Table Of ContentSpringerSeriesin
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
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SeriesEditors:
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114 InteratomicPotential 126 PhysicalPropertiesofQuasicrystals
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Editors:K.TerakuraandH.Akai 127 PositronAnnihilation
115 UltrafastSpectroscopy inSemiconductors
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SemiconductorNanostructures ByR.Krause-Rehberg
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116 ElectronSpectrum 128 Magneto-Optics
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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
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125 PhysicsandChemistry
ofTransition-MetalOxides
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andN.Nagaosa
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The Springer Series in Solid-State Sciences consists of fundamental scientific books
preparedbyleadingresearchersinthefield.Theystrivetocommunicate,inasystematic
andcomprehensiveway,thebasicprinciplesaswellasnewdevelopmentsintheoreticaland
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136 NanoscalePhaseSeparation 144 PhysicsofTransitionMetalOxides
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138 PhaseSeparation 147 ElectronScatteringinSolidMatter
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MicellarSolutions,Microemulsions, andComputationalTreatise
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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,
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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
