Many-Particle Physics,9780306463389

Many-Particle Physics

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Edition: 3rd
ISBN13: 9780306463389
ISBN10: 0306463385
Format: Hardcover
Pub. Date: 2000-10-31
Publisher(s): Plenum Pub Corp
List Price: $235.38

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Summary

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 been added, while original sections have been modified to include recent applications. This text is ideal for third- or fourth-year graduate students and includes numerous study problems and an extensive bibliography.

Table of Contents

Introductory Material
1(64)
Harmonic Oscillators and Phonons
1(10)
Second Quantization for Particles
11(15)
Electron--Phonon Interactions
26(10)
Interaction Hamiltonian
27(2)
Localized Electron
29(2)
Deformation Potential
31(1)
Piezoelectric Interaction
32(2)
Polar Coupling
34(2)
Spin Hamiltonians
36(12)
Homogeneous Spin Systems
38(5)
Impurity Spin Models
43(5)
Photons
48(10)
Gauges
49(4)
Lagrangian
53(2)
Hamiltonian
55(3)
Pair Distribution Function
58(7)
Problems
62(3)
Green's Functions at Zero Temperature
65(44)
Interaction Representation
66(4)
Schrodinger
66(1)
Heisenberg
66(1)
Interaction
67(3)
S Matrix
70(1)
Green's Functions
71(5)
Wick's Theorem
76(5)
Feynman Diagrams
81(2)
Vacuum Polarization Graphs
83(3)
Dyson's Equation
86(4)
Rules for Constructing Diagrams
90(5)
Time-Loop S Matrix
95(7)
Six Green's Functions
96(3)
Dyson's Equation
99(3)
Photon Green's Functions
102(7)
Problems
106(3)
Nonzero Temperatures
109(78)
Introduction
109(3)
Matsubara Green's Functions
112(6)
Retarded and Advanced Green's Functions
118(10)
Dyson's Equation
128(8)
Frequency Summations
136(6)
Linked Cluster Expansions
142(12)
Thermodynamic Potential
142(10)
Green's Functions
152(2)
Real-Time Green's Functions
154(6)
Wigner Distribution Function
157(3)
Kubo Formula for Electrical Conductivity
160(14)
Transverse Fields, Zero Temperature
163(5)
Nonzero Temperatures
168(2)
Zero Frequency
170(3)
Photon Self-Energy
173(1)
Other Kubo Formulas
174(13)
Pauli Paramagnetic Susceptibility
174(3)
Thermal Currents and Onsager Relations
177(4)
Correlation Functions
181(2)
Problems
183(4)
Exactly Solvable Models
187(108)
Potential Scattering
187(20)
Reaction Matrix
189(3)
T Matrix
192(3)
Friedel's Theorem
195(4)
Impurity Scattering
199(5)
Ground State Energy
204(3)
Localized State in the Continuum
207(11)
Independent Boson Models
218(29)
Solution by Canonical Transformation
218(3)
Feynman Disentangling of Operators
221(3)
Einstein Model
224(4)
Optical Absorption and Emission
228(8)
Sudden Switching
236(5)
Linked Cluster Expansion
241(6)
Bethe Lattice
247(9)
Electron Green's Function
247(4)
Ising Model
251(5)
Tomonaga Model
256(20)
Tomonaga Model
257(5)
Spin Waves
262(2)
Luttinger Model
264(3)
Single-Particle Properties
267(5)
Interacting System of Spinless Fermions
272(4)
Polaritons
276(19)
Semiclassical Discussion
276(2)
Phonon--Photon Coupling
278(4)
Exciton--Photon Coupling
282(9)
Problems
291(4)
Homogeneous Electron Gas
295(80)
Exchange and Correlation
295(16)
Kinetic Energy
297(1)
Hartree
297(1)
Exchange
297(4)
Seitz's Theorem
301(2)
σ(2a)
303(1)
σ(2b)
304(1)
σ(2c)
305(1)
High-Density Limit
306(2)
Pair Distribution Function
308(3)
Wigner Lattice
311(4)
Metallic Hydrogen
315(1)
Linear Screening
316(7)
Model Dielectric Functions
323(23)
Thomas--Fermi
323(2)
Lindhard, or RPA
325(11)
Hubbard
336(2)
Singwi--Sjolander
338(3)
Local field Corrections
341(2)
Vertex Corrections
343(3)
Properties of the Electron Gas
346(12)
Pair Distribution Function
346(1)
Screening Charge
346(1)
Correlation Energies
347(5)
Compressibility
352(4)
Pauli Paramagnetic Susceptibility
356(2)
Sum Rules
358(4)
One-Electron Properties
362(13)
Renormalization Constant ZF
365(3)
Effective Mass
368(1)
Mean-Free-Path
369(3)
Problems
372(3)
Strong Correlations
375(58)
Kondo Model
375(14)
High-Temperature Scattering
376(7)
Low-Temperature State
383(4)
Kondo Temperature
387(1)
Kondo Resonance
387(2)
Single-Site Anderson Model
389(14)
No Hybridization
391(4)
With Hybridization
395(1)
Self-Energy of Electrons
396(7)
Hubbard Model
403(8)
Spin and Charge Separation
404(5)
Exchange Graphs
409(2)
Hubbard Model: Magnetic Phases
411(22)
Ferromagnetism
413(3)
Antiferromagnetism
416(6)
An Example
422(5)
Local Field Corrections
427(3)
Problems
430(3)
Electron--Phonon Interaction
433(66)
Frohlich Hamiltonian
433(21)
Brillouin--Wigner Perturbation Theory
434(4)
Rayleigh--Schrodinger Perturbation Theory
438(6)
Strong Coupling Theory
444(4)
Linked Cluster Theory
448(6)
Small Polaron Theory
454(13)
Large Polarons
455(1)
Small Polarons
456(2)
Diagonal Transitions
458(1)
Nondiagonal Transitions
459(4)
Kubo Formula
463(4)
Heavily Doped Semiconductors
467(14)
Screened Interaction
468(6)
Experimental Verifications
474(1)
Electron Self-Energies
475(6)
Metals
481(18)
Phonons in Metals
482(5)
Electron Self-Energies
487(8)
Problems
495(4)
dc Conductivities
499(80)
Electron Scattering by Impurities
499(18)
Boltzmann Equation
499(6)
Kubo Formula: Approximate Solution
505(9)
Ward Identities
514(3)
Mobility of Frohlich Polarons
517(7)
Electron--Phonon Relaxation Times
524(10)
Metals
526(1)
Semiconductors
527(4)
Temperature Relaxation
531(3)
Electron--Phonon Interactions in Metals
534(15)
Force--Force Correlation Function
534(3)
Kubo Formula
537(8)
Mass Enhancement
545(1)
Thermoelectric Power
545(4)
Quantum Boltzmann Equation
549(12)
Derivation of the QBE
550(4)
Gradient Expansion
554(3)
Electron Scattering by Impurities
557(4)
Quantum Dot Tunneling
561(18)
Electron Tunneling
561(6)
Quantum Dots
567(4)
Rate Equations
571(4)
Quantum Conductance
575(1)
Problems
576(3)
Optical Properties of Solids
579(48)
Nearly Free-Electron Systems
579(13)
General Properties
579(2)
Force--Force Correlation Functions
581(4)
Frohlich Polarons
585(3)
Interband Transitions
588(2)
Phonons
590(2)
Wannier Excitons
592(11)
The Model
592(4)
Solution by Green's Functions
596(4)
Core-Level Spectra
600(3)
X-ray Spectra in Metals
603(24)
Physical Model
603(4)
Edge Singularities
607(5)
Orthogonality Catastrophe
612(9)
MND Theory
621(3)
XPS Spectra
624(2)
Problems
626(1)
Superconductivity
627(50)
Cooper Instability
628(16)
BCS Theory
635(9)
Superconducting Tunneling
644(20)
Normal--Superconductor
645(3)
Two Superconductors
648(4)
Josephson Tunneling
652(8)
Infrared Absorption
660(4)
Strong Coupling Theory
664(6)
Transition Temperature
670(7)
Problems
674(3)
Superfluids
677(88)
Liquid 4He
677(36)
Hartree and Exchange
679(3)
Bogoliubov Theory of 4He
682(4)
Off-Diagonal Long-Range Order
686(4)
Correlated Basis Functions
690(7)
Experiments on nk
697(5)
Bijl-Feynman Theory
702(5)
Improved Excitation Spectra
707(3)
Superfluidity
710(3)
Liquid 3He
713(29)
Fermi Liquid Theory
714(6)
Experiments and Microscopic Theories
720(3)
Interaction Between Quasiparticles: Excitations
723(6)
Quasiparticle Transport
729(6)
Superfluid 3He
735(7)
Quantum Hall Effects
742(23)
Landau Levels
742(3)
Classical Hall Effect
745(2)
Quantum Hall Effect
747(2)
Fixed Density
749(1)
Fixed Chemical Potential
749(1)
Impurity Dominated
750(2)
Laughlin Wave Function
752(5)
Collective Excitations
757(1)
Magnetorotons
757(3)
Quasiholes
760(1)
Problems
761(4)
References 765(12)
Author Index 777(4)
Subject Index 781

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