Economou Green's Functions in Quantum Physics

3rd Auflage 2006
ISBN: 978-3-540-28841-1
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 7, 480 Seiten

Reihe: Springer Series in Solid-State Sciences

Mathematical and Computational Physics - Short description currently not available.

Autoren/Hrsg.

Economou, Eleftherios N.

Inhaltsverzeichnis

1;Preface to the Third Edition;9
2;Preface to the Second Edition;10
3;Preface to the First Edition;12
4;Contents;14
5;Part I Green’s Functions in Mathematical Physics;19
5.1;1 Time-Independent Green’s Functions;20
5.1.1;1.1 Formalism;20
5.1.2;1.2 Examples;26
5.1.3;1.3 Summary;31
5.1.4;Further Reading;34
5.1.5;Problems7;34
5.2;2 Time-Dependent Green’s Functions;37
5.2.1;2.1 First-Order Case;37
5.2.2;2.2 Second-Order Case;42
5.2.3;2.3 Summary;49
5.2.4;Further Reading;52
5.2.5;Problems;52
6;Part II Green’s Functions in One-Body Quantum Problems;54
6.1;3 Physical Signi.cance of Application to the Free-Particle Case;55
6.1.1;3.1 General Relations;55
6.1.2;3.2 The Free-Particle Case;57
6.1.3;3.3 The Free-Particle Klein–Gordon Case;61
6.1.4;3.4 Summary;64
6.1.5;Further Reading;65
6.1.6;Problems;65
6.2;4 Green’s Functions and Perturbation Theory;68
6.2.1;4.1 Formalism;68
6.2.2;4.2 Applications;77
6.2.3;4.3 Summary;84
6.2.4;Further Reading;87
6.2.5;Problems;87
6.3;5 Green’s Functions for Tight-Binding Hamiltonians;89
6.3.1;5.1 Introductory Remarks;89
6.3.2;5.2 The Tight-Binding Hamiltonian (TBH);92
6.3.3;5.3 Green’s Functions;99
6.3.4;5.4 Summary;113
6.3.5;Further Reading;114
6.3.6;Problems;114
6.4;6 Single Impurity Scattering;123
6.4.1;6.1 Formalism;123
6.4.2;6.2 Explicit Results for a Single Band;130
6.4.3;6.3 Applications;137
6.4.4;6.4 Summary;149
6.4.5;Further Reading;151
6.4.6;Problems;152
6.5;7 Two or More Impurities; Disordered Systems;153
6.5.1;7.1 Two Impurities;153
6.5.2;7.2 In.nite Number of Impurities;162
6.5.3;7.3 Summary;180
6.5.4;Further Reading;181
6.5.5;Problems;181
6.6;8 Electrical Conductivity and Green’s Functions;184
6.6.1;8.1 Electrical Conductivity and Related Quantities;184
6.6.2;8.2 Various Methods of Calculation;187
6.6.3;8.3 Conductivity in Terms of Green’s Functions;194
6.6.4;8.4 Summary;206
6.6.5;Further Reading;208
6.6.6;Problems;208
6.7;9 Localization, Transport, and Green’s Functions;210
6.7.1;9.1 An Overview;210
6.7.2;9.2 Disorder, Di.usion, and Interference;214
6.7.3;9.3 Localization;219
6.7.4;9.4 Conductance and Transmission;227
6.7.5;9.5 Scaling Approach;230
6.7.6;9.6 Other Calculational Techniques;235
6.7.7;9.7 Localization and Green’s Functions;237
6.7.8;9.8 Applications;249
6.7.9;9.9 Summary;251
6.7.10;Further Reading;254
6.7.11;Problems;254
7;Part III Green’s Functions in Many-Body Systems;258
7.1;10 Definitions;259
7.1.1;10.1 Single-Particle Green’s Functions in Terms;259
7.1.2;of Field Operators;259
7.1.3;10.2 Green’s Functions for Interacting Particles;263
7.1.4;10.3 Green’s Functions for Noninteracting Particles;267
7.1.5;10.4 Summary;270
7.1.6;Further Reading;271
7.1.7;Problems;271
7.2;11 Properties and Use of the Green’s Functions;273
7.2.1;11.1 Analytical Properties of;273
7.2.2;and;273
7.2.3;11.2 Physical Signi.cance and Use of;278
7.2.4;and;278
7.2.5;11.3 Quasiparticles;285
7.2.6;11.4 Summary;291
7.2.7;Further Reading;293
7.2.8;Problems;293
7.3;12 Calculational Methods for;294
7.3.1;12.1 Equation of Motion Method;294
7.3.2;12.2 Diagrammatic Method for Fermions at;298
7.3.3;= 0;298
7.3.4;12.3 Diagrammatic Method for;307
7.3.5;0;307
7.3.6;12.4 Partial Summations. Dyson’s Equation;309
7.3.7;12.5 Other Methods of Calculation;315
7.3.8;12.6 Summary;315
7.3.9;Further Reading;316
7.3.10;Problems;316
7.4;13 Applications;318
7.4.1;13.1 Normal Fermi Systems. Landau Theory;318
7.4.2;13.2 High-Density Electron Gas;321
7.4.3;13.3 Dilute Fermi Gas;328
7.4.4;13.4 Superconductivity;331
7.4.5;13.5 The Hubbard Model;336
7.4.6;13.6 Summary;341
7.4.7;Further Reading;342
7.4.8;Problems;343
8;Appendices;345
8.1;A Dirac’s delta Function;345
8.2;B Dirac’s bra and ket Notation;348
8.3;C Solutions of Laplace and Helmholtz Equations in Various Coordinate Systems1;352
8.3.1;C.1 Helmholtz Equation (.;352
8.3.2;+;352
8.3.3;(;352
8.3.4;= 0;352
8.3.5;C.2 Vector Derivatives;354
8.3.6;C.3 Schr¨ odinger Equation in Centrally Symmetric;355
8.3.7;3- and 2-Dimensional Potential;355
8.4;D Analytic Behavior of G(z) Near a Band Edge;357
8.5;E Wannier Functions;360
8.6;F Renormalized Perturbation Expansion (RPE);361
8.7;G Boltzmann’s Equation;366
8.8;H Transfer Matrix, S-Matrix, etc.;371
8.8.1;Further Reading;380
8.9;I Second Quantization;381
8.10;Solutions of Selected Problems;392
8.10.1;Chapter 1;392
8.10.2;Chapter 2;407
8.10.3;Chapter 3;408
8.10.4;Chapter 4;413
8.10.5;Chapter 5;420
8.10.6;Chapter 6;426
8.10.7;Chapter 7;430
9;References;447
10;Index;461