - mills theory . |
supersymmetric yang - mills quantum mechanics ( symqm ) provides the quantitative model of m - theory @xcite . even though much simpler than the original theory the model
is not solved in spite of its long history@xcite .
we have therefore decided to set up a systematic lattice survey of symqm beginning with the simplest case of @xmath1(quenched)@xcite and gradually extending it as far as possible towards the bfss limit _
i.e. _ @xmath2 and @xmath3 . in this talk
i will report on the second step along this programme : the first results for higher n will be presented .
the action of the symqm reads @xmath4 where @xmath5 , and all fields are independent of the space coordinates @xmath6 .
the supersymmetric fermionic partners belong to the addjoint representation of su(n ) . the discretized system is put on a @xmath7 dimensional hypercubic lattice @xmath8 which is reduced in all space directions to @xmath9 , @xmath10 .
the gauge part of the action has now the usual form s_g=-_m=1^n_t _
> 1n re ( u_(m ) ) , [ sg ] with = 2n / a^3 g^2 , [ beta ] and @xmath11 , @xmath12 , where @xmath13 denotes the lattice constant and @xmath14 is the gauge coupling in one dimension .
the integer time coordinate along the lattice is @xmath15 .
periodic boundary conditions @xmath16 , @xmath17 , guarantee that wilson plaquettes @xmath18 tend , in the classical continuum limit , to the appropriate components @xmath19 without the space derivatives .
up to date we have addressed the two problems : 1 ) extracting the continuum limit from the lattice data , and 2 ) the search for the nontrivial phase structure .
the first point is essential in any approach based on the discretization . in particular restoration of the continuum supersymmetry , of the full unquenched model ,
may crucially depend on the ability to control the continuum limit .
the second issue is connected to the problem of the bekenstein - hawking entropy which has an elegant solution in the framework of m - theory @xcite .
namely the supersymmetric , extremal black holes found in the latter can be viewed as composed of the elementary d0 brane excitations , providing the statistical interpretation of the area of the `` schwarzschild '' horizon which is known to behave as an etropy . in particular , the theory also predicts existence of the two phases in which the gravity and the elementary d0 branes provide good description respectively@xcite .
we have found in @xcite that the continuum limit of the model can be readily extracted with the bare parameters scaling with canonical dimensions .
this is expected for the one dimensional system . to search for the phase transition we have studied the distribution of the eigenvalues of the polyakov line @xmath20 , which is a very sensitive determinant of the phase structure in gauge theories .
it was found that , similarly to the large volume qcd , in the low temperature phase the eigenvalues are concentrated around zero , while at high temperature the distribution is peaked around @xmath21 which constitute the center of su(2 ) . in the space
extended theories the @xmath22 symmetry is spontaneously broken in the infinite volume limit and only one direction is populated . in the present 0-volume system , this may happen only in the infinite - n limit , the gross - witten model being a known example of the critical behaviour emerging at large n.
for higher groups we find now the same behaviour , see fig.1 . since @xmath23 , the histograms correspond to the low and high temperature regions for a range of @xmath24 .
evidently they change from convex to concave at some critical value of @xmath25 similary to the n=2 case .
the nature of the transition is not resolved yet .
nevertheless , our data show unambiguously that the system behaves differently in both regions .
for example , we have also measured the dependence of the size of the system , @xmath26 , on the temperature , and found that it is definitely different , and the change in the behaviour occurs at the same t where the distributions in fig .
1 change their shapes .
it is also possible , for the first time to confront the n dependence of the transition temperature with theoretical expectations .
it follows from eq.([beta ] ) and @xmath27 , that the t hooft scaling @xmath28 implies that the lattice coupling @xmath29 at fixed @xmath30 .
fig.2 shows the @xmath24 dependence of @xmath31 for available range of n together with the fit of the first @xmath32 correction .
indeed , the reduced critical coupling seems to saturate towards higher n and one can estimate that @xmath33 result is within @xmath34 15% of the @xmath35 one ( a horizontal line ) .
we have also studied the new , noncompact formulation of the model which has better numerical behaviour @xcite . in this approach
the @xmath36 spatial degrees of freedom are noncompact @xmath37 and are defined at the discrete time intervals , while the temporal one remains compact @xmath38 .
the action @xmath39 reads @xmath40 the covariant finite difference along the time direction @xmath41 takes into account the parallel transport between adjacent lattice sites .
this system has the same local gauge invariance as the compact version , eq.([sg ] ) . with the new action
we have extended previous study to higher dimensions , d=6 and d=10 .
preliminary simulations confirm results found for d=4 . in particular
the average size of the system @xmath42 shows a characteristic break in the temperature dependence at the position consistent with the t hooft scaling .
moreover , the @xmath42 decreases with d in agreement with the mean field results @xcite .
quantitative lattice study of the yang - mills quantum mechanics , and possibly the m - theory , have just begun .
quenched results are encouraging , but a lot remains to be done .
simulations work for all interesting values of the dimension @xmath7 and are feasible for a range of n. recent results give us a rough idea how the large n limit is approached and where the asymptotics sets it .
all quenched simulations performed up do date indicate existence of the two regions at finite temperature .
this intriguing correspondence with the predictions of the m - theory should be further quantified .
of course , the next step is to include the dynamical fermions .
this can be done by a brute force for d=4 and for the first few n s at d=10
. the one dimensional nature of the system should help considerably . for higher n , at d=10 ,
we face the problem of the complex pfaffian . an important insight into the whole subject may be gained by applying the full potential of the small volume approach @xcite .
9 t. banks , w. fishler , s. shenker and l. susskind , .
m. claudson and m. b. halpern , .
u. h. danielsson , g. ferretti and b. sundborg , . m. b. halpern and c. schwartz , . r. a. janik and j. wosiek , ; hep - lat/0011031 .
a. strominger and c. vafa , .
e. j. martinec , hep - th/9909049 .
p. bialas and j. wosiek , hep - lat/0109031 .
d. kabat , g. lifszytz and d. a. lowe , .
m. lscher , ; p. van baal , ; p. van baal , hep - ph/0008206 . | we present new results of the quenched simulations of the reduced d=4 supersymmetric yang - mills quantum mechanics for larger gauge groups su(n ) , @xmath0 .
the model , studied at finite temperature , reveals existence of the two distinct regions which may be precursors of a black hole and the elementary d0 branes phases of m - theory conjectured in the literature .
present results for higher groups confirm the picture found already for n=2 .
similar behaviour is observed in the preliminary simulations for the d=6 and d=10 models . |
99 f. nozzoli , presentation given at this conference ( taup 2009 ) http://taup2009.lngs.infn.it/slides/jul3/nozzoli.pdf or http://people.roma2.infn.it/ dama / pdf / nozzoli_taup09.pdf .
r. bernabei et al .
instr . & meth . a 592 ( 2008 ) 297 .
r. bernabei et al .
, isbn 978 - 88 - 95688 - 12 - 1 , pages 1 - 53 ( 2009 ) exorma ed .
( arxiv:0806.0011[astro - ph ] ) .
see e.g. r.m .
kippen , new astr .
48 ( 2004 ) 221 .
v. kundryavtsev , presentation given at this conference ( taup 2009 ) ; v. kudryavtsev et al . ,
r. bernabei et al .
j. c 56 ( 2008 ) 333 .
r. bernabei et al .
phys . a 21 ( 2006 ) 1445 .
r. bernabei et al .
d 77 ( 2008 ) 023506 .
r. bernabei et al . , mod .
lett . a 23 ( 2008 )
r. bernabei et al . , int . j. mod
a 22 ( 2007 ) 3155 .
r. bernabei et al .
j. c 53 ( 2008 ) 205 .
j. angle et al .
( 2008 ) 021303 .
a. benoit et al . , phys .
b 637 ( 2006 ) 156 . | a variety of detectors has been proposed for dark matter direct detection , but most of them by the fact are still at r&d stage . in many cases , it is claimed that the lack of an adequate detectors radio - purity might be compensated through heavy uses of montecarlo simulations , subtractions and handlings of the measured counting rates , in order to claim higher sensitivity ( just for a particular scenario ) .
the relevance of a correct evaluation of systematic effects in the use of montecarlo simulations at very low energy ( which has always been safely discouraged in the field so far ) and of multiple subtractions and handling procedures applied to the measured counting rate is shortly addressed here at some extent .
many other aspects would also deserve suitably deep investigations . in this paper
some arguments presented at the taup09 conference will be shortly summarized .
more details , tables and figures can be found in the slides at the conference site@xcite .
let us firstly comment the possibility of reliable evaluations of the background contributions at the kev energy region in the field of dark matter searches . as well known , it has been generally discouraged this procedure in the field of dark matter over more than twenty years .
in fact , the estimation by a montecarlo simulation of the background component in the counting rate from the residual radioactivity requires a detailed knowledge of : i ) the exact set - up geometry ( detector or detectors matrix , all materials , details of the assembling , of the shield layers , of the site , etc . ) ; ii ) the detector response function ( e.g. energy resolution , @xmath0 ratio , channeling , etc . ) ; iii ) the nature , the position and the concentration of all the existing radioactive contaminants ; iv ) etc .. unfortunately , apart from the geometrical layout of the set - up that are generally well known by people inside the experimental group , all the other quantities necessary in the montecarlo simulation require dedicated measurements .
moreover , there are some quantities ( such as concentration of residual contaminants , etc . ) that can be poorly known and just upper / lower limits are available ; in some cases these quantities can be even totally unknown .
as an example , the experimental energy resolution as a function of the energy and the energy scale should be measured / verified down to the energy threshold , as done e.g. by the dama / libra experiment where they are continuously measured by external / internal known sources from mev down to the energy threshold @xcite . on the contrary , in other experiments these quantities
are instead extrapolated from calibrations at much higher energy ( as done e.g. by liquid noble gas set - ups , where the energy threshold and the few kev energy scale are generally unproven , also because of position dependence , of non - uniform signal collection , etc . ; see e.g. @xcite ) .
regarding the presence of residual contaminants in the set - up , generally only limits on the contributions of the `` standard '' contaminants are given ; these limits forbid any reliable estimation of the background ( being unknown the exact values ) and can not be obviously exceeded ( see also later ) .
moreover , possible presence of many non - standard contaminants should be also included .
in addition , the montecarlo simulation also depends on the precise location of all the contaminants that is generally unknown even for the `` standard '' ones in complex set - ups .
the situation is more complex for multi - detectors set - up and when the energy distribution refers to events where each detector has all the others in anticoincidence ( _ single - hit _ events ) .
thus , it is trivial to conclude that a reliable precise simulation of the background counting rate in particular at kev energy region is not univocally determined and is a quite impossible task .
in addition , beyond the fore - mentioned arguments , we need to take into account that a montecarlo code can not manage all the possible low energy atomic physical processes .
this argument is still subject of improvements ; in fact , as an example , non - negligible differences are also obtained by different versions of the same montecarlo code @xcite .
some instructive examples are given by the trails in montecarlo simulations in ref .
@xcite .
as shown there , these simulations noticeably differ from the measured energy distributions in the cases of xenon-10 and of zeplin - iii .
in fact , they predict twice the measured rate for xenon-10 near 200 kev , and more than one order of magnitude the measured rate for zeplin - iii in the mev range @xcite .
the same approach has been also pursued by the same authors @xcite trying a montecarlo simulation of the background in the dama / libra set - up .
in particular , apart from errors in the details of the set - up geometry reconstruction and in the multiple - hit definition , many crude and arbitrary approximations in the nature and in the location of the residual contaminants have been arbitrarily assumed ; in fact , e.g. : i ) only standard contaminants , ii ) only unbroken chains , iii ) only uniform location of contaminants in the detectors , etc . have been taken into account . as a result of this rough , partial and arbitrary approach ,
the predicted rate has been estimated within a factor 10 lower than the measured one . instead of refining the quality of the simulation or reasonably recognizing the impossibility of precise determination , the authors just pursued the exercise of arbitrarily increasing `` by hand '' the assumed values of the contaminants at levels much larger than the measured experimental limits @xcite .
this also implies an overestimate of the background in higher energy region with respect to the measured experimental rate . in conclusion , although the arbitrary and the erroneous adopted procedures , these authors do not succeed in reproducing either the low or the high energy spectra .
nevertheless , as a conclusion of this arbitrary exercise @xcite , this artificially - boosted simulated spectrum has been subtracted by the measured one , attempting to obtain a limit for the unmodulated dark matter signal component .
this example shows how subtraction procedures using montecarlo simulations in the few kev energy region can give rise to erroneous conclusions ; thus , any constraint on dark matter signal on this basis would be an artefact .
furthermore , let us also note that the measured spectra e.g. of the existing / past nai(tl ) detectors ( such as e.g. anais , frejus , naiad , elegant , etc ... ) do not support even the shape presented in ref .
@xcite .
in addition , well different counting rates at kev energy region are present even for detectors of the same experimental group , as e.g. the case of naiad in 1996 and in 2003 @xcite . in conclusion
, it does not exist an unique recipe for a precise and reliable montecarlo simulation of whatever set - up , and for nai(tl ) in particular .
let us finally remind that a safer approach has been presented in this conference by dama collaboration ; this shows that enough space is present in the measured counting rate of the dama / libra kev energy spectrum for the unmodulated component of dark matter signal @xcite .
in the second part of this contribution @xcite , problems related to the application of multiple subtraction procedures of the measured counting rate , as pursued by experiments trying to identify the presence of recoil nuclei in the measured energy spectrum , have been summarized . in fact , many of the existing dark matter candidates also in the wimp class can give rise to signals that either have totally an electromagnetic nature ( see e.g. @xcite ) or involve electromagnetic signals associated to nuclear recoils ( see e.g. @xcite ) ; obviously , approaches that are based on multiple subtraction procedure of the electromagnetic component of the counting rate are blind to similar scenarios .
moreover , well known side processes exist for recoils ( such as recoils induced by neutrons , fission fragments , end - range alphas , surface electrons , etc . ) .
this approach is generally pursued when the detectors suffer from a not - suitable radiopurity level in the sensitive target - material and in the surroundings .
those activities generally apply a large number of cut procedures to the data ; each one is affected by non - negligible systematic errors which are usually not suitable quantified . as an example , the xenon-10 experiment applies more than 10 different cuts to the data ; the experiment collects @xmath1 events but only 10 are claimed to survive to the cuts and handling procedures @xcite .
very high reduction factors following applied multiple cuts are dangerous because of the difficult precise estimate of all the involved systematics . for example , it has been shown in ref .
@xcite that zeplin - i has claimed a sensitivity 3 orders of magnitude larger than the one properly obtained when accounting for systematics .
thus , the robustness of some results appeared in the `` race for the best exclusion - plot '' ( valid just in a single set of assumptions for a certain kind of wimp ) should be considered `` cum grano salis '' .
for example , for some liquid noble gas set - ups , apart from the robustness of the applied cuts themselves , the very low energy scale and the energy threshold are determined by extrapolating from calibrations at much higher energy and applying some kind of corrections for relevant non - uniformity of the detector s response ; with a light yield of about 2.2 photoelectrons / kev and not specific calibrations even @xmath2 1.5 - 2 kev electron equivalent is claimed as energy threshold @xcite .
considering the energy threshold dependence of the exclusion plots , up to several orders of magnitude differences can be present between claimed and realistic evaluation of the experimental sensitivity .
another crucial aspect is the proper accounting for the existing experimental and theoretical uncertainties in the calculation and in the comparison of experiments using different target materials and approaches . |
financial support from the dfg is gratefully acknowledged by jk and tp . financial support from the australian research council
is gratefully acknowledged by alo and ar .
alo also thanks the institut fr theoretische physik at the technische universitt clausthal . | a self - interacting polymer with one end attached to a sticky surface has been studied by means of a flat - histogram stochastic growth algorithm known as flatperm .
we examined the four - dimensional parameter space of the number of monomers up to 91 , self - attraction , surface attraction and force applied to an end of the polymer . using this powerful algorithm the _ complete _ parameter space of interactions and
force has been considered .
recently it has been conjectured that a hierarchy of states appears at low temperature / poor solvent conditions where a polymer exists in a finite number of layers close to a surface .
we find re - entrant behaviour from a stretched phase into these layering phases when an appropriate force is applied to the polymer .
we also find that , contrary to what may be expected , the polymer desorbs from the surface when a sufficiently strong critical force is applied and does _ not _ transcend through either a series of de - layering transitions or monomer - by - monomer transitions .
new experimental methods in the physics of macromolecules @xcite have been used to study and manipulate single molecules and their interactions .
these methods make a contribution to our understanding of such phenomena as protein folding or dna un - zipping ; one can push or pull a single molecule and watch how it responds .
it is possible to apply ( and measure ) forces large enough to induce structural deformation of single molecules .
one can monitor the mechanism of some force - driven phase transition occurring at the level of a single molecule .
theoretical understanding of this behaviour has attracted much attention @xcite .
the response of a single polymer to an external force under good solvent conditions was considered some time ago@xcite .
the response under poor solvent conditions ( below the @xmath0-point ) , where the self - attraction and an external force compete with each other , was examined later @xcite .
another phenomenon commonly studied in polymer physics is the adsorption of a polymer tethered to a `` sticky '' wall .
the response of such a polymer to a force perpendicular to the wall has also recently been considered @xcite .
however , when both the self - attraction ( ie .
monomer - monomer attraction that leads to polymer collapse ) and the surface attraction ( ie monomer - wall attraction that leads to adsorption ) compete the response to an external force has not yet been elucidated ( some interesting results can be found in @xcite ) .
certainly , the full phase diagram has not been considered .
making such a study now is all the more timely because of the very recent discovery @xcite of a new low temperature phenomenon of layering transitions ( without a force ) .
it is this layering phenomenon that raises the intriguing question about the response a low - temperature polymer may have to an external force . in the layering state a polymer is tightly confined within a fixed number of layers above the wall .
it may be therefore be especially interesting experimentally to examine such a situation .
we demonstrate for the _ first _ time how the full two - dimensional phase diagram of surface and self - attraction changes as the force is increased .
the desorbed extended regime , which changes its scaling behaviour as soon as the force is made non - zero , simply grows as the force is increased .
the second - order phase transitions of adsorption and collapse become first order .
the rest of the phase diagram remains relatively unaffected as long as the force is small .
after the force passes a critical value , which depends on the zero temperature force required to pull a polymer from a wall , a re - entrant behaviour occurs at low temperatures . for different values of the force
, this re - entrant behaviour occurs for both the adsorption and collapse of polymers , including the layering phases mentioned above .
we provide a full force - temperature diagram for all ratios of surface attraction to self - attraction .
all this is achieved with the use of a recently developed algorithm , flatperm @xcite , that is specifically designed to obtain information about the whole phase diagram in one simulation run : it is effectively a stochastic enumeration algorithm that estimates the complete density of states .
the model we have considered is a self - avoiding walk on a three - dimensional cubic lattice in a half - space .
the self - avoiding walk is attached at one end to the wall with surface energy per monomer of @xmath1 for _ visits _ to the wall .
the self - avoiding walk self - interacts via a nearest - neighbour energy of attraction @xmath2 per monomer - monomer _ contact_. ( note that the attractive energies @xmath2 and @xmath1 are taken to be positive . ) a force @xmath3 is applied in the direction perpendicular to the boundary of the half - space ( wall ) .
the total energy of a configuration @xmath4 of length ( number of monomers ) @xmath5 is given by @xmath6 and depends on the number of non - consecutive nearest - neighbour pairs ( contacts ) along the walk @xmath7 , the number of visits to the planar surface @xmath8 , and the height @xmath9 in the direction perpendicular to the boundary ( wall ) of the half - space .
figure 1 shows a diagram of the two - dimensional analogue . for convenience ,
we define @xmath10 , @xmath11 and @xmath12 where @xmath13 is the temperature and @xmath14 is the boltzmann constant .
the partition function is given by @xmath15 with @xmath16 being the density of states .
it is this density of states that is estimated directly by the flatperm simulation .
our algorithm grows a walk monomer - by - monomer starting on the surface .
we obtained data for each value of @xmath5 up to @xmath17 , and all permissible values of @xmath7 , @xmath8 , and @xmath9 . when @xmath18 the phase diagram of the model contains several phases and transitions between them @xcite .
[ cols="^,^ " , ] for small @xmath19 and @xmath20 there is a desorbed extended ( de ) phase with the polymer behaving as a free flexible polymer in solution ( ie . swollen or extended in three dimensions ) . for @xmath19
fixed and small , increasing @xmath20 leads to a second - order phase transition ( adsorption ) to a state in which the polymer is adsorbed onto the wall and behaves in a swollen two - dimensional fashion ( ae ) .
alternately , if @xmath19 is increased at small @xmath20 a second - order collapse transition occurs to a state resembling a dense liquid drop .
this phase is known as desorbed collapsed ( dc ) on the assumption that it has little contact with the wall @xcite .
however , it has been subsequently argued @xcite that for larger @xmath19 there is also a polymer - surface transition to a surface - attached globule ( sag ) phase , where the polymer behave as a liquid drop partially wetting the wall .
this transition will not be seen directly by studying thermodynamic polymer quantities as it occurs as a singularity in the surface free energy and not the bulk free energy of the polymer . when @xmath20 is large ,
so that the polymer is adsorbed onto the wall , increasing @xmath19 will result in a two - dimensional ( second - order ) transition to a adsorbed and collapsed phase ( ac ) . in recent work @xcite this ac phase
was also referred to as the _
1-layer _ phase because for very large @xmath19 and @xmath21 there exist meta - stable @xmath22-layer phases where the polymer is two - dimensionally collapsed and more - or - less restricted to @xmath22 layers parallel to the wall ( for small @xmath22 ) .
a series of first - order transitions between adjacent values of @xmath22 occur as @xmath20 is varied at fixed @xmath19 .
all these transition lines can be seen in the figure 2 ( a ) which shows a plot of the logarithm of the maximum eigenvalue of the ( @xmath23 ) matrix of second derivatives in the variables @xmath19 and @xmath20 of @xmath24 for fixed @xmath25 .
the local maxima indicate transitions .
the transition to the ac phase is expected to be first order in the thermodynamic limit .
using the evidence available in the literature @xcite , let us now consider what we can expect when @xmath26 . the first important feature to note is that the isotropic de phase is replaced by an anisotropic phase in which the height of the end point of the polymer scales linearly with @xmath5 ; we denote this phase as the _ stretched _ phase .
consequently the transition from stretched to adsorbed phases becomes first - order @xcite .
likewise , at least in three dimensions @xcite , the transition from the vertically stretched phase to the collapsed phase also becomes first - order .
this implies that the multicritical point ( where for @xmath18 the de , ae and dc phases meet ) is now a triple point : the meeting of three first order lines .
the transition from the ae to ac phases should not be effected by the application of a small force as it acts in a direction perpendicular to the driving phenomenon of planar collapse . to a polymer in
the 2-layer adsorbed collapsed phase._,width=302 ] finally , it is intriguing to ask what happens to the layering phases observed in @xcite .
one can imagine that the force simply extends a vertical ` tail ' from a layered block ( see figure 3 ) and that as the force is increased the monomers are peeled off one at a time with corresponding micro - transitions @xcite for each monomer pulled until a vertical rod is achieved .
instead we see at some point a sharp first order transition between the highly stretched vertical rod and a layered system with short tail . in figures 2(b ) and 2(c ) we show plots of the logarithm of the maximum eigenvalue of the matrix of second derivatives in the variables @xmath19 and @xmath20 of @xmath24 at fixed @xmath27 ( as in figure 2(a ) ) but at values of @xmath27 being @xmath28 and @xmath29 .
it is clear that as @xmath27 is increased the stretched phase that occurs for small @xmath19 and @xmath20 expands while the positions of the other phases and transitions move little .
we immediately note that these plots _ do not _ tell the whole story since physically one is usually interested in fixing the force @xmath3 rather than @xmath27 : fixing @xmath27 implies that the force applied goes to zero at low temperatures .
it is for this reason that the re - entrant behaviour for absorbing polymers @xcite is not seen directly in these plots .
however , re - entrant behaviour does occur and occurs for _ any _ ratio of surface to bulk energies .
let us now consider the more traditional force - temperature diagram and return to this point . in figure 4 a plot of the force @xmath30 needed to pull a polymer from the wall for a ranges of temperatures and a parameter @xmath31 which measures the relative strength of the surface ( wall ) interaction to the self - interaction .
needed to pull a polymer from the surface against temperature @xmath13 and a parameter @xmath31 .
the parameter @xmath31 controls the relative strength of wall attraction and self - attraction with @xmath32 and @xmath33 .
the limiting cases of surface desorption and of pulling a collapsed polymer are easily visible in the plot for @xmath34 and @xmath35 , respectively._,width=325 ] we have parameterised the energies of surface and self - attraction as @xmath32 and @xmath36 respectively .
using this parameterisation for @xmath37 gives the whole range of attractive activities : the ratio of surface to bulk activities is given as @xmath38 and so is constant for fixed @xmath31 .
for @xmath35 we have @xmath39 and @xmath40 which corresponds to pure self - attraction while the other boundary of the parameter space with @xmath34 gives @xmath41 and @xmath42 which is the pure surface adsorption case .
this extends the diagrams given in @xcite in which only adsorption is considered . if a force smaller than @xmath43 is applied the polymer is in the phase appropriate to the value of @xmath31 : either collapsed or adsorbed or both .
on the other hand for forces larger than @xmath43 the polymer is in the ` stretched ' phase .
we immediately note that the reentrant behaviour observed in the adsorption - only case @xcite persists for all @xmath31 . fixing the force to be at a value slightly larger than the zero temperature critical force and then increasing the temperature leads to transitions from the stretched state to a non - stretched phase and back again to the stretched state .
this arises due to the entropy of the zero temperature state ; one can easily extend the arguments in @xcite to demonstrate that re - entrant behaviour can occur even when the zero - temperature configuration of the non - stretched state is a hamiltonian ( fully compact ) walk in a cube rather than a totally adsorbed polymer .
let us discuss the re - entrant behaviour returning to the ( @xmath19,@xmath20,@xmath27)-parametrisation .
for fixed @xmath2 , @xmath1 , and @xmath3 , changing the temperature @xmath13 implies moving on a ray in the ( @xmath19,@xmath20,@xmath27)-space . at high temperatures the system is in the stretched phase near the origin . at low temperatures ,
the state of the system depends on the choice of @xmath2 , @xmath1 , and @xmath3 . for very large @xmath3
the system remains stretched at all temperatures , whereas for very small @xmath3 and low temperatures , the system is in a layered phase .
the re - entrant behaviour manifests itself in the following way : there is a range of @xmath3 for which the system , when moving along a ray in the ( @xmath19,@xmath20,@xmath27)-space ( ie . for fixed @xmath2 , @xmath1 , and @xmath3 ) , changes from a stretched state near the origin to a layered one at intermediate temperatures and then changes back to a stretched state as @xmath19 , @xmath20 , and @xmath27 become larger .
if the critical force is zero then the curve in the @xmath44 plane corresponds to the phase boundary of the de phase with the apex of the curve around @xmath45 being the location of the multicritical point . on the other hand for @xmath46
there is a kink in the function @xmath47 at exactly @xmath48 which is a consequence of the first order point coming from the transition from sag / layer phases from small @xmath31 to the ac phase for larger @xmath31 .
there is the appearance of a kink joining the multicritical point to the zero temperature transition which is presumably a finite temperature effect of the transition to the ac phase . in this paper
we have studied how the phase diagram of a self - attracting polymer that is also attracted and tethered to a flat wall changes as a vertical force is applied to the un - tethered end of the polymer .
we have accomplished this using a flat histogram monte carlo simulation that is capable of studying the whole range of microscopic energies , temperature and polymer length up to a maximum of @xmath49 monomers .
we demonstrate that re - entrant behaviour occurs at low temperature and for a range of forces for _ all _ relative strengths of self - attraction and surface attraction . for small forces
we have found that only the transition boundary of the `` stretched '' phase moves with increasing force while the rest of the phase diagram is relatively unchanged . in contradiction to what may be expected we have found that the novel layering meta - phases found for large but finite polymer length are unaffected by small forces . |
a framing for a smooth @xmath0-manifold @xmath1 is a smooth choice of ordered basis @xmath2 for the tangent space at each point of @xmath1 .
a _ projective _ framing is a smooth choice of a _ pair _ of bases of the form @xmath3 .
it has long been established that any orientable 3-manifold admits a framing ( s ) and any non - orientable 3-manifold admits a projective framing ( hh ) .
the original proofs rely on the notion of characteristic classes .
we present a proof for compact @xmath1 , which will only use basic facts about immersions of surfaces in 3-space .
we now present the facts on immersions that we will need .
denote @xmath4 , which is a cyclic group of order 4 .
let @xmath5 denote an annulus or mobius band .
there are two regular homotopy classes of immersions of @xmath5 into @xmath6 .
to each such class we attach a value in @xmath7 as follows : for @xmath5 an annulus , the regular homotopy class of immersions which includes an embedding whose image is @xmath8 { \subseteq}{{\bbb r}}^2 \times { { \bbb r}}= { { { \bbb r}^3}}$ ] , will have value @xmath9 .
the other class , ( containing an embedding differing from the previous embedding by one full twist ) will have value @xmath10 . for @xmath5 a mobius band we attach once and for all the value @xmath11 to one of the classes and the value @xmath12 to the other ( which again differ from the previous by one full twist ) .
now let @xmath13 be a closed surface and @xmath14 an immersion .
we define a map @xmath15 as follows : given @xmath16 let @xmath17 be an embedded circle which represents @xmath18 .
let @xmath5 be a thin neighborhood of @xmath19 in @xmath13 , then @xmath5 is an annulus or mobius band .
we define @xmath20 to be the value in @xmath7 attached above to the immersion @xmath21 .
it has been shown in p that @xmath22 is indeed well defined on @xmath23 and satisfies the following property : @xmath24 where @xmath25 denotes the intersection form on @xmath23 .
note @xmath26 .
we remark that the notation in p differs from ours in that @xmath7 is taken there to be @xmath27 rather than @xmath28 .
and so the numerical value of @xmath22 appearing there is twice the value here , and our property ( fp ) appearing above is replaced there by @xmath29 .
we point out that the above facts about immersions are indeed basic , in the sense that they may be obtained without knowledge of the smale - hirsch theorem .
e.g. for the classification of regular homotopy classes of immersions of @xmath5 into @xmath6 where @xmath5 is an annulus or mobius band , one needs to show that the easily constructed map into @xmath30 is bijective . in general
one would use the smale - hirsch theorem , but in this case surjectivity follows by direct construction of the two immersions , and injectivity follows by familiarity with the `` belt trick '' .
we will prove the statement for @xmath1 a closed 3-manifold .
the statement for @xmath1 with boundary will follow by restricting a framing from the double of @xmath1 .
so let @xmath1 be a closed 3-manifold , and let @xmath31 be a heegard surface , i.e. @xmath13 splits @xmath1 into two handlebodies @xmath32 ( orientable or non - orientable ) with common boundary @xmath13 .
let @xmath33 be a system of disjoint circles which may be compressed in @xmath34 , reducing @xmath34 to a ball , and let @xmath35 be such system compressible in @xmath36 .
then a thin neighborhood @xmath5 of each of the @xmath37s and @xmath38s is an annulus .
if @xmath1 is orientable then embed @xmath34 into @xmath6 as in figure f1a .
this induces an embedding @xmath14 as its boundary .
if @xmath1 is non - orientable , then take an immersion @xmath39 into @xmath6 as in figure f1b . in both cases we have @xmath40 for all @xmath41 .
( we allow @xmath37 to denote both the circle in @xmath13 and its homology class in @xmath23 . ) for any diffeomorphism @xmath42 , define @xmath44 by @xmath45 .
note that indeed @xmath46 and by ( fp ) @xmath47 is a linear functional .
let @xmath48 denote the dehn twist along @xmath37 , then the induced homomorphism @xmath49 is given by @xmath50 .
we get ( by ( fp ) ) for all @xmath16 : @xmath51 let @xmath52 be the subspaces spanned by the @xmath37s and @xmath38s respectively , then the intersection form vanishes on @xmath53 and @xmath54 .
it follows by ( fp ) that @xmath55 is identically 0 and @xmath56 is a @xmath57 valued linear functional . by ( e2 ) @xmath53 is contained in the kernel of each @xmath58 and since the intersection form is non - degenerate on @xmath23 , @xmath59 span all linear functionals on @xmath23 which vanish on @xmath53 . in particular , they span a linear functional @xmath60 vanishing on @xmath53 and satisfying @xmath61 .
now let @xmath62 be the composition of dehn twists along those @xmath37s participating in the presentation of @xmath60 as linear combination of @xmath59 , then @xmath63 and so for all @xmath41 : @xmath64 .
we now change the gluing between @xmath34 and @xmath36 using the @xmath42 given by lemma dhn .
this does not change the diffeomorphism type of @xmath1 since dehn twists along the @xmath37s may be extended to @xmath34 . after this change of gluing we have that @xmath65 for all @xmath41 , and still @xmath40 for all @xmath41 .
we will first construct a ( projective ) framing on @xmath66 .
let @xmath67 denote the tangent spaces of @xmath13 and @xmath1 at @xmath68 .
let @xmath69 be the unit vector normal to @xmath70 and pointing away from @xmath34 .
( assume we have chosen a riemannian metric on @xmath1 . )
if @xmath1 is orientable then there is well defined a unit normal @xmath71 at @xmath72 pointing away from the embedding of @xmath34 . and
so @xmath73 together with the choice of normals @xmath74 and @xmath71 induce an isomorphism of @xmath75 with @xmath76 , with which we pull back the standard framing of @xmath76 to @xmath75 .
if @xmath1 is non - orientable then a normal to @xmath77 may not be well chosen .
let @xmath71 be one of the two unit normals .
we define the isomorphism from @xmath75 to @xmath76 using this @xmath71 , and pull back the frame in @xmath76 which is obtained from the standard frame by rotating it by @xmath78 around @xmath71 in the positive sense defined by the direction of @xmath71 .
when choosing the opposite @xmath71 , then the isomorphism will differ by the reflection defined by @xmath71 , and the frame we pull back from @xmath6 will differ by a @xmath79 rotation around @xmath71 , and so altogether the frame induced in @xmath75 will differ by @xmath80 .
so such pull back defines a projective framing on @xmath66 . the next step is to extend the framing to a thin neighborhood of the compressing discs of the @xmath37s and @xmath38s in @xmath32 .
let @xmath19 be one of the circles @xmath37 or @xmath38 and let @xmath5 be a thin neighborhood of @xmath19 in @xmath13 , then @xmath5 is an annulus , and since @xmath81 , there is a regular homotopy @xmath82 , @xmath83 , with @xmath84 and @xmath85 an embedding with image @xmath86 where @xmath87 denotes @xmath88 $ ] . let @xmath89 be a neighborhood of the compressing disc of @xmath19 in @xmath34 or @xmath36 , so @xmath90 where @xmath5 corresponds to @xmath91
. for @xmath92 let @xmath93 denote @xmath94 where @xmath95 are respectively the disc and circle of radius @xmath96 in @xmath97 .
for any @xmath98 take @xmath74 to be the unit normal to @xmath99 pointing inward in @xmath89 . now
if @xmath1 is orientable then we follow the increasing time @xmath83 of our regular homotopy @xmath100 with decreasing radius from @xmath101 to @xmath102 in @xmath97 , and pull back the standard framing of @xmath6 to any point @xmath103 as before , using the normal @xmath74 , and normal @xmath71 to the image of the immersion in @xmath6 , where the side of the normal is chosen at time 0 to be pointing outward from the embedding of @xmath34 .
this extends the framing we have constructed in @xmath13 . at @xmath104 we have an embedding of @xmath105 as @xmath106 , and by additional regular homotopy if necessary we may assume the normals @xmath71 are pointing inward .
this extends to an embedding of @xmath107 onto @xmath108 .
now if the metric on @xmath1 is chosen so that this embedding of @xmath107 into @xmath6 is isometric , then the pull back of the standard framing of @xmath6 to @xmath105 that we have , coincides with the one induced by this embedding of @xmath107 , and so the framing can be extended to the whole of @xmath109 .
this completes the construction of the framing in @xmath89 .
we now only need to extend the framing to the remaining 3-balls in @xmath34 and @xmath36 , but this may always be done ( e.g. since @xmath110 ) .
this completes the proof for the case @xmath1 is orientable . for non - orientable @xmath1
we argue as follows : since @xmath5 is an annulus , it is orientable and so we may choose a unit normal @xmath71 in @xmath6 along @xmath111 . from the projective framing we have defined along @xmath13 select the proper ( i.e. non - projective ) framing determined above by this choice of @xmath71 .
we will extend this to a proper framing on @xmath89 as in the orientable case , only that now the framing in @xmath89 will be defined in three layers , @xmath112 , @xmath113 , @xmath114 . in the outer layer we will realize a rotation of the framing around @xmath71 in the negative sense , until we have the actual pull back of the framing in @xmath6 .
then the middle and inner layers will be defined as in the orientable case , using a regular homotopy of @xmath5 to a standard annulus in @xmath6 .
again we may complete the framing to the remaining balls in @xmath32 since once we have a projective framing on the boundary of such ball , we may select a proper framing from it ( since the ball is orientable ) , and then extend the framing to the ball as before . | we give an elementary proof of the fact that any orientable 3-manifold admits a framing ( i.e. is parallelizable ) and any non - orientable 3-manifold admits a projective framing .
the proof uses only basic facts about immersions of surfaces in 3-space .
[ section ] [ thm]lemma [ thm]proposition [ thm]corollary [ thm]definition [ thm]remark |
the torque on an electric dipole * p * , at rest in a uniform electric field * e * , is @xmath0 the torque on a magnetic dipole * m * , at rest in a uniform magnetic field * b * , is @xmath1 but what if the dipole is moving , at a constant velocity * v * ?
it is well known that a moving electric dipole acquires a _
dipole moment @xcite @xmath2
so one might guess that the torque on a moving electric dipole in uniform electric and magnetic fields would be @xcite @xmath3 similarly , a moving magnetic dipole acquires an _ electric _ dipole moment @xcite @xmath4 and one might guess that the torque on a moving magnetic dipole would be @xmath5 but these formulas are incorrect ; in each case there is a third term:@xcite @xmath6 in general , then , @xmath7 our purpose in this note is to derive that result
. @xcite -.1in[.7 ] -.5 in
an electric dipole consists of positive and negative charges @xmath8 separated by a displacement @xmath9 ( figure 1 ) .
the force on a point charge is @xmath10 so the torque @xcite on a dipole of moment @xmath11 is @xmath12\nonumber\\ & = & q{\bf d}\times\left({\bf e}+{\bf v}\times { \bf b}\right)\nonumber\\ & = & ( { \bf p}\times { \bf e})+{\bf p}\times({\bf v}\times { \bf b}).\end{aligned}\ ] ] using the vector identity @xmath13 , the previous result becomes @xmath14 that is surely the _ easiest _ way to obtain eq .
( 7 ) ( it borrows from an argument by v. namias@xcite ) .
but the magnetic analog is not so straightforward,@xcite
so let s repeat the derivation , this time treating the electric dipole as the point limit of a uniformly polarized object.@xcite polarization ( * p * ) and magnetization ( * m * ) together constitute an antisymmetric second - rank tensor : @xmath15 and the transformation rule gives@xcite @xmath16 we use primes for the proper " ( rest ) system of the dipole ( @xmath17 ) ; no prime means the lab " frame ( @xmath18 ) , through which the dipole is moving with velocity @xmath19 . notice that if @xmath20 , then @xmath21 , confirming eq .
( 3 ) , and if @xmath22 , then @xmath23 , confirming eq . ( 5 ) . now , suppose we have an electric dipole @xmath24 at rest at the origin in @xmath25 : @xmath26 assume first that @xmath24 is perpendicular to * v * , say @xmath27 then @xmath28 and all other components are zero . according to the lorentz law , the force density is @xmath29 where @xcite @xmath30 in our case,@xcite @xmath31 @xmath32,\ ] ] @xmath33 so @xmath34 and @xmath35.\ ] ] the torque is @xmath36,\end{aligned}\ ] ] where @xmath37 .
the @xmath38 and @xmath39 components of the integral are zero ; the @xmath40 component is @xcite @xmath41 so @xmath42= ( { \bf p}_0\times { \bf e } ) + { \bf p}_0 \times ( { \bf v } \times { \bf b}),\ ] ] which agrees with eq . (
11 ) , and hence confirms eq .
( 7 ) for the case @xmath24 perpendicular to * v*. ( for this orientation the electric dipole moments in @xmath18 and @xmath25 are the same there is no lorentz contraction .
this can be confirmed by integrating eq . (
18 ) : @xmath43 . ) if @xmath24 is parallel to * v * , @xmath44 giving @xmath45 with all other components of * p * and * m * being zero . in this case ,
@xmath46 and @xmath47 so that @xmath48.\ ] ] the torque is @xmath49.\ ] ] because of lorentz contraction , @xmath50as is confirmed by integrating eq .
( 31)and again we recover eq .
now , suppose we have a magnetic dipole @xmath51 , at rest at the origin , in @xmath25 : @xmath52 assume first that @xmath51 is perpendicular to * v * , say @xmath53 from the transformation rule , @xmath54 this time @xmath55 @xmath56,\ ] ] @xmath57 so @xmath58,\ ] ] and @xmath59\nonumber\\ & & \quad\quad\quad\times { \bf b}.\end{aligned}\ ] ] the torque is @xmath60 in agreement with eq .
( 8) , for @xmath51 perpendicular to * v*. ( in this orientation , the magnetic dipole moments in @xmath18 and @xmath25 are the same , as we confirm by integrating eq .
( 39 ) : @xmath61 . ) if @xmath51 is parallel to * v * , @xmath62 giving @xmath63 with all other components of * p * and * m * being zero . in this case
@xmath64 and @xmath65 vanish , leaving @xmath66,\ ] ] so @xmath67\times{\bf b},\ ] ] and the torque is @xmath68 which is again consistent with eq .
( 8) because in this orientation @xmath69 and , integrating eq .
( 47 ) , @xmath70 .
in the presence of an electric field , a magnetic dipole ( a loop of electric current ) carries
hidden momentum"@xcite @xmath71 and hence also hidden momentum @xmath72 it is hidden " in the sense that it is not associated with overt motion of the object as a whole ; it occurs in systems with internally moving parts , such as current loops.@xcite the _ total _ angular momentum is the sum of overt " and hidden components : @xmath73 and the torque is its rate of change:@xcite @xmath74 thus , combining eqs .
( 9 ) and ( 53 ) , the overt " torque on a moving dipole is @xmath75 by contrast , a ( stationary ) _ electric _ dipole has no internally moving parts , and it harbors no hidden momentum.@xcite however , when it is in _ motion _ it picks up a magnetic dipole moment @xmath76 [ eq .
( 3 ) ] that _ does _ carry hidden momentum,@xcite so eq . ( 54 ) ( with @xmath77 ) applies to this case as well.@xcite
co - authored this note in his private capacity ; no official support or endorsement by the centers for disease control and prevention is intended or should be inferred .
see , for instance , v. hnizdo , magnetic dipole moment of a moving electric dipole , " am . j. phys .
* 80 * , 645 - 647 ( 2012 ) . in this paper , except for eqs .
( 1 ) and ( 2 ) , * p * and *
m * are the dipole moments of the _ moving _ dipoles_not _ the proper " moments in the dipoles rest frame .
see , for example , k. w. h. panofsky and m. phillips , _ classical electricity and magnetism _
( dover , new york , 2005 ) , sec .
18 - 4 . in a recent article [ d. j. griffiths and v. hnizdo ,
mansuripur s paradox , " am . j. phys . * 81 * , 570 - 574 ( 2013 ) ] we stated that there is no third term " in the torque formula .
this was misleading : there _ is _ a third term ( in general ) , but it was zero ( in that context ) because @xmath78 at the location of the dipole .
if the fields are _ non_uniform , the torque ( 9 ) is supplemented by @xmath79 $ ] , where @xmath80 is the dipole s displacement from the point with respect to which torques are calculated .
the term inside the brackets comprises the force on a moving dipole [ g. e. vekstein , on the electromagnetic force on a moving dipole , " eur .
* 18 * , 113117 ( 1997 ) ] .
this additional term vanishes when torques are calculated with respect to the position of the dipole .
we shall calculate all torques and angular momenta with respect to the origin .
v. namias , electrodynamics of moving dipoles : the case of the missing torque , " am . j. phys .
* 57 * , 171 - 177 ( 1989 ) . of course , you could model * m * as separated monopoles ( this is what namias did in ref . 7 ) , but it turns out the torque is different for gilbert " dipoles and ampre " dipoles ( tiny current loops ) .
see ref .
this approach is based on an argument by m. mansuripur ,
trouble with the lorentz law of force : incompatibility with special relativity and momentum conservation , " phys .
lett . * 108 * , 193901 - 1 - 4 ( 2012 ) .
a simpler version starts by representing stationary electric and magnetic by their charge and current densities : @xmath81 and lorentz transforming the 4-vector @xmath82 to get @xmath64 and @xmath83 for _ moving _ dipoles [ eqs .
( 22 ) , ( 25 ) , ( 40 ) , and ( 43 ) ] .
see , for example , d. j. griffiths , _ introduction to electrodynamics _
( pearson , boston , 2013 ) , eq .
( 12.118 ) .
10 , section 7.3.5 .
when attached to a delta function , the prime denotes differentiation with respect to its argument .
here we integrate by parts .
w. shockley and r. p. james , ` try simplest cases ' discovery of ` hidden momentum ' forces on ` magnetic currents ' , " phys .
lett . * 18 * , 876 - 879 ( 1967 ) ; w. h. furry , examples of momentum distributions in the electromagnetic field and in matter , " am . j. phys . * 37 * , 621 - 636 ( 1969 ) ; l. vaidman , torque and force on a magnetic dipole , " am . j. phys . * 58 * , 978 - 983 ( 1990 ) .
hidden momentum is mechanical in nature , even though it arises ( typically ) in electromagnetic contexts .
for details see ref . 4 , or ref . 10 ( example 12.13 ) .
if the electric field is a function of time , there will be an additional term of the form @xmath84 $ ] , but it vanishes if the torque is calculated with respect to the dipole s location .
there is no term involving @xmath85 , since the dipole moments are assumed to be constant .
d. j. griffiths,dipoles at rest , " am .
* 60 * , 979 - 987 ( 1992 ) .
note that a moving electric dipole carries a component of circulating current ; see hnizdo , ref . 1 .
a. l. kholmetskii , o. v. missevitch , and t. yarman , torque on a moving electric / magnetic dipole , " prog .
b * 45 * , 83 - 99 ( 2012 ) . these authors claim that the last two terms are new discoveries , but both these terms were obtained already by namias ( ref . 7 , eqs . ( 1 ) and ( 3 ) ; the 3rd term is implicit in the former equation ) .
incidentally , the same result [ eq .
( 54 ) ] holds for @xmath86 and @xmath87 constructed from magnetic monopoles and their currents , though ( curiously ) the roles of the last two terms are reversed : the fourth appears already in the analog to eq .
( 9 ) , while the third is due to hidden momentum . | we calculate the torque on an ideal ( point ) dipole moving with constant velocity through uniform electric and magnetic fields . |
in this paper we briefly discuss the usage of multigrid ( mg ) iteration schemes to solve the non - lte problem of the 2nd kind as defined by @xcite .
the era of extensive development of mg methods started in 1970 s by the work of @xcite .
several steps in using mg methods applied to radiative transfer were made by @xcite , @xcite , and @xcite .
these authors showed that this technique leads to a great improvement of the convergence rate .
this paper demonstrates how to apply these methods to a more general solution of polarized radiative transfer with realistic multilevel atomic models and complicated structure of overlapping lines .
the effects of depolarizing collisions is taken into account .
for the description of the atomic state , we adopt the density - matrix formalism and the representation in the basis of irreducible tensorial operators ( e.g. , * ? ? ?
* ; * ? ? ?
the elements of atomic density matrix have the usual form @xmath2 , where @xmath3 is the energy level of total angular momentum @xmath4 , and ( @xmath5 ) are the multipolar components of the level ( @xmath6 , @xmath7 ) . in stationary regime ,
the density - matrix elements are solutions of the local statistical equilibrium equations , @xmath8 the structure of the @xmath9-matrix has been extensively discussed by @xcite , @xcite , and @xcite .
we assume that this matrix has the form @xmath10 , where @xmath11 is the matrix of radiative rates , and @xmath12 is the matrix of collisional rates ( impact approximation ) . the radiative transfer equation for the set of four stokes parameters @xmath13 has the usual form @xmath14 where @xmath15 is the emission vector of the local sources , @xmath16 is the absorption matrix , and @xmath17 is the matrix of stimulated emission .
all these quantities are dependent on radiation frequency , @xmath18 , position vector , @xmath19 , and direction of propagation determined by the unit vector @xmath20 .
finally , @xmath21 is the parametrization of the radiation path along the @xmath20 direction .
most of the existing non - lte solvers use the methods based on @xmath22-operator splitting similar to the one of @xcite . depending on organization , these schemes are numerically equivalent to the jacobi or gauss - seidel smoothing procedures ( for details , see * ? ? ? * ; * ? ? ?
these smoothing procedures do reduce high frequencies of the solution fast , but poor convergence is achieved for low frequencies .
( with `` high frequencies '' we mean those which are comparable to the spatial frequency of grid points approximating the continuous scale . ) the principles of mg schemes are based on the idea of using coarse grids to reduce the low frequencies , and fine grids to smooth their high - frequency components .
it can be showed that such a process may lead to the optimal cpu time demands of @xmath1 , @xmath0 being the number of points per decade of optical scale . for comparison ,
the jacobi and gauss - seidel methods scales approximately as @xmath23 .
we have applied the non - linear version of the _ standard multigrid _ scheme based on the coarse grid correction ( cgc ) technique ( for details , see * ? ? ?
* ; * ? ? ?
cgc is the process of correction of the fine - grid approximation of the solution using the solutions on the coarse grids .
schematically , it can be described in the following way : the defect ( or residuum ) of the fine - grid approximation is computed by several calls of the sweeping procedure ( jacobi , etc . ) ; then both defect and the initial guess of the solution are restricted to the coarse grid , and a new solution on the coarse grid is obtained using these data .
this coarse - grid solution is interpolated to the fine grid , and the density - matrix components are corrected .
this process can be repeated recursively for every grid in order of increasing grid steps .
this recursive process leads to the so - called v , w , or more complicated diagrams , depending on the way in which the recursion is implemented @xcite . in our code
we use the parabolic short - characteristics technique of @xcite , and as a smoothing algorithm we use the jacobi iteration , similar to the one of @xcite , with modifications to include the effects of line overlapping .
for demonstrating the possibilities of this technique , we chose the model of a semi - infinite , plane - parallel , atmosphere .
the atmosphere is isothermal ( @xmath24k ) , with constant volume density of neutral hydrogen , @xmath25 , thermal electrons , @xmath26 , and protons , @xmath27 .
no magnetic field is taken into account .
the scattering of radiation is supposed to fulfill the conditions of complete frequency redistribution , and the @xmath28 and @xmath29 stokes parameters vanish due to the symmetries of the problem .
we adopted a hydrogen atomic model with 9 fine - structure energy levels ( @xmath30 to @xmath31 ) and all the non - vanishing multipole components @xmath32 of density matrix .
all the coherence elements ( @xmath33 ) are identically zero due to the model s symmetries . the coherences between different energy levels have been neglected due to the small natural widths of the levels in comparison to their separations , and due to the selection rules for dipole radiative transitions . collisional rates with thermal electrons and protons for fine structure transitions , @xmath34 , were computed in part using the semiclassical theory of @xcite , for transitions within the same shell , and in part using the data of collisional cross - sections from the atomic and molecular data information system ( amdis ; ` http://www-amdis.iaea.org/ ` ) , for transitions between different shells .
the number of logarithmically spaced nodes in the fine grid is @xmath35 and 5 grids were used in total .
the number of nodes in the `` @xmath36 '' grid is equal to @xmath37 .
the initial guess for the atomic density - matrix elements is given by the lte populations determined in the unpolarized case .
of atomic populations , @xmath38 , in the mg case ( solid line ) is compared to the jacobi solution ( dashed line ) .
the maximum relative error @xmath39 ( with respect to the fully converged solution ) for mg case ( dotted line ) and jacobi case ( dot - dashed line ) is showed as well .
the norm used is @xmath40 ( see * ? ? ?
* ; * ? ? ?
the graph shows the effect of 11 v - cycles with 2 pre- and 15 post - smoothing jacobi iterations.,width=457 ]
figure [ fig1 ] shows a comparison between the convergence rates of the jacobi and the mg methods . the effect of coarse - grid solutions is reflected by the dramatic evolution of the maximum relative change of the populations .
the coarser the grid the shorter the evaluation time , and the higher the rate of approaching to the truncation error of the grid . the maximum relative error dominated by the long - period components
is strongly reduced by the recursive cgc during the v - cycles .
the time saving of the mg method in this particular model is about a factor 4 compared to the jacobi method .
it must be noticed that the efficiency of mg increases as fast as the efficiency of the smoothing procedure .
the most important benefit from mg s is the asymptotical @xmath1 behavior , which designates the method for use in solutions of problems that necessitate strong refinements .
moreover the presented 1d geometry is the slowest case as pointed out by @xcite and @xcite .
bommier , v. , & sahal - brchot , s. 1978 , , 69 , 57 bommier , v. 1980 , , 87 , 109 brandt , a. 1977 , math.comp .
, 31 , 333 fabiani bendicho , p. , trujillo bueno , j. , & auer , l. 1997 , , 324 , 161 fano , u. 1957 , rev.mod.phys . , 29 , 74 hackbush , w. 1985 , multi - grid methods and applications ( berlin : springer ) kunasz , p. , & auer , l.h .
1988 , jqsrt , 39 , 67 .
landi deglinnocenti , e. 1987 , in numerical radiative transfer , ed .
w. kalkofen ( cambridge : cambridge univ . ) , 265 manso sainz , r. , & trujillo bueno , j. 2003 , in asp conf .
307 , solar polarization 3 , ed .
j. trujillo bueno & snchez almeida ( san francisco : asp ) , 251 paletou , f. , & lger , l. 2005 ` ( astro - ph/0507021 ) ` rybicki , g. b. , & hummer , d. g. 1991 , , 245 , 171 rybicki , g. b. , & hummer , d. g. 1992 , , 262 , 209 sahal - brchot , s. 1977 , 213 , 887 - 899 sahal - brchot , s. , vogt , e. , thoraval , s. , & diedhiou , i. 1996 , , 309 , 317 steiner , o. 1991 , , 242 , 290 vth , h. m. 1994 , , 284 , 319 | a new iterative method for non - lte multilevel polarized radiative transfer in hydrogen lines is presented .
iterative methods ( such as the jacobi method ) tend to damp out high - frequency components of the error fast , but converges poorly due to slow reduction of low - frequency components .
the idea is to use a set of differently coarsed grids to reduce both the short- and long - period errors .
this leads to the so - called multigrid ( mg ) methods . for the grid of @xmath0 spatial points , the number of iterations required to solve a non - lte transfer problem is of the order of @xmath1
this fact could be of great importance for problems with fine structure and for multi - dimensional models .
the efficiency of the so - called standard mg iteration in comparison to jacobi iteration is shown .
the formalism of density matrix is applied to the demonstrative example of 1d , semi - infinite , non - magnetic , 3-principal level hydrogen atmospheric model .
the effect of depolarizing collisions with thermal electrons is taken into account as well as general treatment of overlapping profiles . |
despite decades of study our knowledge of the fundamental resonance spectrum of the nucleon is still incomplete . many resonance properties are uncertain and some resonances predicted to exist are yet to be observed .
most predictions of the resonance spectrum are based on phenomenological models , such as the constituent quark model or the di - quark model , but lattice predictions directly from quantum chromodynamics ( qcd ) are fast developing . experimental differentiation between these theoretical approaches based on the presently established resonance spectrum
is , however , inconclusive due to the many `` missing '' and poorly established resonances . insufficient accuracy and quantity of observables
obtained results in too many ambiguities and the famous case of the missing resonances in baryon spectroscopy @xcite .
have they not yet been observed or are they simply not there ? a promising tool to learn about the resonance spectrum is the photoproduction of pions from nucleon targets , as many resonances are expected to couple to the pion decay channel and polarised real photons , with a well - understood electromagnetic interaction , provide a powerful probe . in such pseudo - scalar meson production reactions
the measurement of differential cross section , all three single - polarisation ( beam , target , recoil nucleon ) and a total of four well chosen double - polarisation observables has the potential to give the first model independent extraction of the production amplitudes .
this will greatly enhance our capabilities to determine the nucleon excitation spectrum in a nearly model - independent way .
. this effort is being carried out at various electron - beam facilities worldwide .
one of the three single - polarisation observables , and a crucial one to constrain pwa s , is the beam asymmetry , @xmath0 , from linearly polarised photons : @xmath4 where @xmath5 is the linear beam polarisation and @xmath6 is the angle between the reaction plane and the photon polarisation plane .
data from the neutron is crucial in determining the resonance isospin and achieving a reliable extraction of the electromagnetic couplings of the excited states .
the world dataset on the neutron , however , is extremely sparse , consisting of only three fixed - angle experiments limited to the 1.70 - 2.05 gev range in energy and 35@xmath7 - 90@xmath7 in scattering angle . @xcite@xmath3@xcite@xmath3@xcite . a new , extensive photoproduction experiment using a polarised photon beam and
a liquid deuterium target has been carried out at jefferson laboratory , virginia , usa , march - june 2007 .
the experiment ran with both a circularly and a linearly polarised beam .
the linear polarisation plane was flipped frequently between two orthogonal orientations , parallel and perpendicular to the lab floor .
six photon energy settings were employed between 1.1 and 2.3 gev ( produced via coherent bremsstrahlung from an electron beam at 3.3 - 5.2 gev ) .
a single charged particle trigger was used , yielding a total of @xmath8 events recorded .
we present very preliminary measurements of @xmath0 from the analysis of the @xmath9 channel .
jefferson laboratory is home to a 1.4 km race - track electron accelerator operating at energies up to 6 gev ( an upgrade to 12 gev is currently underway ) .
200 @xmath10a of continuous current is split and delivered simultaneously to three experimental halls .
our experiment was conducted in hall b , where the electron beam is passed through a diamond crystal emitting linearly polarised photons via the process of coherent bremsstrahlung .
the scattered electrons are momentum analysed in the hall b photon tagging facility@xcite , which serves to `` tag '' the photons through a coincidence timing measurement between the deflected electrons and the event time in the detector .
the target cell is positioned in the centre of clas .
clas @xcite is a formidable multi - layer onion of detectors ( scintillators , drift chambers and calorimeters ) providing nearly full coverage in the azimuthal angle and from 8@xmath11 to 140@xmath11 in scattering angle ( lab frame ) which , combined with a toroidal magnetic field , offer excellent sensitivity to charged particles .
the reaction of interest can be considered as quasi - free with a spectator proton : @xmath12 the following data cuts are then applied to obtain a first selection of the @xmath9 channel : select two - particle events with particle masses of the @xmath13 and _ p _ in the final state .
cut on `` missing mass '' of the recoiling system to be consistent with the mass of a spectator proton .
select low `` missing momentum '' in the spectator system - below 0.15 gev / c .
cut on _ p _ and @xmath13 being back - to - back in centre - of - mass system ( cms ) .
the exact photon was identified through timing coincidence of the reaction in clas with the tagger .
this is made possible by the bunched nature of the beam , which arrives at 2 ns intervals .
as can be seen from ( [ asym_eq ] ) , the beam asymmetry is extracted from a @xmath14 fit to the @xmath6-distribution .
@xmath6 is , as before , the angle between the reaction plane and the photon polarisation plane . to make the following simplification possible
, we need to keep the plane from which we measure @xmath6 constant , so we choose to always measure from the horizontal polarisation plane , which is also the horizontal plane of clas in the lab frame . in order to reduce systematics ,
the polarisation plane was rotated between two orthogonal directions during the experiment , with @xmath6 being always measured from the horizontal plane of clas , simplifying the expression thus ( fig .
[ f5 ] ) : @xmath15 @xmath16 @xmath17 where @xmath18 is the differential cross - section from ( [ asym_eq ] ) using a parallel beam polarisation and @xmath19 , consequently , a perpendicular polarisation .
we make the assumption that @xmath20 .
calibrations are still underway , but a very preliminary evaluation of @xmath21 0.4@xmath22 of the data indicates a tiny statistical uncertainty ( fig .
it is our goal to reduce systematics , which are currently very large , to @xmath21 5@xmath22 .
4.7 cm 4.7 cm
the determination of the beam asymmetry , @xmath0 , from a linearly polarised photon beam incident on a neutron ( in a liquid deuterium target ) is underway .
early analysis shows that the data quality is good , statistical uncertainty is tiny and a sizeable asymmetry can be seen at backward angles .
a full analysis is to follow soon in scattering angle range 20@xmath11 - 145@xmath11 ( in cms ) and entire photon energy range 1.1 - 2.3 gev .
the measurement promises to greatly expand the sparse world data - set on the neutron and aid in constraining the determination of the reaction amplitudes in pion photoproduction thus providing strong constraints on the nucleon excitation spectrum .
9 v. burkert , t. s. h. lee , _ int .
j. of mod .
* 13 * , 1035 ( 2004 ) .
i. barker , a. donnachie , j. storrow , _ nucl .
b _ * 95 * , 347 ( 1975 ) . w .-
chiang , f. tabakin , _ phys .
c _ * 55 * , 2054 ( 1997 ) .
j. alspector _
_ , _ phys .
_ * 28 * , 1403 ( 1972 )
. l. abrahamian _
. j. nucl .
phys . _ * 32 * , 69 ( 1980 ) .
f. adamyan _
_ , _ j. phys
. g _ * 15 * , 1797 ( 1989 ) . d.
sober _ et al .
_ , _ nucl .
instr . and meth . a _ * 440 * , 263 ( 2000 ) . b. mecking
_ , _ nucl . instr . and meth .
a _ * 503 * , 513 ( 2003 ) . | we present a preliminary analysis of the photon beam asymmetry observable ( @xmath0 ) from the photoproduction reaction channel @xmath1 .
this new data was obtained using the near-@xmath2 cebaf large acceptance spectrometer ( clas ) at jefferson laboratory , usa , employing a linearly polarised photon beam with an energy range 1.1 - 2.3 gev .
the measurement will provide new data to address the poorly established neutron excitation spectrum and will greatly expand the sparse world data - set both in energy and angle . |