Condensation Transitions in a One-Dimensional Zero-Range Process with a Single Defect Site

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1、CondensationTransitionsinaOne-DimensionalZero-RangeProcesswithaSingleDefectSiteA.G.Angel,1M.R.Evans,1andD.Mukamel21SchoolofPhysics,UniversityofEdinburgh,MayfieldRoad,EdinburghEH93JZ,UK2DepartmentofPhysicsofComplexSystems,WeizmannInstituteofScience,Rehovot,Israe

2、l76100(Dated:February2,2008)Condensationoccursinnonequilibriumsteadystateswhenafinitefractionofparticlesinthesystemoccupiesasinglelatticesite.Westudycondensationtransi-tionsinaone-dimensionalzero-rangeprocesswithasingledefectsite.Thesystemisanalysedinthegrandca

3、nonicalandcanonicalensemblesandthetwoarecontrasted.Twodistinctcondensationmechanismsarefoundinthegrandcanonicalensemble.Discrepanciesbetweentheinfiniteandlargebutfinitesystems’particlecurrentver-susparticledensitydiagramsareinvestigatedandanexplanationforhowthefi

4、nitecurrentgoesaboveamaximumvaluepredictedforinfinitesystemsisfoundinthecanonicalensemble.I.INTRODUCTIONCondensationtransitions[1]havebeenobservedinawidevarietyofnonequilibriumsteadystates[2,3].Suchatransitionoccurswhenasinglelatticesitecontainsafinitefractionof

5、particlesofthesystem.Condensationtransitionsarealsomanifestedinadifferentguiseindrivendiffusivesystems,wheretypicallytheparticlesobeyhard-coreexclusion.Therethecondensationappearsasatransitionfromafreelyflowingfluidphasetoajammedphase[2].Suchjammingtransitionshave

6、beenreported,forexample,inthecontextoftrafficflowmodelling[4].arXiv:cond-mat/0401262v1[cond-mat.stat-mech]15Jan2004AsimplelatticemodelknownastheZero-RangeProcess(ZRP)[5]illustratesanequiva-lencebetweencondensationandjammingtransitionsandprovidesaframeworkwithinwh

7、ichcondensationtransitionsmaybeanalysed[1,2,6].Inthemodelparticleshopbetweenlat-ticesiteswithrateswhichdependonthenumberofparticlesatthedeparturesite.Iftheratesdecaytozerooriftheydecayslowlyenoughtoafinitevalueastheparticlenum-berisincreased,onefindsacondensatio

8、ntransitionwherebyasinglelatticesitebecomesmacroscopicallyoccupied.TheconnectionbetweencondensationandjammingtransitionswasfirstmadeinthecontextoftheBusRouteModel[2]whereanapproxima