Lectures on non-equilibrium theory of condensed matter

Ladislaus Alexander Banyai9812567496, 9789812567499

This book discusses in depth many of the key problems in non-equilibrium physics. The origin of macroscopic irreversible behavior receives particular attention and is illustrated in the framework of solvable models. An updated discussion on the linear response focuses on the correct electrodynamic aspects, which are essential for example, in the proof of the Nyquist theorem. The material covers the scaling relationship between different levels of description (kinetic to hydrodynamic) as well as spontaneous symmetry breaking in real time in terms of nonlinear dynamics (attractors), illustrated using the example of Bose-Einstein condensation. The presentation also includes the latest developments – quantum kinetics – related to modern ultrafast spectroscopy, where transition from reversible to irreversible behavior occurs.

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Table of contents :
Contents……Page 10
Preface……Page 8
1. Introduction (Why and how non-equilibrium?)……Page 14
2. Time-reversal and evolution toward equilibrium……Page 18
3. The 1D model of Caldeira and Leggett……Page 22
4. The classical polaron in a d.c. field……Page 26
5. Schrodinger equation versus Master equation……Page 38
6. Naive deduction of the rate equation from the equation of motion……Page 42
7. Naive quantum kinetics……Page 46
8.1 Properties of the Master equation……Page 50
8.2 Rate equations……Page 53
8.3 Scattered versus hopping electrons……Page 57
9. The Boltzmann equation……Page 58
10. Hydrodynamics as scaling of kinetic theory……Page 62
10.1 Macroscopic description of charge evolution in a semiconductor……Page 65
10.2 The scale projection conjecture……Page 68
10.3 Scaling in a neutral hopping model……Page 70
10.4 Scaling in a charged hopping model……Page 75
10.5 Scaling in a charged Boltzmann model……Page 80
11. Linear response to external perturbations……Page 88
12. The Nyquist theorem……Page 94
13.1 The Kubo formula for the electric conductivity……Page 100
13.2 The non-mechanical kinetic coefficients……Page 103
13.3 Symmetry relations dispersion relations and sum rules……Page 107
13.4 Implementation of the Master (rate) – approach into the Kubo formulae. Transport by scattered electrons versus transport by hopping electrons……Page 109
13.5 Ideal relaxation……Page 113
13.6 The transverse strong-field magneto-resistance……Page 115
14. Excitonic absorption in a semiconductor……Page 120
15. The longitudinal dielectric function of crystals……Page 126
16.1 Classical microscopical theory……Page 130
16.2 Non-relativistic quantum electrodynamics……Page 132
16.3 The transverse dielectric function in the nonrelativistic quantum electrodynamics……Page 136
16.4 One-loop (RPA) susceptibility……Page 138
17. Master equations for the density operator (Reservoir theory)……Page 142
18. Two-level atom interacting with light……Page 150
19. Master equations for the density operator with particle-particle collisions (The super-projector approach)……Page 154
20. Van Hove’s weak coupling limit and Davies’s generalization……Page 162
21. Bose-Einstein condensation in real time……Page 172
21.1 BEC of the free Bose gas as an equilibrium phase transition……Page 173
21.2 Markovian real-time description of non-interacting bosons in contact with a thermal bath……Page 176
21.3 BEC in real time of the free Bose gas……Page 179
21.4 Spontaneous symmetry breaking in a finite volume. A solvable model of BEC……Page 182
22. Real-time experiments: Ultra-short-time spectroscopy……Page 188
23.1 Equilibrium Green functions……Page 192
23.2 Non-equilibrium Keldysh-Green Functions……Page 194
24. Keldysh-Green functions and time-reversal……Page 200
25. Time-dependent Hartree-Fock treatment of Coulomb interaction. The exciton……Page 206
26. Quantum kinetics of electrons and holes scattered by LO phonons within the s.c. RPA and the Kadanoff-Baym approximation……Page 210
27. Full two-time quantum-kinetics of electrons and holes scattered by LO phonons within the s.c. RPA……Page 214
28. Coulomb quantum kinetics of electrons and holes within the s.c. RPA and the Kadanoff-Baym approximation. Time dependent screening……Page 220
29. Full two-time quantum kinetics of an electron-hole Coulomb system. Ward identities……Page 226
Appendix A H-theorem for bosons……Page 234
Bibliography……Page 240
Index……Page 244