Many-Particle Physics / Edition 2

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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.

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Editorial Reviews

Booknews
Teaches techniques of many-body theory and applies techniques to specific problems. After a chapter on introductory material, coverage includes Green's functions at zero temperature, nonzero temperatures, exactly solvable models, homogeneous electron gas, strong correlations, electron-phonon interaction, dc conductivities, optical properties of solids, superconductivity, and superfluids. This third edition covers more applications, and offers new material on Bethe lattice, different mean-free-paths, Hubbard model, Coulomb blockade, and the Quantum Hall effect. Mahan is affiliated with the University of Tennessee, and Oak Ridge National Laboratory. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From the Publisher
About the First Edition:
'This is a worthy newcomer and will make an excellent teaching text.'
Physics Bulletin
'The book should serve as a valuable contribution to the library of students and researchers in solid state and theoretical physics.'
Philosophical Magazine

About the Second Edition:
'Since its first edition, this book has become one of the most popular textbooks in quantum many-body theory, thus guaranteeing the interest of the scientific community in this second edition.'
Mathematical Reviews

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Product Details

  • ISBN-13: 9780306434235
  • Publisher: Springer US
  • Publication date: 3/31/1990
  • Series: Physics of Solids and Liquids Series
  • Edition description: 2nd ed. 1990
  • Edition number: 2
  • Pages: 1046
  • Product dimensions: 9.21 (w) x 6.14 (h) x 2.13 (d)

Table of Contents

1. Introductory Material 1
1.1. Harmonic Oscillators and Phonons 1
1.2. Second Quantization for Particles 11
1.3. Electron-Phonon Interactions 26
1.3.1. Interaction Hamiltonian 27
1.3.2. Localized Electron 29
1.3.3. Deformation Potential 31
1.3.4. Piezoelectric Interaction 32
1.3.5. Polar Coupling 34
1.4. Spin Hamiltonians 36
1.4.1. Homogeneous Spin Systems 38
1.4.2. Impurity Spin Models 43
1.5. Photons 48
1.5.1. Gauges 49
1.5.2. Lagrangian 53
1.5.3. Hamiltonian 55
1.6. Pair Distribution Function 58
Problems 62
2. Green's Functions at Zero Temperature 65
2.1. Interaction Representation 66
2.1.1. Schrodinger 66
2.1.2. Heisenberg 66
2.1.3. Interaction 67
2.2. S Matrix 70
2.3. Green's Functions 71
2.4. Wick's Theorem 76
2.5. Feynman Diagrams 81
2.6. Vacuum Polarization Graphs 83
2.7. Dyson's Equation 86
2.8. Rules for Constructing Diagrams 90
2.9. Time-Loop S Matrix 95
2.9.1. Six Green's Functions 96
2.9.2. Dyson's Equation 99
2.10. Photon Green's Functions 102
Problems 106
3. Nonzero Temperatures 109
3.1. Introduction 109
3.2. Matsubara Green's Functions 112
3.3. Retarded and Advanced Green's Functions 118
3.4. Dyson's Equation 128
3.5. Frequency Summations 136
3.6. Linked Cluster Expansions 142
3.6.1. Thermodynamic Potential 142
3.6.2. Green's Functions 152
3.7. Real-Time Green's Functions 154
3.7.1. Wigner Distribution Function 157
3.8. Kubo Formula for Electrical Conductivity 160
3.8.1. Transverse Fields, Zero Temperature 163
3.8.2. Nonzero Temperatures 168
3.8.3. Zero Frequency 170
3.8.4. Photon Self-Energy 173
3.9. Other Kubo Formulas 174
3.9.1. Pauli Paramagnetic Susceptibility 174
3.9.2. Thermal Currents and Onsager Relations 177
3.9.3. Correlation Functions 181
Problems 183
4. Exactly Solvable Models 187
4.1. Potential Scattering 187
4.1.1. Reaction Matrix 189
4.1.2. T Matrix 192
4.1.3. Friedel's Theorem 195
4.1.4. Impurity Scattering 199
4.1.5. Ground State Energy 204
4.2. Localized State in the Continuum 207
4.3. Independent Boson Models 218
4.3.1. Solution by Canonical Transformation 218
4.3.2. Feynman Disentangling of Operators 221
4.3.3. Einstein Model 224
4.3.4. Optical Absorption and Emission 228
4.3.5. Sudden Switching 236
4.3.6. Linked Cluster Expansion 241
4.4. Bethe Lattice 247
4.4.1. Electron Green's Function 247
4.4.2. Ising Model 251
4.5. Tomonaga Model 256
4.5.1. Tomonaga Model 257
4.5.2. Spin Waves 262
4.5.3. Luttinger Model 264
4.5.4. Single-Particle Properties 267
4.5.5. Interacting System of Spinless Fermions 272
4.6. Polaritons 276
4.6.1. Semiclassical Discussion 276
4.6.2. Phonon-Photon Coupling 278
4.6.3. Exciton-Photon Coupling 282
Problems 291
5. Homogeneous Electron Gas 295
5.1. Exchange and Correlation 295
5.1.1. Kinetic Energy 297
5.1.2. Hartree 297
5.1.3. Exchange 297
5.1.4. Seitz's Theorem 301
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 Limit 306
5.1.9. Pair Distribution Function 308
5.2. Wigner Lattice 311
5.3. Metallic Hydrogen 315
5.4. Linear Screening 316
5.5. Model Dielectric Functions 323
5.5.1. Thomas-Fermi 323
5.5.2. Lindhard, or RPA 325
5.5.3. Hubbard 336
5.5.4. Singwi-Sjolander 338
5.5.5. Local Field Corrections 341
5.5.6. Vertex Corrections 343
5.6. Properties of the Electron Gas 346
5.6.1. Pair Distribution Function 346
5.6.2. Screening Charge 346
5.6.3. Correlation Energies 347
5.6.4. Compressibility 352
5.6.5. Pauli Paramagnetic Susceptibility 356
5.7. Sum Rules 358
5.8. One-Electron Properties 362
5.8.1. Renormalization Constant Z[subscript F] 365
5.8.2. Effective Mass 368
5.8.3. Mean-Free-Path 369
Problems 372
6. Strong Correlations 375
6.1. Kondo Model 375
6.1.1. High-Temperature Scattering 376
6.1.2. Low-Temperature State 383
6.1.3. Kondo Temperature 387
6.1.4. Kondo Resonance 387
6.2. Single-Site Anderson Model 389
6.2.1. No Hybridization 391
6.2.2. With Hybridization 395
6.2.3. Self-Energy of Electrons 396
6.3. Hubbard Model 403
6.3.1. Spin and Charge Separation 404
6.3.2. Exchange Graphs 409
6.4. Hubbard Model: Magnetic Phases 411
6.4.1. Ferromagnetism 413
6.4.2. Antiferromagnetism 416
6.4.3. An Example 422
6.4.4. Local Field Corrections 427
Problems 430
7. Electron-Phonon Interaction 433
7.1. Frohlich Hamiltonian 433
7.1.1. Brillouin-Wigner Perturbation Theory 434
7.1.2. Rayleigh-Schrodinger Perturbation Theory 438
7.1.3. Strong Coupling Theory 444
7.1.4. Linked Cluster Theory 448
7.2. Small Polaron Theory 454
7.2.1. Large Polarons 455
7.2.2. Small Polarons 456
7.2.3. Diagonal Transitions 458
7.2.4. Nondiagonal Transitions 459
7.2.5. Kubo Formula 463
7.3. Heavily Doped Semiconductors 467
7.3.1. Screened Interaction 468
7.3.2. Experimental Verifications 474
7.3.3. Electron Self-Energies 475
7.4. Metals 481
7.4.1. Phonons in Metals 482
7.4.2. Electron Self-Energies 487
Problems 495
8. dc Conductivities 499
8.1. Electron Scattering by Impurities 499
8.1.1. Boltzmann Equation 499
8.1.2. Kubo Formula: Approximate Solution 505
8.1.3. Ward Identities 514
8.2. Mobility of Frohlich Polarons 517
8.3. Electron-Phonon Relaxation Times 524
8.3.1. Metals 526
8.3.2. Semiconductors 527
8.3.3. Temperature Relaxation 531
8.4. Electron-Phonon Interactions in Metals 534
8.4.1. Force-Force Correlation Function 534
8.4.2. Kubo Formula 537
8.4.3. Mass Enhancement 545
8.4.4. Thermoelectric Power 545
8.5. Quantum Boltzmann Equation 549
8.5.1. Derivation of the QBE 550
8.5.2. Gradient Expansion 554
8.5.3. Electron Scattering by Impurities 557
8.6. Quantum Dot Tunneling 561
8.6.1. Electron Tunneling 561
8.6.2. Quantum Dots 567
8.6.3. Rate Equations 571
8.6.4. Quantum Conductance 575
Problems 576
9. Optical Properties of Solids 579
9.1. Nearly Free-Electron Systems 579
9.1.1. General Properties 579
9.1.2. Force-Force Correlation Functions 581
9.1.3. Frohlich Polarons 585
9.1.4. Interband Transitions 588
9.1.5. Phonons 590
9.2. Wannier Excitons 592
9.2.1. The Model 592
9.2.2. Solution by Green's Functions 596
9.2.3. Core-Level Spectra 600
9.3. X-ray Spectra in Metals 603
9.3.1. Physical Model 603
9.3.2. Edge Singularities 607
9.3.3. Orthogonality Catastrophe 612
9.3.4. MND Theory 621
9.3.5. XPS Spectra 624
Problems 626
10. Superconductivity 627
10.1. Cooper Instability 628
10.1.1. BCS Theory 635
10.2. Superconducting Tunneling 644
10.2.1. Normal-Superconductor 645
10.2.2. Two Superconductors 648
10.2.3. Josephson Tunneling 652
10.2.4. Infrared Absorption 660
10.3. Strong Coupling Theory 664
10.4. Transition Temperature 670
Problems 674
11. Superfluids 677
11.1. Liquid [superscript 4]He 677
11.1.1. Hartree and Exchange 679
11.1.2. Bogoliubov Theory of [superscript 4]He 682
11.1.3. Off-Diagonal Long-Range Order 686
11.1.4. Correlated Basis Functions 690
11.1.5. Experiments on n[subscript k] 697
11.1.6. Bijl-Feynman Theory 702
11.1.7. Improved Excitation Spectra 707
11.1.8. Superfluidity 710
11.2. Liquid [superscript 3]He 713
11.2.1. Fermi Liquid Theory 714
11.2.2. Experiments and Microscopic Theories 720
11.2.3. Interaction Between Quasiparticles: Excitations 723
11.2.4. Quasiparticle Transport 729
11.2.5. Superfluid [superscript 3]He 735
11.3. Quantum Hall Effects 742
11.3.1. Landau Levels 742
11.3.2. Classical Hall Effect 745
11.3.3. Quantum Hall Effect 747
11.3.3.1. Fixed Density 749
11.3.3.2. Fixed Chemical Potential 749
11.3.3.3. Impurity Dominated 750
11.3.4. Laughlin Wave Function 752
11.3.5. Collective Excitations 757
11.3.5.1. Magnetorotons 757
11.3.5.2. Quasiholes 760
Problems 761
References 765
Author Index 777
Subject Index 781
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