Field Theory of Non-Equilibrium Systems

Cover......Page 1
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
1.1 Closed time contour......Page 17
1.2 The outline of this book......Page 22
2.1 Bosonic coherent states......Page 26
2.2 Partition function......Page 28
2.3 Bosonic Gaussian integrals......Page 30
2.4 Normalization and continuum notation......Page 31
2.5 Green functions......Page 33
2.6 Keldysh rotation......Page 35
2.7 Keldysh action and its structure......Page 38
2.8 External sources......Page 40
3.1 Harmonic oscillator......Page 45
3.2 Quantum particle in contact with an environment......Page 48
3.3 From Matsubara to Keldysh......Page 50
3.4 Quantum tunneling in a time-dependent potential......Page 52
3.5 Dissipative quantum tunneling......Page 55
4.1 Classical dissipative action......Page 60
4.2 Langevin equation......Page 61
4.3 Multiplicative noise and Martin–Siggia–Rose method......Page 62
4.4 Optimal path approximation......Page 65
4.5 Fokker–Planck equation......Page 69
4.6 Ito vs. Stratonovich......Page 73
4.7 Noise with a finite correlation time......Page 75
4.8 Kramers problem......Page 76
4.9 Fluctuation relation......Page 78
4.10 Reaction models......Page 81
4.11 Time-dependent problems......Page 85
4.12 Large deviations in multivariable systems......Page 88
5.1 Complex bosonic fields......Page 92
5.2 Interactions......Page 94
5.3 Dyson equation......Page 96
5.4 Real bosonic fields......Page 99
5.5 Self-energy......Page 102
5.6 Wigner transformation......Page 103
5.7 Kinetic term......Page 105
5.8 Collision integral......Page 108
6.1 Plasma action......Page 113
6.2 Plasmons and Landau damping......Page 117
6.3 Acoustic modes in plasma......Page 118
6.4 Random phase approximation......Page 120
6.5 Beyond linearized dynamics......Page 124
6.6 Non-linear Landau damping......Page 128
7.1 Gross–Pitaevskii equation......Page 131
7.2 Quasiparticles......Page 134
7.3 Collisionless relaxation of the condensate fluctuations......Page 139
7.4 Condensate growth and collapse......Page 142
7.5 Fluctuations......Page 147
7.6 Semiclassical dynamics of the condensate......Page 151
7.7 Quasiparticle collision integral......Page 153
7.8 Dynamics of a quantum impurity in a superfluid......Page 157
8.1 Dissipative chains and membranes......Page 163
8.2 Equilibrium statistical mechanics......Page 165
8.3 Critical nucleation in first order transitions......Page 167
8.4 Critical dynamics near a classical second order transition......Page 170
8.5 Hohenberg–Halperin classification......Page 176
8.6 Quantum phase transitions......Page 179
8.7 Absorbing state transitions in reaction-diffusion models......Page 182
8.8 Dynamics of growing surfaces......Page 192
9.1 Grassmann variables, fermionic coherent states and Gaussian integrals......Page 199
9.2 Partition function......Page 202
9.3 Green functions and Keldysh rotation......Page 204
9.4 Free fermionic fields and their action......Page 206
9.5 External fields and sources......Page 207
9.6 Free degenerate Fermi gas......Page 212
9.7 Interactions......Page 213
9.8 Kinetic equation......Page 217
9.9 Stoner instability......Page 221
10.1 Landauer formula......Page 226
10.2 Shot noise......Page 229
10.3 Counting statistics......Page 231
10.4 Fluctuation relation......Page 237
10.5 Adiabatic pumping......Page 238
10.6 Spin torque......Page 241
11.1 Kinetic equation approach......Page 250
11.2 Averaging over the quenched disorder......Page 253
11.3 Non-linear sigma-model......Page 257
11.4 Stationary point and fluctuations......Page 261
11.5 Sources and external fields......Page 264
11.6 Kubo formula and linear response......Page 266
11.7 Cooper channel......Page 268
11.8 Weak localization and scaling......Page 271
12.1 Spectral statistics......Page 276
12.2 Wigner–Dyson statistics......Page 280
12.3 Universal conductance fluctuations......Page 283
12.4 Full counting statistics in a disordered wire......Page 286
12.5 Tunneling action......Page 290
12.6 Chaotic cavity......Page 293
13.1 K-gauge......Page 296
13.2 Non-linear sigma-model for interacting systems......Page 300
13.3 Zero bias anomaly......Page 302
13.4 Altshuler–Aronov effect......Page 306
13.5 Kinetic equation......Page 309
14.1 Cooper channel interactions......Page 314
14.2 Usadel equation......Page 317
14.3 Stationary superconductivity......Page 321
14.4 SNS system......Page 324
14.5 Collective modes of disordered superconductors......Page 328
14.6 Time-dependent Ginzburg–Landau theory......Page 335
14.7 Fluctuating superconductivity......Page 344
References......Page 347
Index......Page 355