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Cover Zaitsev R.O. Introduction to Modern Kinetic Theory: A Set of Lectures
Id: 185199
 
29.9 EUR

Introduction to Modern Kinetic Theory: A Set of Lectures

URSS. 520 pp. (English). Paperback. ISBN 978-5-396-00611-9.

 Summary

The proposed Lectures supplement the course by Landau and Lifshitz with some new sections, without which it is impossible to solve the problems in modern theoretical physics.

This book consists of Lectures which the author has been reading in Moscow Institute of Physical Technology since 2003. The first six Lectures present the traditional university course of physical kinetics. The transport equations for ideal Fermi and Bose gases are considered. In other Lectures non-ideal systems are considered on the basis of two-component Green's functions. Non-equilibrium properties of metals, dielectrics, and superconductors are studied in the framework of this method. The non-stationary Ginzburg---Landau equation is derived. The theory of stationary tunneling phenomena and the non-stationary Josephson effect are considered.

The linear and non-linear theories of noise in electric circuits are studied. The equations which allow to determine low frequency asymptotic of non-linear four-current correlator (the so called $1/f^{alpha}$ noise) are obtained.

The book is intended for researches, graduate and undergraduate students studying physical kinetics.


 Contents

Contents

CONTENTS

CONTENTS 3

INTRODUCTION 11

Lecture I. THE BOLTZMANN THEORY 14
§ 1. The Boltzmann equation 16
Problem 1. Molecule collision number 20
§ 2. The Boltzmann iï-theorem 21
§ 3. Conservation laws 25
P r o b 1 e m 2. Locally equilibrium distributions 26
§ 4. The r-approximation 27
P r o b 1 e m 3. The thermal conductivity in the
r-approximation 28
P r o b 1 e m 4. The coefficient of viscosity in the
r-approximation 30
§ 5. An approximate solution of the
Boltzmann equation 31
§5.1. The thermal conductivity 35
§ 5.2. Coefficients of viscosity 37
§ 6. The Boltzmann equation for a binary mixture 41
§ 7. The Chapman—Enskog equation for a binary
mixture 43
§7.1. The system of algebraic equations 47
§ 7.2. Diffusion and thermal diffusion 51
§ 7.3. The thermal conductivity of a gas mixture 53
§ 7.4. The transversal viscosity of a gas mixture 55
P r o b 1 e m 5. The diffusion coefficient 56
P r o b 1 e m 6. The thermal diffusion coefficient 59
Appendix. The Bogolubov dynamical theory .... 62 References 66

Lecture II. HYDRODYNAMIC EQUATIONS 67
§ 1. General relations 68
§ 1.1. Mass conservation law 68 § 1.2. Momentum conservation law 69
§ 1.3. Energy conservation law 70
§ 2. The closed system of equations 72
§ 3. Linearized hydrodynamic equations 75
§ 4. Hydrodynamic excitations 77
§ 5. Excitations in a charged system 79
§ 6. Meteorologist's equations 80
References 82

Lecture III. THE ENSKOG THEORY 83
§ 1. The Enskog equation 84
§ 2. Conservation laws 88
§ 3. Linearization of the collision integral 91
§ 4. The equations of hydrodynamics 95
§ 5. Solution of the transport equation 96
§ 6. Calculation of the transport coefficients 97
§6.1. transport corrections 97
§ 6.2. Corrections caused by momentum transfer 99
§ 6.3. The shear and volume viscosity factors 101
§ 6.4. Corrections caused by energy transfer 102
§ 6.5. The thermal conductivity 104
§ 7. Conclusions 104
Appendix. Calculation of angular integrals 105
References 110

Lecture IV. TRANSPORT EQUATIONS
FOR CHARGED PARTICL Ill
§ 1. Small momentum transfer 112
§ 2. Landau's collision integral 114
Problem 1. Transport coefficients
in the r-approximation 119
P r o b 1 e m 2. The cooling rate of hot electrons 122
§ 3 The H theorem for Landau's collision integral .... 124
§ 4. The Fokker—Planck collision integral 126
§ 4.1. The Fokker-Planck equation for charged particles 127 § 4.2. The Fokker-Planck equation for heavy particles 130
P r o b 1 e m 3. The mobility of heavy particles 131
P r o b 1 e m 4. The diffusion and thermodiffusion coefficients 132 References 134

Lecture V. ELECTRONS IN A METAL (T < 6) 135
§ 1. The equation for the distribution function 136
Problem 1. The residual resistance 141
P r o b 1 e m 2. The electron thermal conductivity 142
P r o b 1 e m 3. The thermoelectric effect 143
P r o b 1 e m 4. The law of increasing entropy 144
§ 2. The Kondo effect 146
§ 2.1. The perturbation theory 146
§ 2.2. The temperature correction 153
§ 2.3. Reducing to a one-dimensional problem 156
§ 3. Non-stationary phenomena 157
§ 3.1. Longitudinal fields 157
§3.2. Transversal fields 161
References 166

Lecture VI. ELECTRONS AND PHONONS IN
A METAL 167
§ 1. The electron—phonon interaction 168
§ 2. The transport equation in metals 170
§ 2.1. The if-theorem on entropy increase 171
§ 3. The transport equation at equilibrium phonons ...174
§ 3.1. Integration over virtual electron momenta 180
§ 3.2. Integration over scattering angles 180
§ 3.3. A trial function of the first approximation 181
§ 3.4. The Bloch-GrMneisen equation 182
§ 4. The resistance in dependence of temperature .... 183 § 5. The thermal conductivity in dependence of
temperature 186
§ 5.1. Low temperatures T < O 186
§ 5.2. The kernel of the integral equation 190 § 5.3. High temperatures T ^> 0 191
Problem 1. Qualitative considerations 192
P r o b 1 e m 2. The rate of phonon relaxation 195
P r o b 1 e m 3. The rate of electron relaxation 196
§ 6. The conductivity of semiconductors 198
§ 7. Umpklapp processes and their role 200
References 205

Lecture VII. NON-STATIONARY PERTURBATION
THEORY 206
§ 1. The Schwinger—Mills—Keldysh theory 207
§ 1.1. The transition to the interaction representation 208
§ 1.2. Averaging over the states of an ideal gas 209
§ 1.3. The diargammatic technique 212
§ 2. Tunneling through a fiat interface 214
§ 3. The Kubo formula 217
§ 4. A longitudinal external field 219
§4.1. The longitudinal non-stationary correction 220
§ 4.2. The longitudinal dielectric permittivity 222
§ 5. A transversal external field 224
§5.1. The transversal non-stationary correction 226
§ 5.2. The transversal dielectric permittivity 226
§ 5.3. The calculation of the penetration depth 231
§ 6. The rate of relaxation of impurity spins 232
References 237

Lecture VIII. THE TUNNELING CURRENT AND
THE JOSEPHSON EFFECT 238
§ 1. Tunneling at a given voltage applied 239
§ 1.1. The tunneling Hamiltonian and average current 239
§ 1.2. The (u-v) transformation with a phase factor 241
§ 1.3. The calculation of the volt ampere characteristic 243
§ 2. The stationary (d.c.) supercurrent 249
§2.1. The calculation of the Josephson current amplitude ... .250 § 3. The non-stationary Josephson effect 256 §3.1. The Josephson current. The temperature T <^ Tc 258
§ 3.2. The interference current. The temperature T < Tc .... 262
§ 4. Conclusion 264
Appendix The calculation of elliptic integrals 266
References 270

Lecture IX. QUANTUM TRANSPORT
PHENOMENA 271
§ 1. The equation for the density matrix 272
§ 2. The quantum transport equation 277
§ 3. The Dyson equation 280
§ 4. Collision integrals 285
§4.1. The scattering by impurities 288
§ 4.2. The scattering by equilibrium phonons 289
§ 4.3. The electron-electron interaction 292
§ 4.4. The Landau collision integral 295
§ 5. The screening and plarization 298
§5.1. The plasmon exchange 305
§ 6. The retarded and advanced Green functions 305
§ 7. Diffusons and Coopérons 310
§ 7.1. "Long tails" of correlation functions 319
References 321

Lecture X. NOISE IN ELECTRICAL CIRCUITS ...322
§ 1. The fluctuation-dissipation theorem 324
§ 1.1. The Kubo formula 325
§ 1.2. The white noise 326
§ 2. The 1//-noise in electrical circuits 330
§ 2.1. The l//-noise. Description of phenomenon 330
§ 2.2. The 1/f -noise. The setting of problem 330
§ 3. The equations at T = 0 331
§3.1. The equation for four-current correlator 333
§ 3.2. Equations for two-current vertices 336
§ 3.3. Equations for scalar vertices 339
§ 3.4. Calculation of the exponent a 342 § 4. The l//a-noise at a finite temperature 343
§4.1. Experimental data 343
§ 4.2. Scheme of calculations 344
§ 4.3. Formulation of problem 347
§ 5. Renormalization-group equations 351
§5.1. Equations for scalar vertices 351
§ 5.2. Equations for two-current verticies 354
§ 5.3. Equations for four-current vertices 356
§ 6. Calculation of the exponent a 357
§ 7. Calculation of ip values 360
§7.1. Low temperatures (T < O) 362
§ 7.2. High temperatures (T ^> 0) 363
§ 7.3. Qualitative comparisons with experiment 364
§ 7.4. Conclusions 365
References 366

Lecture XL TRANSPORT EQUATION FOR
PHONONS 367
§ 1. The transport equation 368
§ 2. The phonon—phonon interaction 368
§ 3. The three—phonon collision integral 370
§ 4. The H-theorem 373
§ 5. The thermal conductivity of dielectrics 377
§5.1. The equation at a given temperature gradient 377
§ 5.2. The thermal conductivity at high temperatures 379
§ 5.3. The thermal conductivity at low temperatures 380
§ 6. The phonon hydrodynamics equations 384
§ 7. Sound absorbtion. Short waves 387
§ 8. Sound absorbtion. Long waves 392
§ 8.1. Long waves. High temperatures T ^ 0 395
§ 8.2. Long waves. Low temperatures T < O 396
Problem. Sound absorbtion in the r approximation 397
References 402
Lecture XII. TRANSPORT PHENOMENA IN
FERMI-LIQUID 403
§ 1. The equation for the distribution function 404
§ 2. The relaxation time in dependence of tempera- ture 406
§ 3. The conservation laws 407
§3.1. The continuity equation for quasi-particles 407
§ 3.2. The momentum conservation law 408
§ 3.3. The energy conservation law 409
§ 4. Linearization of the transport equation 410
Problem 1. The thermal conductivity in dependence of
temperature 412
Problem 2. The viscosity in dependence of temperature 415
Problem 3. Electron's entrainment 417
§ 5. The exact solution of the transport equation 418
§ 5.1 Separation of variables 418
§ 5.2 Transformation of the kernel of the integral
equation 418
§ 6. Solution of integral equations 425
§ 6.1. The inhomogeneous equation. Even functions 426
§ 6.2. The inhomogeneous equation. Odd functions 429
§ 7. The shear viscosity. The exact solution 431
§ 8. The thermal conductivity. The exact solution 434
§ 9. The second viscosity 436
§ 10. The sound propagation in a Fermi-liquid 438
§ 10.1. The zero sound in a Fermi-liquid 438
§ 10.2. The velocity of hydrodynamic sound 438
§ 10.3. The sound absorbtion in the r-approximation 441
§ 11. The if-theorem 451
Appendix A. The effective mass 455
Appendix B. Calculation of integrals 457
Appendix C. Calculation of angular integrals 460
References 462
Lecture XIII. TRANSPORT PHENOMENA IN
SUPERCONDUCTORS 463
§ 1. The non-stationary Meissner effect 464
§ 1.1. The Pippard case 472
§ 1.2. The London case 477
§ 2. The absorbtion of ultrasound 480
§ 3. The rate of relaxation of the nuclear spins 485
§ 4. The thermal conductivity of a superconductor .... 489 § 5. The Ginzburg—Landau non-stationary
equations 495
Problem 1: The gauge invariant GLAG equation 501
P r o b 1 e m 2: Relaxation in an ideal superconductor 502
P r o b 1 e m 3: Relaxation in a non-ideal superconductor .... 503 References 510

BIBLIOGRAPHY 511

Manuals and monographs 515

 About the author

Rogdai Olegovich Zaitsev was born in Moscow in 1938. He graduated from the physical faculty of the Moscow State University in 1961; worked in the Kurchatov Institute of Nuclear Energy from 1965 to 2008. Now he works in the Moscow Institute of Physics and Technology as a professor of theoretical physics.

His scientific interests are devoted to theories of solid state, superconductivity, ferromagnetism, and the non-linear theory of noise.


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