Chapter 14_ Fluctuations .pdf

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1、Chapter14ElectromagneticFluctuationsThethermalandzero-pointmotionofelectricallychargedparticlesinsidematerialsgivesrisetoafluctuatingelectromagneticfield.Quantumtheorytellsusthatthefluctuatingparticlescanonlyassumediscreteenergystatesand,asaconsequence,theemittedfluctuat

2、ingradiationtakesonthespectralformofblackbodyradiation.However,whilethefamiliarblackbodyradiationformulaisstrictlycorrectonlyatthermalequilibrium,itisonlyanapproximationfornon-equilibriumsituations.Thisapproximationisreasonableatlargerdistancesfromtheemittingmaterial

3、(farfield)butitcanstronglydeviatefromthetruebehaviorclosetomaterialsurfaces(near-field).Becausefluctuationsofchargeandcurrentinmaterialsleadtodissipationviaradiationnoobjectatfinitetemperaturecanbeinthermalequilibriuminfreespace.Equilibriumwiththeradiationfieldcanonlybeac

4、hievedbyconfiningtheradiationtoafinitespace.However,inmostcasestheobjectcanbeconsideredtobeclosetoequilibriumandthenon-equilibriumbehaviorcanbedescribedbylinearresponsetheory.Inthisregime,themostimportanttheoremisthefluctuation-dissipationthe-orem.Itrelatestherateofener

5、gydissipationinanon-equilibriumsystemtothefluctuationsthatoccurspontaneouslyatdifferenttimesinequilibriumsystems.Thefluctuation-dissipationtheoremisofrelevancefortheunderstandingoffluc-tuatingfieldsnearnanoscaleobjectsandopticalinteractionsatnanoscaledistances.Thischapter

6、isintendedtoprovideadetailedderivationofsomeimportantaspectsinfluctuationalelectrodynamics.12CHAPTER14.ELECTROMAGNETICFLUCTUATIONS14.1TheFluctuation-DissipationTheoremThefluctuation-dissipationtheoremismostcommonlyderivedbyapplyingFermi’sGoldenRuleandevaluatingquantumc

7、orrelationfunctions.ThetheoremhasitsrootsinNyquist’srelationforvoltagefluctuationsacrossaresistor.However,itwasCallenandWeltonwhoderivedthetheoreminitsgeneralform[1].Theherepresentedderivationispurelyclassical.AsubstitutionattheendofthederivationintroducesPlanck’scons

8、tantintothetheorem.Althoughthefluctuation-dissipationtheoremcanbederivedinquitegeneraltermsusingunspecifiedvariables,itismoreintuitiv