Restricted quantum-classical correspondence and counting statistics for a coherent transiti

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1、Restrictedquantum-classicalcorrespondenceandcountingstatisticsforacoherenttransitionMayaChuchemandDoronCohenDepartmentofPhysics,Ben-GurionUniversity,Beer-Sheva84105,IsraelTheconventionalprobabilisticpointofviewimpliesthatifaparticlehasaprobabilityptomakeatransitionfromonesitetoanot

2、hersite,thentheaveragetransportshouldbehQi=pwithavarianceVar(Q)=(1−p)p.Inthequantummechanicalcontextthisobservationbecomesanon-trivialmanifestationofrestrictedquantum-classicalcorrespondence.Wedemonstratethisobservationbyconsideringthefullcountingstatisticswhichisassociatedwithatwo

3、levelcoherenttransitioninthecontextofacontinuousquantummeasurementprocess.InparticularwetestthepossibilityofgettingavalidresultforVar(Q)withintheframeworkoftheadiabaticpicture,analyzingthesimplestnon-trivialexampleofaLandau-Zenercrossing.I.INTRODUCTIONparticleeithermakesthetransiti

4、onornot.AccordinglytheintegratedcurrentfromthefirsttothesecondsiteiseitherQ=1orQ=0respectively.ItfollowsthatThediscussionofquantum-classicalcorrespondence(QCC)inthemathematicalphysicsliteratureisasoldhQi=p(1)asthehistoryofquantummechanics.Traditionallyonehasinmindcomplicatedsemiclas

5、sicalapproximationwiththevarianceschemesforcalculatingthepropagationofwavepackets.Amoreelaboratedanalysisofthespreadingprocess[1],Var(Q)=(1−p)p(2)leadstothedistinctionbetweenrobustrestrictedQCCandfragiledetailedQCC.RestrictedQCCmeansthatThisclassicalprobabilisticpointofviewdoesnoth

6、oldhAiqm≈hAiclholdsonlyforarestrictedsetofobserv-inthequantummechanicalreality.Thecharacterizationables,andsurviveseveninthepresenceofdiffraction,ofthefullcountingstatisticsrequiressomecareinwhiledetailedQCCmeanshAiqm≈hAiclforallthewellthedescriptionofacontinuousquantummeasurement.b

7、ehavedobservables,andrequiressmoothpotentialsasAccordinglyonehastodistinguishbetweenthenaiveinthetraditionalformulation.mathematicaldefinition[8]oftheQprobabilitydistribu-tionP(Q),andtheproperphysicaldefinition[20]oftheControllingatomsinafewsitesystemisstateofthequasi-probabilitydist

8、ributionP(Q;x),wherexsigni