Many-Particle Physics / Edition 3
  • Many-Particle Physics / Edition 3
  • Many-Particle Physics / Edition 3

Many-Particle Physics / Edition 3

by Gerald D. Mahan
     
 

This comprehensive textbook utilizes Green's functions and the equations derived from them to solve real physical problems in solid-state theoretical physics. Green's functions are used to describe processes in solids and quantum fluids and to address problems in areas such as electron gas, polarons, electron transport, optical response, superconductivity and… See more details below

Overview

This comprehensive textbook utilizes Green's functions and the equations derived from them to solve real physical problems in solid-state theoretical physics. Green's functions are used to describe processes in solids and quantum fluids and to address problems in areas such as electron gas, polarons, electron transport, optical response, superconductivity and superfluidity.

The updated third edition features several new chapters on different mean-free paths, Hubbard model, Coulomb blockade, and the quantum Hall effect. New sections have

This text is ideal for third- or fourth-year graduate students and includes numerous study problems and an extensive bibliography.

Product Details

ISBN-13:
9780306463389
Publisher:
Springer US
Publication date:
10/28/2000
Series:
Physics of Solids and Liquids Series
Edition description:
3rd ed. 2000
Pages:
785
Product dimensions:
6.98(w) x 10.28(h) x 1.79(d)

Table of Contents

1.Introductory Material1
1.1.Harmonic Oscillators and Phonons1
1.2.Second Quantization for Particles11
1.3.Electron-Phonon Interactions26
1.3.1.Interaction Hamiltonian27
1.3.2.Localized Electron29
1.3.3.Deformation Potential31
1.3.4.Piezoelectric Interaction32
1.3.5.Polar Coupling34
1.4.Spin Hamiltonians36
1.4.1.Homogeneous Spin Systems38
1.4.2.Impurity Spin Models43
1.5.Photons48
1.5.1.Gauges49
1.5.2.Lagrangian53
1.5.3.Hamiltonian55
1.6.Pair Distribution Function58
Problems62
2.Green's Functions at Zero Temperature65
2.1.Interaction Representation66
2.1.1.Schrodinger66
2.1.2.Heisenberg66
2.1.3.Interaction67
2.2.S Matrix70
2.3.Green's Functions71
2.4.Wick's Theorem76
2.5.Feynman Diagrams81
2.6.Vacuum Polarization Graphs83
2.7.Dyson's Equation86
2.8.Rules for Constructing Diagrams90
2.9.Time-Loop S Matrix95
2.9.1.Six Green's Functions96
2.9.2.Dyson's Equation99
2.10.Photon Green's Functions102
Problems106
3.Nonzero Temperatures109
3.1.Introduction109
3.2.Matsubara Green's Functions112
3.3.Retarded and Advanced Green's Functions118
3.4.Dyson's Equation128
3.5.Frequency Summations136
3.6.Linked Cluster Expansions142
3.6.1.Thermodynamic Potential142
3.6.2.Green's Functions152
3.7.Real-Time Green's Functions154
3.7.1.Wigner Distribution Function157
3.8.Kubo Formula for Electrical Conductivity160
3.8.1.Transverse Fields, Zero Temperature163
3.8.2.Nonzero Temperatures168
3.8.3.Zero Frequency170
3.8.4.Photon Self-Energy173
3.9.Other Kubo Formulas174
3.9.1.Pauli Paramagnetic Susceptibility174
3.9.2.Thermal Currents and Onsager Relations177
3.9.3.Correlation Functions181
Problems183
4.Exactly Solvable Models187
4.1.Potential Scattering187
4.1.1.Reaction Matrix189
4.1.2.T Matrix192
4.1.3.Friedel's Theorem195
4.1.4.Impurity Scattering199
4.1.5.Ground State Energy204
4.2.Localized State in the Continuum207
4.3.Independent Boson Models218
4.3.1.Solution by Canonical Transformation218
4.3.2.Feynman Disentangling of Operators221
4.3.3.Einstein Model224
4.3.4.Optical Absorption and Emission228
4.3.5.Sudden Switching236
4.3.6.Linked Cluster Expansion241
4.4.Bethe Lattice247
4.4.1.Electron Green's Function247
4.4.2.Ising Model251
4.5.Tomonaga Model256
4.5.1.Tomonaga Model257
4.5.2.Spin Waves262
4.5.3.Luttinger Model264
4.5.4.Single-Particle Properties267
4.5.5.Interacting System of Spinless Fermions272
4.6.Polaritons276
4.6.1.Semiclassical Discussion276
4.6.2.Phonon-Photon Coupling278
4.6.3.Exciton-Photon Coupling282
Problems291
5.Homogeneous Electron Gas295
5.1.Exchange and Correlation295
5.1.1.Kinetic Energy297
5.1.2.Hartree297
5.1.3.Exchange297
5.1.4.Seitz's Theorem301
5.1.5.[Sigma superscript (2a)]303
5.1.6.[Sigma superscript (2b)]304
5.1.7.[Sigma superscript (2c)]305
5.1.8.High-Density Limit306
5.1.9.Pair Distribution Function308
5.2.Wigner Lattice311
5.3.Metallic Hydrogen315
5.4.Linear Screening316
5.5.Model Dielectric Functions323
5.5.1.Thomas-Fermi323
5.5.2.Lindhard, or RPA325
5.5.3.Hubbard336
5.5.4.Singwi-Sjolander338
5.5.5.Local Field Corrections341
5.5.6.Vertex Corrections343
5.6.Properties of the Electron Gas346
5.6.1.Pair Distribution Function346
5.6.2.Screening Charge346
5.6.3.Correlation Energies347
5.6.4.Compressibility352
5.6.5.Pauli Paramagnetic Susceptibility356
5.7.Sum Rules358
5.8.One-Electron Properties362
5.8.1.Renormalization Constant Z[subscript F]365
5.8.2.Effective Mass368
5.8.3.Mean-Free-Path369
Problems372
6.Strong Correlations375
6.1.Kondo Model375
6.1.1.High-Temperature Scattering376
6.1.2.Low-Temperature State383
6.1.3.Kondo Temperature387
6.1.4.Kondo Resonance387
6.2.Single-Site Anderson Model389
6.2.1.No Hybridization391
6.2.2.With Hybridization395
6.2.3.Self-Energy of Electrons396
6.3.Hubbard Model403
6.3.1.Spin and Charge Separation404
6.3.2.Exchange Graphs409
6.4.Hubbard Model: Magnetic Phases411
6.4.1.Ferromagnetism413
6.4.2.Antiferromagnetism416
6.4.3.An Example422
6.4.4.Local Field Corrections427
Problems430
7.Electron-Phonon Interaction433
7.1.Frohlich Hamiltonian433
7.1.1.Brillouin-Wigner Perturbation Theory434
7.1.2.Rayleigh-Schrodinger Perturbation Theory438
7.1.3.Strong Coupling Theory444
7.1.4.Linked Cluster Theory448
7.2.Small Polaron Theory454
7.2.1.Large Polarons455
7.2.2.Small Polarons456
7.2.3.Diagonal Transitions458
7.2.4.Nondiagonal Transitions459
7.2.5.Kubo Formula463
7.3.Heavily Doped Semiconductors467
7.3.1.Screened Interaction468
7.3.2.Experimental Verifications474
7.3.3.Electron Self-Energies475
7.4.Metals481
7.4.1.Phonons in Metals482
7.4.2.Electron Self-Energies487
Problems495
8.dc Conductivities499
8.1.Electron Scattering by Impurities499
8.1.1.Boltzmann Equation499
8.1.2.Kubo Formula: Approximate Solution505
8.1.3.Ward Identities514
8.2.Mobility of Frohlich Polarons517
8.3.Electron-Phonon Relaxation Times524
8.3.1.Metals526
8.3.2.Semiconductors527
8.3.3.Temperature Relaxation531
8.4.Electron-Phonon Interactions in Metals534
8.4.1.Force-Force Correlation Function534
8.4.2.Kubo Formula537
8.4.3.Mass Enhancement545
8.4.4.Thermoelectric Power545
8.5.Quantum Boltzmann Equation549
8.5.1.Derivation of the QBE550
8.5.2.Gradient Expansion554
8.5.3.Electron Scattering by Impurities557
8.6.Quantum Dot Tunneling561
8.6.1.Electron Tunneling561
8.6.2.Quantum Dots567
8.6.3.Rate Equations571
8.6.4.Quantum Conductance575
Problems576
9.Optical Properties of Solids579
9.1.Nearly Free-Electron Systems579
9.1.1.General Properties579
9.1.2.Force-Force Correlation Functions581
9.1.3.Frohlich Polarons585
9.1.4.Interband Transitions588
9.1.5.Phonons590
9.2.Wannier Excitons592
9.2.1.The Model592
9.2.2.Solution by Green's Functions596
9.2.3.Core-Level Spectra600
9.3.X-ray Spectra in Metals603
9.3.1.Physical Model603
9.3.2.Edge Singularities607
9.3.3.Orthogonality Catastrophe612
9.3.4.MND Theory621
9.3.5.XPS Spectra624
Problems626
10.Superconductivity627
10.1.Cooper Instability628
10.1.1.BCS Theory635
10.2.Superconducting Tunneling644
10.2.1.Normal-Superconductor645
10.2.2.Two Superconductors648
10.2.3.Josephson Tunneling652
10.2.4.Infrared Absorption660
10.3.Strong Coupling Theory664
10.4.Transition Temperature670
Problems674
11.Superfluids677
11.1.Liquid [superscript 4]He677
11.1.1.Hartree and Exchange679
11.1.2.Bogoliubov Theory of [superscript 4]He682
11.1.3.Off-Diagonal Long-Range Order686
11.1.4.Correlated Basis Functions690
11.1.5.Experiments on n[subscript k]697
11.1.6.Bijl-Feynman Theory702
11.1.7.Improved Excitation Spectra707
11.1.8.Superfluidity710
11.2.Liquid [superscript 3]He713
11.2.1.Fermi Liquid Theory714
11.2.2.Experiments and Microscopic Theories720
11.2.3.Interaction Between Quasiparticles: Excitations723
11.2.4.Quasiparticle Transport729
11.2.5.Superfluid [superscript 3]He735
11.3.Quantum Hall Effects742
11.3.1.Landau Levels742
11.3.2.Classical Hall Effect745
11.3.3.Quantum Hall Effect747
11.3.3.1.Fixed Density749
11.3.3.2.Fixed Chemical Potential749
11.3.3.3.Impurity Dominated750
11.3.4.Laughlin Wave Function752
11.3.5.Collective Excitations757
11.3.5.1.Magnetorotons757
11.3.5.2.Quasiholes760
Problems761
References765
Author Index777
Subject Index781

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