Many-particle physics /

Many-particle physics /

Show other versions (6)

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...

Full description

Bibliographic Details
Main Author: Mahan, Gerald D
Corporate Author: Alumni and Friends Memorial Book Fund
Format: Book
Language:English
Published: New York : Kluwer Academic/Plenum Publishers, [2000], ©2000
New York : Kluwer Academic / Plenum Publishers, c2000
New York : ©2000
New York : 2000
Edition:3rd ed
Series:Physics of solids and liquids
Physics of solids and liquids
Subjects:
Green's functions
Many-body problem
Solid state physics
Table of Contents:
  • 1 Introductory Material
  • 1.1. Harmonic Oscillators and Phonons
  • 1.2. Second Quantization for Particles
  • 1.3. Electron-Phonon Interactions
  • 1.4. Spin Hamiltonians
  • 1.5. Photons
  • 1.6. Pair Distribution Function
  • 2. Green's Functions at Zero Temperature
  • 2.1. Interaction Representation
  • 2.2. S Matrix
  • 2.3. Green's Functions
  • 2.4. Wick's Theorem
  • 2.5. Feynman Diagrams
  • 2.6. Vacuum Polarization Graphs
  • 2.7. Dyson's Equation
  • 2.8. Rules for Constructing Diagrams
  • 2.9. Time-Loop S Matrix
  • 2.10. Photon Green's Functions
  • 3. Nonzero Temperatures
  • 3.1. Introduction
  • 3.2. Matsubara Green's Functions
  • 3.3. Retarded and Advanced Green's Functions
  • 3.4. Dyson's Equation
  • 3.5. Frequency Summations
  • 3.6. Linked Cluster Expansions
  • 3.7. Real-Time Green's Functions
  • 3.8. Kubo Formula for Electrical Conductivity
  • 3.9. Other Kubo Formulas
  • 4. Exactly Solvable Models
  • 4.1. Potential Scattering
  • 4.2. Localized State in the Continuum
  • 4.3. Independent Boson Models
  • 4.4. Bethe Lattice
  • 4.5. Tomonaga Model
  • 4.6. Polaritons
  • 5. Homogeneous Electron Gas
  • 5.1. Exchange and Correlation
  • 5.2. Wigner Lattice
  • 5.3. Metallic Hydrogen
  • 5.4. Linear Screening
  • 5.5. Model Dielectric Functions
  • 5.6. Properties of the Electron Gas
  • 5.7. Sum Rules
  • 5.8. One-Electron Properties
  • 6. Strong Correlations
  • 6.1. Kondo Model
  • 6.2. Single-Site Anderson Model
  • 6.3. Hubbard Model
  • 6.4. Hubbard Model: Magnetic Phases
  • 7. Electron-Phonon Interaction
  • 7.1. Frohlich Hamiltonian
  • 7.2. Small Polaron Theory
  • 7.3. Heavily Doped Semiconductors
  • 7.4. Metals
  • 8. dc Conductivities
  • 8.1. Electron Scattering by Impurities
  • 8.2. Mobility of Frohlich Polarons
  • 8.3. Electron-Phonon Relaxation Times
  • 8.4. Electron-Phonon Interactions in Metals
  • 8.5. Quantum Boltzmann Equation
  • 8.6. Quantum Dot Tunneling
  • 9. Optical Properties of Solids
  • 9.1. Nearly Free-Electron Systems
  • 9.2. Wannier Excitons
  • 9.3. X-ray Spectra in Metals
  • 10. Superconductivity
  • 10.1. Cooper Instability
  • 10.2. Superconducting Tunneling
  • 10.3. Strong Coupling Theory
  • 10.4. Transition Temperature
  • 11. Superfluids
  • 11.1. Liquid [superscript 4]He
  • 11.2. Liquid [superscript 3]He
  • 11.3. Quantum Hall Effects.
  • 1 Introductory Material. 1.1. Harmonic Oscillators and Phonons. 1.2. Second Quantization for Particles. 1.3. Electron-Phonon Interactions. 1.4. Spin Hamiltonians. 1.5. Photons. 1.6. Pair Distribution Function
  • 2. Green's Functions at Zero Temperature. 2.1. Interaction Representation. 2.2. S Matrix. 2.3. Green's Functions. 2.4. Wick's Theorem. 2.5. Feynman Diagrams. 2.6. Vacuum Polarization Graphs. 2.7. Dyson's Equation. 2.8. Rules for Constructing Diagrams. 2.9. Time-Loop S Matrix. 2.10. Photon Green's Functions
  • 3. Nonzero Temperatures. 3.1. Introduction. 3.2. Matsubara Green's Functions. 3.3. Retarded and Advanced Green's Functions. 3.4. Dyson's Equation. 3.5. Frequency Summations. 3.6. Linked Cluster Expansions. 3.7. Real-Time Green's Functions. 3.8. Kubo Formula for Electrical Conductivity. 3.9. Other Kubo Formulas
  • 4. Exactly Solvable Models. 4.1. Potential Scattering. 4.2. Localized State in the Continuum.
  • 1 Introductory Material. 1.1. Harmonic Oscillators and Phonons. 1.2. Second Quantization for Particles. 1.3. Electron-Phonon Interactions. 1.4. Spin Hamiltonians. 1.5. Photons. 1.6. Pair Distribution Function
  • 2. Green's Functions at Zero Temperature. 2.1. Interaction Representation. 2.2. S Matrix. 2.3. Green's Functions. 2.4. Wick's Theorem. 2.5. Feynman Diagrams. 2.6. Vacuum Polarization Graphs. 2.7. Dyson's Equation. 2.8. Rules for Constructing Diagrams. 2.9. Time-Loop S Matrix. 2.10. Photon Green's Functions
  • 3. Nonzero Temperatures. 3.1. Introduction. 3.2. Matsubara Green's Functions. 3.3. Retarded and Advanced Green's Functions. 3.4. Dyson's Equation. 3.5. Frequency Summations. 3.6. Linked Cluster Expansions. 3.7. Real-Time Green's Functions. 3.8. Kubo Formula for Electrical Conductivity. 3.9. Other Kubo Formulas
  • 4. Exactly Solvable Models. 4.1.++
  • 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
  • 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
  • 3. Nonzero Temperatures 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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.
  • Introductory material
  • 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
  • Superfluids
  • Potential Scattering 4.2. Localized State in the Continuum. 4.3. Independent Boson Models. 4.4. Bethe Lattice. 4.5. Tomonaga Model. 4.6. Polaritons
  • 5. Homogeneous Electron Gas. 5.1. Exchange and Correlation. 5.2. Wigner Lattice. 5.3. Metallic Hydrogen. 5.4. Linear Screening. 5.5. Model Dielectric Functions. 5.6. Properties of the Electron Gas. 5.7. Sum Rules. 5.8. One-Electron Properties
  • 6. Strong Correlations. 6.1. Kondo Model. 6.2. Single-Site Anderson Model. 6.3. Hubbard Model. 6.4. Hubbard Model: Magnetic Phases
  • 7. Electron-Phonon Interaction. 7.1. Frohlich Hamiltonian. 7.2. Small Polaron Theory. 7.3. Heavily Doped Semiconductors. 7.4. Metals
  • 8. dc Conductivities. 8.1. Electron Scattering by Impurities. 8.2. Mobility of Frohlich Polarons. 8.3. Electron-Phonon Relaxation Times. 8.4. Electron-Phonon Interactions in Metals. 8.5.++
  • Quantum Boltzmann Equation 8.6. Quantum Dot Tunneling
  • 9. Optical Properties of Solids. 9.1. Nearly Free-Electron Systems. 9.2. Wannier Excitons. 9.3. X-ray Spectra in Metals
  • 10. Superconductivity. 10.1. Cooper Instability. 10.2. Superconducting Tunneling. 10.3. Strong Coupling Theory. 10.4. Transition Temperature
  • 11. Superfluids. 11.1. Liquid [superscript 4]He. 11.2. Liquid [superscript 3]He. 11.3. Quantum Hall Effects.
  • 4.3 Independent Boson Models. 4.4. Bethe Lattice. 4.5. Tomonaga Model. 4.6. Polaritons
  • 5. Homogeneous Electron Gas. 5.1. Exchange and Correlation. 5.2. Wigner Lattice. 5.3. Metallic Hydrogen. 5.4. Linear Screening. 5.5. Model Dielectric Functions. 5.6. Properties of the Electron Gas. 5.7. Sum Rules. 5.8. One-Electron Properties
  • 6. Strong Correlations. 6.1. Kondo Model. 6.2. Single-Site Anderson Model. 6.3. Hubbard Model. 6.4. Hubbard Model: Magnetic Phases
  • 7. Electron-Phonon Interaction. 7.1. Frohlich Hamiltonian. 7.2. Small Polaron Theory. 7.3. Heavily Doped Semiconductors. 7.4. Metals
  • 8. dc Conductivities. 8.1. Electron Scattering by Impurities. 8.2. Mobility of Frohlich Polarons. 8.3. Electron-Phonon Relaxation Times. 8.4. Electron-Phonon Interactions in Metals. 8.5. Quantum Boltzmann Equation. 8.6. Quantum Dot Tunneling
  • 9. Optical Properties of Solids. 9.1. Nearly Free-Electron Systems. 9.2. Wannier Excitons.
  • 9.3 X-ray Spectra in Metals
  • 10. Superconductivity. 10.1. Cooper Instability. 10.2. Superconducting Tunneling. 10.3. Strong Coupling Theory. 10.4. Transition Temperature
  • 11. Superfluids. 11.1. Liquid [superscript 4]He. 11.2. Liquid [superscript 3]He. 11.3. Quantum Hall Effects.

Similar Items