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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