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1、DynamicPhaseDiagramfortheQuantumPhaseModelP.Buonsante,1L.Orefice,1,2andA.Smerzi11QSTARandINO-CNR,LargoFermi2,50125Firenze,Italia2DipartimentodiFisica,Universit`adegliStudidiBologna,ViaIrnerio46,40126Bologna,ItaliaWeaddressthestabilityofsuperfluidcurrentsinasystemofintera
2、ctinglatticebosons.WeconsidervariousGutzwillertrialstatesforthequantumphasemodelwhichprovidesagoodapprox-imationfortheBose-Hubbardmodelinthelimitoflargeinteractionsandbosonpopulations.Wethoroughlyanalyzethecurrent-carryingstationarystatesofthedynamicsensuingfromaGaussi
3、anansatz,andderiveanalyticalresultsforthecriticallinessignalingtheirmodulationalandener-geticinstability,aswellasthemaximumofthecarriedcurrent.WeshowthattheseanalyticalresultsareingoodqualitativeagreementwiththoseobtainednumericallyinpreviousworksontheBose-Hubbardmodel
4、,andinthepresentworkforthequantumphasemodel.I.INTRODUCTIONWediscusssomeartifactsintheabovepicture,bycom-paringitagainstnumericalresultsforthemostgeneralproducttrialstate.Finally,weintroduceanewana-Current-carryingstationarystatesofultracoldbosonslyticallytractabletrial
5、state,whosefactorsdependonainopticallatticesareknowntoundergoadynamicaltran-singleparameter,andshowthatitprovidesaremarkablysitionwhenthephasegradientassociatedwiththeflowgoodapproximationforsomeofthenumericallyobtainedexceedsacriticalvalue.Intheregimeoflargedensi-resul
6、ts.tiesandsmallinteractions,wherethediscretenonlinearSchr¨odingerequationsresultingfromatight-bindingap-Theplanofthepaperisthefollowing:InSectionIIweproximationoftheGross-Pitaevskiiequationapply,thebrieflyreviewtheQPManditsrelationwiththeBose-criticalphasegradientturnso
7、uttobep=π[30–33].The2Hubbardmodel;InSectionIIIweintroduceourGaussianinclusionofquantumfluctuationsinthetight-bindingde-ansatz,anddiscussthecharacterofthecurrent-carryingscription,viaaGutzwillertrialstate,revealsthatthestationarystatesthereof;InSectionIVwecomparethecriti
8、calvalueisadecreasingfunctionoftheeffectivein-analyticalresultsderivedinSectionIIIagainstthoseteraction.Specifically,th
