Greens Functions in Quantum Physics PDF
Preview Greens Functions in Quantum Physics
SpringerSeriesin solid-state sciences 7 SpringerSeriesin solid-state sciences SeriesEditors: M.Cardona P.Fulde K.vonKlitzing R.Merlin H.-J.Queisser H.Sto¨rmer 90 EarlierandRecentAspects 102 ConjugatedConductingPolymers ofSuperconductivity Editor:H.Kiess Editor:J.G.BednorzandK.A.Mu¨ller 103 MolecularDynamicsSimulations 91 ElectronicProperties Editor:F.Yonezawa andConjugatedPolymersIII 104 ProductsofRandomMatrices Editors:H.Kuzmany,M.Mehring, inStatisticalPhysics ByA.Crisanti, andS.Roth G.Paladin,andA.Vulpiani 92 PhysicsandEngineering 105 Self-TrappedExcitons ApplicationsofMagnetism 2ndEdition Editors:Y.IshikawaandN.Miura ByK.S.SongandR.T.Williams 93 Quasicrystals 106 PhysicsofHigh-Temperature Editor:T.FujiwaraandT.Ogawa Superconductors 94 ElectronicConductioninOxides Editors:S.MaekawaandM.Sato 2nd Edition By N.Tsuda,K.Nasu, 107 ElectronicPropertiesofPolymers A.Fujimori,andK.Siratori OrientationandDimensionality 95 ElectronicMaterials ofConjugatedSystems ANewErainMaterialsScience Editors:H.Kuzmany,M.Mehring, Editors:J.R.Chelikowski andS.Roth andA.Franciosi 108 SiteSymmetryinCrystals 96 ElectronLiquids TheoryandApplications 2ndEdition ByA.Isihara 2ndEdition 97 LocalizationandConfinement ByR.A.EvarestovandV.P.Smirnov ofElectronsinSemiconductors 109 TransportPhenomena Editors:F.Kuchar,H.Heinrich, inMesoscopicSystems andG.Bauer Editors:H.FukuyamaandT.Ando 98 MagnetismandtheElectronic 110 Superlattices StructureofCrystals andOtherHeterostructures ByV.A.Gubanov,A.I.Liechtenstein, SymmetryandOpticalPhenomena andA.V.Postnikov 2ndEdition 99 ElectronicProperties ByE.L.IvchenkoandG.E.Pikus ofHigh-TcSuperconductors 111 Low-DimensionalElectronicSystems andRelatedCompounds NewConcepts Editors:H.Kuzmany,M.Mehring, Editors:G.Bauer,F.Kuchar, andJ.Fink andH.Heinrich 100 ElectronCorrelationsinMolecules 112 PhononScattering andSolids inCondensedMatterVII 3rdEdition ByP.Fulde Editors:M.MeissnerandR.O.Pohl 101 HighMagneticFields 113 ElectronicProperties inSemiconductorPhysicsIII ofHigh-TcSuperconductors QuantumHallEffect,Transport Editors:H.Kuzmany,M.Mehring, andOptics ByG.Landwehr andJ.Fink SpringerSeriesin solid-state sciences SeriesEditors: M.Cardona P.Fulde K.vonKlitzing R.Merlin H.-J.Queisser H.Sto¨rmer 114 InteratomicPotential 126 PhysicalPropertiesofQuasicrystals andStructuralStability Editor:Z.M.Stadnik Editors:K.TerakuraandH.Akai 127 PositronAnnihilation 115 UltrafastSpectroscopy inSemiconductors ofSemiconductorsand DefectStudies SemiconductorNanostructures ByR.Krause-Rehberg ByJ.Shah andH.S.Leipner 116 ElectronSpectrum 128 Magneto-Optics ofGaplessSemiconductors Editors:S.SuganoandN.Kojima ByJ.M.Tsidilkovski 129 ComputationalMaterialsScience 117 ElectronicPropertiesofFullerenes FromAbInitiotoMonteCarlo Editors:H.Kuzmany,J.Fink, Methods. ByK.Ohno,K.Esfarjani, M.Mehring,andS.Roth andY.Kawazoe 118 CorrelationEffectsinLow- 130 Contact,AdhesionandRupture DimensionalElectronSystems ofElasticSolids Editors:A.OkijiandN.Kawakami ByD.Maugis 119 SpectroscopyofMottInsulators 131 Field Theories for Low-Dimensional andCorrelatedMetals CondensedMatterSystems Editors:A.FujimoriandY.Tokura SpinSystems 120 OpticalProperties andStronglyCorrelatedElectrons ofIII–VSemiconductors ByG.Morandi,P.Sodano, TheInfluenceofMulti-ValleyBand A.Tagliacozzo,andV.Tognetti Structures ByH.Kalt 132 VorticesinUnconventional 121 ElementaryProcessesinExcitations SuperconductorsandSuperfluids andReactionsonSolidSurfaces Editors: R.P.Huebener, N.Schopohl, Editors:A.Okiji,H.Kasai, andG.E.Volovik andK.Makoshi 133 TheQuantumHallEffect 122 TheoryofMagnetism ByD.Yoshioka ByK.Yosida 134 MagnetismintheSolidState 123 QuantumKineticsinTransport ByP.Mohn andOpticsofSemiconductors 135 Electrodynamics ByH.HaugandA.-P.Jauho ofMagnetoactiveMedia 124 RelaxationsofExcitedStatesand ByI.Vagner,B.I.Lembrikov, Photo-InducedStructural andP.Wyder PhaseTransitions Editor:K.Nasu 125 PhysicsandChemistry ofTransition-MetalOxides Editors:H.Fukuyama andN.Nagaosa SpringerSeriesin solid-state sciences SeriesEditors: M.Cardona P.Fulde K.vonKlitzing R.Merlin H.-J.Queisser H.Sto¨rmer The Springer Series in Solid-State Sciences consists of fundamental scientific books preparedbyleadingresearchersinthefield.Theystrivetocommunicate,inasystematic andcomprehensiveway,thebasicprinciplesaswellasnewdevelopmentsintheoreticaland experimentalsolid-statephysics. 136 NanoscalePhaseSeparation 144 PhysicsofTransitionMetalOxides andColossalMagnetoresistance ByS.Maekawa,T.Tohyama, ThePhysicsofManganites S.E.Barnes,S.Ishihara, andRelatedCompounds W.Koshibae,andG.Khaliullin ByE.Dagotto 145 Point-ContactSpectroscopy 137 QuantumTransport ByY.G.NaidyukandI.K.Yanson inSubmicronDevices 146 OpticsofSemiconductors ATheoreticalIntroduction andTheirNanostructures ByW.MagnusandW.Schoenmaker Editors:H.KaltandM.Hetterich 138 PhaseSeparation 147 ElectronScatteringinSolidMatter inSoftMatterPhysics ATheoretical MicellarSolutions,Microemulsions, andComputationalTreatise CriticalPhenomena ByJ.Zabloudil,R.Hammerling, ByP.K.KhabibullaevandA.A.Saidov L.Szunyogh,andP.Weinberger 139 OpticalResponseofNanostructures 148 PhysicalAcousticsintheSolidState MicroscopicNonlocalTheory ByB.Lu¨thi ByK.Cho 149 SolitaryWaves 140 FractalConcepts inComplexDispersiveMedia inCondensedMatterPhysics Theory·Simulation·Applications ByT.NakayamaandK.Yakubo ByV.Yu.BelashovandS.V.Vladimirov 141 ExcitonsinLow-Dimensional 150 TopologyinCondensedMatter Semiconductors Editor:M.I.Monastyrsky Theory,NumericalMethods, 151 ParticlePenetrationandRadiation Applications ByS.Glutsch Effects 142 Two-DimensionalCoulombLiquids ByP.Sigmund andSolids 152 Magnetism ByY.MonarkhaandK.Kono FromFundamentals 143 X-RayMultiple-WaveDiffraction toNanoscaleDynamics TheoryandApplication ByH.C.SiegmannandJ.Sto¨hr ByS.-L.Chang Volumes90–135arelistedattheendofthebook. Eleftherios N. Economou Green’s Functions in Quantum Physics ThirdEdition With60Figures 123 EleftheriosN.Economou UniversityofCrete FoundationforResearchandTechnology-Hellas(FORTH) DepartmentofPhysics P.O.Box1527 71110Heraklion,Crete,Greece E-mail:[email protected] SeriesEditors: ProfessorDr.,Dres.h.c.ManuelCardona ∗ ProfessorDr.,Dres.h.c.PeterFulde ProfessorDr.,Dres.h.c.KlausvonKlitzing ProfessorDr.,Dres.h.c.Hans-JoachimQueisser Max-Planck-Institutfu¨rFestko¨rperforschung,Heisenbergstrasse1,70569Stuttgart,Germany ∗Max-Planck-Institutfu¨rPhysikkomplexerSysteme,No¨thnitzerStrasse38 01187Dresden,Germany ProfessorDr.RobertoMerlin DepartmentofPhysics,5000EastUniversity,UniversityofMichigan AnnArbor,MI48109-1120,USA ProfessorDr.HorstSto¨rmer Dept.Phys.andDept.Appl.Physics,ColumbiaUniversity,NewYork,NY10027and BellLabs.,LucentTechnologies,MurrayHill,NJ07974,USA LibraryofCongressControlNumber:2006926231 ISSN0171-1873 ISBN-10 3-540-28838-4 3rded.SpringerBerlinHeidelbergNewYork ISBN-13 978-3-540-28838-1 3rded.SpringerBerlinHeidelbergNewYork ISBN 3-540-12266-4 2nded.Springer-VerlagBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned, specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproduction onmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofis permittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion, andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliabletoprosecutionunderthe GermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springer.com ©Springer-VerlagBerlinHeidelberg1979,1983,2006 PrintedinGermany Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsand regulationsandthereforefreeforgeneraluse. TypesettingbytheauthorandLE-TEXGbR Coverconcept:eStudioCalamarSteinen Coverproduction:design&productionGmbH,Heidelberg Production:LE-TEXJelonek,Schmidt&VöcklerGbR,Leipzig Printedonacid-freepaper 57/3100/YL-543210 To Sophia Preface to the Third Edition In this third edition the book has been expanded in three directions: 1. Problems have been added at the end of each chapter (40% of which are solved in the last section of the book) together with suggestions for further reading. Furthermore, the number of appendices (marked with a grey stripe) has been substantially enlarged in order to make the book more self-sufficient. These additions, together with many clarifications in the text, render the book more suitable as a companion in a course on Green’s functions and their applications. 2. Theimpressivedevelopmentsofthe1980sand1990sinmesoscopicphysics, and in particular in transport properties, found their way – to a cer- tain extent – in the new Chaps.8 and 9 (which also contain some of the material of the old Chap.7). This is a natural expansion, since Green’s functions have played an important role as a theoretical tool in this new field of physics, a role that continues in nanoregime research (see, e.g., recent publications dealing with carbon nanotubes). Thus, the powerful and unifying formalism of Green’s functions finds applications not only in standard physics subjects such as perturbation and scattering theory, bound-stateformation,etc.,butalsoattheforefrontofcurrentand,most likely, future developments. 3. Overthelast15yearsorsoGreen’sfunctionshavefoundapplicationsnot onlyincondensedmatterelectronicmotionbutinclassicalwavepropaga- tion in both periodic and random media; photonic and phononic crystals aretheoutcomesofthislineofresearchwhoseunderlyingbasictheoretical principles are summarized in Sect.7.2.4. IwouldliketothankMs.MinaPapadakisandDr.StamatisStamatiadiswhose help was invaluable during the writing and typesetting of this drastically re- vised third edition of my book. Heraklion, Crete, March 2005 E.N. Economou Preface to the Second Edition In this edition, the second and main part of the book has been considerably expanded so as to cover important applications of the formalism of Green’s functions. In Chap.5 a section was added outlining the extensive role of the tight- binding (or, equivalently, the linear combination of atomiclike orbitals) ap- proach to many branches of solid-state physics. Some additional information (including a table of numerical values) regarding square and cubic lattice Green’s functions were incorporated. InChap.6thedifficultsubjectsofsuperconductivityandtheKondoeffect are examined employing an appealingly simple connection to the question of the existence of a bound state in a very shallow potential well. The existence ofsuchaboundstatedependsentirelyontheformoftheunperturbeddensity ofstatesnearthe end ofthe spectrum: ifthedensity ofstates blowsup, there is always at least one bound state. If the density of states approaches zero continuously, a critical depth (and/or width) of the well must be reached in order to have a bound state. The borderline case of a finite discontinuity (which is very important to superconductivity and the Kondo effect) always produces a bound state with an exponentially small binding energy. Chapter 7 has been expanded to cover details of the new and fast- developing field of wave propagation in disordered media. The coherent po- tential approximation (a simple but powerful method) is presented with an extensive list of references to the current literature. Then the electrical con- ductivity is examined both because it is an interesting quantity in its own right and because it plays a central role in demonstrating how disorder can createa qualitativelydifferentbehavior.Since the publicationofthe firstedi- tionofthisbook,significantadvancesinthefieldofrandommediahavetaken place.Anefforthasbeenmadetopresentinasimple waytheessentialpoints of these advances (for the reader with a casual interest in this subject) and to review the current literature (for the benefit of the reader whose research activities are or will be related to the field of disordered systems). X Preface to the Second Edition In this edition, eachchapter is precededby a shortoutline ofthe material to be covered and concluded by a summary containing the most important equations numbered as in the main text. I would like to thank A. Andriotis and A. Fertis for pointing out to me severalmisprintsinthe firstedition.Iwouldalsoliketo expressmy gratitude to Exxon Research and Engineering Company for its hospitality during the final stages of this work. Heraklion, Crete, January 1983 E.N. Economou
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