Green's functions and condensed matter / G. Rickayzen, University of Kent.

Format:

Book

Author/Creator:

Rickayzen, G., author.

Language:

English

Subjects (All):

Condensed matter.

Green's functions.

Mathematical physics.

Physical Description:

x, 357 pages : illustrations ; 23 cm

Edition:

Dover edition.

Place of Publication:

Mineola, New York : Dover Publications, Inc., 2013.

Summary:

"Green's functions, named for the mathematician who developed them in the 1830s, possess applications in many areas of physics. This volume presents the basic theoretical formulation, followed by specific applications that include transport coefficients of a metal, the Coulomb gas, Fermi liquids, electrons and phonons, superconductivity, superfluidity, and magnetism. 1984 edition"-- Provided by publisher.

Contents:

Chapter 1 Introduction or "Why Green's Functions?" 1

1.1 Classical Green's functions 1

1.2 Linear response of quantum systems 6

1.3 The simple harmonic oscillator 10

1.4 Single-particle Green's functions 13

1.5 Correlation functions 15

1.6 Semiquantitative considerations 18

1.7 Summary and plan of the book 19

References 20

Problems 20

Chapter 2 Formal Matters 22

2.1 Double-time Green's functions 22

2.2 Formal properties 24

2.3 Single-particle Green's functions 33

2.4 Higher-order Green's functions 39

2.5 Kramers-Krönig relations 41

2.6 Fluctuation-dissipation theorem 42

2.7 Equations of motion for Green's functions 42

2.8 The thermodynamic potential 45

2.9 An equation for a single-particle Green's function in an external field 47

2.10 Summary of results 50

References 51

Problems 52

Chapter 3 General Approximations 54

3.1 Perturbation theory with a single-particle potential 54

3.2 Perturbation theory for interacting particles 59

3.3 Time and translational invariance 71

3.4 A system of weakly interacting fermions 77

3.5 Self-energy 78

3.6 The Hartree-Fock approximation 83

3.7 The Hartree approximation 88

3.8 The random phase approximation and screening 89

3.9 Conservation laws and Ward identities 93

References 94

Problems 95

Chapter 4 Transport Coefficients of a Metal 97

4.1 Introduction 97

4.2 The effect of scattering by impurities 100

4.3 The electrical conductivity 109

References 119

Problems 119

Chapter 5 The Coulomb Gas 121

5.1 Macroscopic considerations 121

5.2 Microscopic theory 125

References 140

Problems 140

Chapter 6 Landau's Theory of Normal Fermi Liquids 141

6.1 The neutral liquid 141

6.2 Microscopic basis of Fermi liquid theory 154

6.3 The charged Fermi liquid 163

References 167

Problems 167

Chapter 7 Electrons and Phonons 168

7.1 Phonons 168

7.2 Neutron scattering by the lattice 171

7.3 Structure factor, Green's functions and sum rule 178

7.4 The interaction between electrons and phonons in a metal 181

7.5 Perturbation theory for phonons 186

7.6 Screening of the electron-phonon interaction 189

7.7 Migdal's theorem 193

7.8 Phonon and electron self-energies 195

References 201

Problems 201

Chapter 8 Superconductivity 202

8.1 Introduction 202

8.2 Instability of the normal state 203

8.3 Thermodynamics of a superconductor 209

8.4 Effects of external fields 220

8.5 Effects of impurities 227

8.6 Phase of the gap parameter and flux quantization 234

8.7 Tunnelling of electrons 235

References 239

Problems 240

Chapter 9 Superfluidity 242

9.1 Introduction 242

9.2 Bose-Einstein condensation 245

9.3 Microscopic theory of liquid helium 246

9.4 Theorem of Hugenholtz and Pines 253

9.5 Low-density Bose gas 256

9.6 The superfluidity and quantization of circulation 259

References 261

Problems 262

Chapter 10 Magnetism 263

10.1 Introduction 263

10.2 Molecular field theory 265

10.3 Green's function approach 271

10.4 Hubbard model 274

References 282

Problems 283

Chapter 11 Disordered Systems 285

11.1 Introduction 285

11.2 One impurity in a lattice 292

11.3 Formalism for many impurities 295

11.4 The virtual crystal approximation 298

11.5 The average t-matrix approximation (ATA) 298

11.6 The coherent potential approximation (CPA) 302

11.7 Electrical conductivity 306

References 310

Problems 311

Chapter 12 Critical Behaviour 312

12.1 Second-order phase transitions 312

12.2 Critical exponents 316

12.3 The sum-over-states and fluctuations 319

12.4 Perturbation theory for the correlation function 324

12.5 The renormalization group and critical phenomena 331.

Notes:

"An unabridged republication of the 1984 corrected edition of the work originally published in 1980 by Academic Press, London."--Title page verso.

Includes bibliographical references and index.

Other Edition:

Reprint of: 9780125879521 Rickayzen, G. First paperback edition London : Academic Press Inc. (London) Ltd., 1984 (x, 357 pages : illustrations ; 23 cm)

ISBN:

9780486499840

0486499847

OCLC:

865566518

Publisher Number:

99954993949