Many-particle physics /
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| Author / Creator: | Mahan, Gerald D. |
|---|---|
| Edition: | 2nd ed. |
| Imprint: | New York : Plenum Press, 1990. |
| Description: | xiv, 1032 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1033755 |
Table of Contents:
- 1.. Introductory Material
- 1.1.. Harmonic Oscillators and Phonons
- 1.2.. Second Quantization for Particles
- 1.3.. Electron-Phonon Interactions
- 1.3.1.. Interaction Hamiltonian
- 1.3.2.. Localized Electron
- 1.3.3.. Deformation Potential
- 1.3.4.. Piezoelectric Interaction
- 1.3.5.. Polar Coupling
- 1.4.. Spin Hamiltonians
- 1.4.1.. Homogeneous Spin Systems
- 1.4.2.. Impurity Spin Models
- 1.5.. Photons
- 1.5.1.. Gauges
- 1.5.2.. Lagrangian
- 1.5.3.. Hamiltonian
- 1.6.. Pair Distribution Function
- Problems
- 2.. Green's Functions at Zero Temperature
- 2.1.. Interaction Representation
- 2.1.1.. Schrodinger
- 2.1.2.. Heisenberg
- 2.1.3.. Interaction
- 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
- 2.9.1.. Six Green's Functions
- 2.9.2.. Dyson's Equation
- 2.10.. Photon Green's Functions
- Problems
- 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
- 3.6.1.. Thermodynamic Potential
- 3.6.2.. Green's Functions
- 3.7.. Real-Time Green's Functions
- 3.7.1.. Wigner Distribution Function
- 3.8.. Kubo Formula for Electrical Conductivity
- 3.8.1.. Transverse Fields, Zero Temperature
- 3.8.2.. Nonzero Temperatures
- 3.8.3.. Zero Frequency
- 3.8.4.. Photon Self-Energy
- 3.9.. Other Kubo Formulas
- 3.9.1.. Pauli Paramagnetic Susceptibility
- 3.9.2.. Thermal Currents and Onsager Relations
- 3.9.3.. Correlation Functions
- Problems
- 4.. Exactly Solvable Models
- 4.1.. Potential Scattering
- 4.1.1.. Reaction Matrix
- 4.1.2.. T Matrix
- 4.1.3.. Friedel's Theorem
- 4.1.4.. Impurity Scattering
- 4.1.5.. Ground State Energy
- 4.2.. Localized State in the Continuum
- 4.3.. Independent Boson Models
- 4.3.1.. Solution by Canonical Transformation
- 4.3.2.. Feynman Disentangling of Operators
- 4.3.3.. Einstein Model
- 4.3.4.. Optical Absorption and Emission
- 4.3.5.. Sudden Switching
- 4.3.6.. Linked Cluster Expansion
- 4.4.. Bethe Lattice
- 4.4.1.. Electron Green's Function
- 4.4.2.. Ising Model
- 4.5.. Tomonaga Model
- 4.5.1.. Tomonaga Model
- 4.5.2.. Spin Waves
- 4.5.3.. Luttinger Model
- 4.5.4.. Single-Particle Properties
- 4.5.5.. Interacting System of Spinless Fermions
- 4.6.. Polaritons
- 4.6.1.. Semiclassical Discussion
- 4.6.2.. Phonon-Photon Coupling
- 4.6.3.. Exciton-Photon Coupling
- Problems
- 5.. Homogeneous Electron Gas
- 5.1.. Exchange and Correlation
- 5.1.1.. Kinetic Energy
- 5.1.2.. Hartree
- 5.1.3.. Exchange
- 5.1.4.. Seitz's Theorem
- 5.1.5.. [Sigma superscript (2a)]
- 5.1.6.. [Sigma superscript (2b)]
- 5.1.7.. [Sigma superscript (2c)]
- 5.1.8.. High-Density Limit
- 5.1.9.. Pair Distribution Function
- 5.2.. Wigner Lattice
- 5.3.. Metallic Hydrogen
- 5.4.. Linear Screening
- 5.5.. Model Dielectric Functions
- 5.5.1.. Thomas-Fermi
- 5.5.2.. Lindhard, or RPA
- 5.5.3.. Hubbard
- 5.5.4.. Singwi-Sjolander
- 5.5.5.. Local Field Corrections
- 5.5.6.. Vertex Corrections
- 5.6.. Properties of the Electron Gas
- 5.6.1.. Pair Distribution Function
- 5.6.2.. Screening Charge
- 5.6.3.. Correlation Energies
- 5.6.4.. Compressibility
- 5.6.5.. Pauli Paramagnetic Susceptibility
- 5.7.. Sum Rules
- 5.8.. One-Electron Properties
- 5.8.1.. Renormalization Constant Z[subscript F]
- 5.8.2.. Effective Mass
- 5.8.3.. Mean-Free-Path
- Problems
- 6.. Strong Correlations
- 6.1.. Kondo Model
- 6.1.1.. High-Temperature Scattering
- 6.1.2.. Low-Temperature State
- 6.1.3.. Kondo Temperature
- 6.1.4.. Kondo Resonance
- 6.2.. Single-Site Anderson Model
- 6.2.1.. No Hybridization
- 6.2.2.. With Hybridization
- 6.2.3.. Self-Energy of Electrons
- 6.3.. Hubbard Model
- 6.3.1.. Spin and Charge Separation
- 6.3.2.. Exchange Graphs
- 6.4.. Hubbard Model: Magnetic Phases
- 6.4.1.. Ferromagnetism
- 6.4.2.. Antiferromagnetism
- 6.4.3.. An Example
- 6.4.4.. Local Field Corrections
- Problems
- 7.. Electron-Phonon Interaction
- 7.1.. Frohlich Hamiltonian
- 7.1.1.. Brillouin-Wigner Perturbation Theory
- 7.1.2.. Rayleigh-Schrodinger Perturbation Theory
- 7.1.3.. Strong Coupling Theory
- 7.1.4.. Linked Cluster Theory
- 7.2.. Small Polaron Theory
- 7.2.1.. Large Polarons
- 7.2.2.. Small Polarons
- 7.2.3.. Diagonal Transitions
- 7.2.4.. Nondiagonal Transitions
- 7.2.5.. Kubo Formula
- 7.3.. Heavily Doped Semiconductors
- 7.3.1.. Screened Interaction
- 7.3.2.. Experimental Verifications
- 7.3.3.. Electron Self-Energies
- 7.4.. Metals
- 7.4.1.. Phonons in Metals
- 7.4.2.. Electron Self-Energies
- Problems
- 8.. dc Conductivities
- 8.1.. Electron Scattering by Impurities
- 8.1.1.. Boltzmann Equation
- 8.1.2.. Kubo Formula: Approximate Solution
- 8.1.3.. Ward Identities
- 8.2.. Mobility of Frohlich Polarons
- 8.3.. Electron-Phonon Relaxation Times
- 8.3.1.. Metals
- 8.3.2.. Semiconductors
- 8.3.3.. Temperature Relaxation
- 8.4.. Electron-Phonon Interactions in Metals
- 8.4.1.. Force-Force Correlation Function
- 8.4.2.. Kubo Formula
- 8.4.3.. Mass Enhancement
- 8.4.4.. Thermoelectric Power
- 8.5.. Quantum Boltzmann Equation
- 8.5.1.. Derivation of the QBE
- 8.5.2.. Gradient Expansion
- 8.5.3.. Electron Scattering by Impurities
- 8.6.. Quantum Dot Tunneling
- 8.6.1.. Electron Tunneling
- 8.6.2.. Quantum Dots
- 8.6.3.. Rate Equations
- 8.6.4.. Quantum Conductance
- Problems
- 9.. Optical Properties of Solids
- 9.1.. Nearly Free-Electron Systems
- 9.1.1.. General Properties
- 9.1.2.. Force-Force Correlation Functions
- 9.1.3.. Frohlich Polarons
- 9.1.4.. Interband Transitions
- 9.1.5.. Phonons
- 9.2.. Wannier Excitons
- 9.2.1.. The Model
- 9.2.2.. Solution by Green's Functions
- 9.2.3.. Core-Level Spectra
- 9.3.. X-ray Spectra in Metals
- 9.3.1.. Physical Model
- 9.3.2.. Edge Singularities
- 9.3.3.. Orthogonality Catastrophe
- 9.3.4.. MND Theory
- 9.3.5.. XPS Spectra
- Problems
- 10.. Superconductivity
- 10.1.. Cooper Instability
- 10.1.1.. BCS Theory
- 10.2.. Superconducting Tunneling
- 10.2.1.. Normal-Superconductor
- 10.2.2.. Two Superconductors
- 10.2.3.. Josephson Tunneling
- 10.2.4.. Infrared Absorption
- 10.3.. Strong Coupling Theory
- 10.4.. Transition Temperature
- Problems
- 11.. Superfluids
- 11.1.. Liquid [superscript 4]He
- 11.1.1.. Hartree and Exchange
- 11.1.2.. Bogoliubov Theory of [superscript 4]He
- 11.1.3.. Off-Diagonal Long-Range Order
- 11.1.4.. Correlated Basis Functions
- 11.1.5.. Experiments on n[subscript k]
- 11.1.6.. Bijl-Feynman Theory
- 11.1.7.. Improved Excitation Spectra
- 11.1.8.. Superfluidity
- 11.2.. Liquid [superscript 3]He
- 11.2.1.. Fermi Liquid Theory
- 11.2.2.. Experiments and Microscopic Theories
- 11.2.3.. Interaction Between Quasiparticles: Excitations
- 11.2.4.. Quasiparticle Transport
- 11.2.5.. Superfluid [superscript 3]He
- 11.3.. Quantum Hall Effects
- 11.3.1.. Landau Levels
- 11.3.2.. Classical Hall Effect
- 11.3.3.. Quantum Hall Effect
- 11.3.3.1.. Fixed Density
- 11.3.3.2.. Fixed Chemical Potential
- 11.3.3.3.. Impurity Dominated
- 11.3.4.. Laughlin Wave Function
- 11.3.5.. Collective Excitations
- 11.3.5.1.. Magnetorotons
- 11.3.5.2.. Quasiholes
- Problems
- References
- Author Index
- Subject Index
