Quantum tunnelling in a dissipative system .pdf

Quantum tunnelling in a dissipative system .pdf

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1、ANNALSOFPHYSICS149,374-456(1983)QuantumTunnellinginaDissipativeSystemA.0.CALDEIRAInstitutedeFisica“GlebWataghin”UniversidadeEstadualdeCampinas,CidadeUniuersitaria,BaraoGeraldo.13-100Campinas,SaoPaula,BrazilANDA.J.LEGGETT*SchoolofMathematicalandPhysicalSciences,UniversityofS

2、ussex.Falmer,BrightonBNl9QH,EnglandReceivedJuly22,1982;revisedDecember20.1982Inthispaperweattempttomotivate,define,andresolvethequestion“Whatistheeffectofdissipationonquantumtunnelling?”Thequestionisofparticularinterestinthecontextoftunnellingofamacroscopicvariablesuchasthe

3、trappedfluxinaSQUID,whereweshowthatitiscrucialtoresolveitinthecontextoftestsofthevalidityofquantummechanicsatthemacroscopiclevel,butitisalsorelevanttovariousmicroscopictunnellingsituations.Wedefinethequestionasfollows:Supposewehaveasystem,whichhasametastableminimumandwhoseq

4、uasiclassicalequationofmotionintheregionneartheminimumisgivenbywherethepotentialV(q)andfrictioncoefficientqareregardedasexperimentallydeterminedquantities(andtheenergydissipatedirreversiblyperunittimeissimply~4’).HowdoesthetunnellingbehaviourofsuchasystematT=0differfromthat

5、ofoneobeyingasimilarequation,withthesamepotentialV(q)andmassM,butwithfrictioncoefficientrjequaltozero?Westartbyarguingthatprovidedanyonedegreeoffreedomoftheenvironmentisonlyweaklyperturbedbythemotionofthesystem,thenatT=0itisalwayspossible,withouranytossofgenerality,torepres

6、enttheenvironmentasabathofharmonicoscillators;moreover,ifthedampedequationofmotionisindeedoftheaboveform,then(barring,possibly,certainapparentlypathologicalcases)itispossibletochoosethesystem-bathcouplingtobelinearinthe(suitablychosen)oscillatorcoordinatesandafunctiononlyof

7、thesystemcoordinate(i.e.,oftheformCjFj(q)xj).Inparticularthisisalwayspossiblefortheimportantcaseofadiabatic*Currentaddress:DepartmentofPhysics,UniversityofIllinois,Urbana,Illinois61801.3740003.4916/83$7.50Copyright01983byAcademicPress,Inc.Allrightsofreproductioninanyformres

8、erved.DISSIPATIONANDQUANTUMTUNNELLING315coupling.Incertaincases(whichwerefertoasca

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