Springer.Braun.D.Dissipative.quantum.chaos.and.decoherence.(STMP.172.Springer.2001)(ISBN.3540411976)(125s)

《Springer.Braun.D.Dissipative.quantum.chaos.and.decoherence.(STMP.172.Springer.2001)(ISBN.3540411976)(125s)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、1.IntroductionThenotionof“chaos”emergedinclassicalphysicsaboutacenturyagowiththepioneeringworkofPoincar´e.AftertwoandahalfcenturiesofapplicationofNewton’slawstomoreandmorecomplicatedastronomicalproblems,hewasprivilegedtodiscoverthateveninverysimplesystemsextremelyco

2、m-plicatedandunstableformsofmotionarepossible[1].Itseemsthatthisfirstappearedacuriositytohiscontemporaries.Moreover,quantummechanicsandrelativisticmechanicsweresoontobediscoveredanddistractedmostoftheattentionfromclassicalproblems.Inanycase,classicalchaosinterestedmo

3、stlyonlymathematicians,fromG.Birkhoffinthe1920stoKolmogorovandhiscoworkersinthe1950s.OnlyEinstein,asearlyas1917,i.e.evenbeforeSchr¨odinger’sequationwasinvented,clearlysawthatchaosinclassi-calmechanicsalsoposedaprobleminquantummechanics[2].Therestoftheworldstartedtore

4、alizetheimportanceofchaosonlywhencomputersallowedustosimulatesimplephysicalsystems.Itthenbecameobviousthatintegrablesystems,withtheirpredictabledynamics,thathadbeentheback-boneofphysicsforbythenthreecenturieswereanexception.Almostalwaysthereareatleastsomeregionsinph

5、asespacewherethedynamicsbecomesirregularandverysensitivetotheslightestchangesintheinitialconditions.Theinprincipleperfectpredictabilityofclassicalsystemsoverarbitrarytimeintervalsgivenapreciseknowledgeofallinitialpositionsandmomentaofallparticlesinvolvedisentirelyus

6、elessforsuch“chaotic”systems,asinitialconditionsareneverpreciselyknown.Theunderstandingofquantummechanicsnaturallydevelopedfirstofallwiththesolutionofthesameintegrablesystemsknownfromclassicalme-chanics,suchasthehydrogenatom(asavariantofKepler’sproblem)ortheharmonico

7、scillator.Withthegrowingconvictionthatintegrablesystemsarearareexception,itbecamenaturaltoaskhowthequantummechanicalbe-haviorofsystemswhoseclassicalcounterpartischaoticmightlook.ResearchinthisdirectionwaspioneeredbyGutzwiller.Intheearly1970shepublisheda“traceformula

8、”whichallowsonetocalculatethespectraldensityofchaoticsystems[3,4].Thatworkwasextendedlaterbyvariousresearcherstootherquantities,suchastran