Nonequilibrium Statistical Mechanics

Contents......Page 5
1.1 Langevin Equation and the Fluctuation-Dissipation Theorem......Page 11
1.2 Time Correlation Functions......Page 15
1.3 Correlation Functions and Brownian Motion......Page 18
1.4 Brownian Motion of Other Variables......Page 22
1.5 Generalizations of Langevin Equations......Page 26
1.6 Brownian Motion in a Harmonic Oscillator Heat Bath......Page 29
1.7 Heavy Mass in a Harmonic Lattice......Page 32
2.1 Liouville Equation in Classical Mechanics......Page 38
2.2 Fokker-Planck Equations......Page 44
2.3 About Fokker-Planck Equations......Page 49
3.1 The Golden Rule......Page 56
3.2 Optical Absorption Coefficient......Page 61
3.3 Quantum Mechanical Master Equations......Page 64
3.4 Other Kinds of Master Equations......Page 69
4.1 Transition State Theory......Page 75
4.2 The Kramers Problem and First Passage Times......Page 81
4.3 The Kramers Problem and Energy Diffusion......Page 86
5.1 Kinetic Models......Page 91
5.2 Kinetic Models and Rotational Relaxation......Page 97
5.3 BGK Equation and the H-Theorem......Page 101
5.4 BGK Equation and Hydrodynamics......Page 104
6.1 The Quantum Liouville Operator......Page 109
6.2 Electron Transfer Kinetics......Page 114
6.3 Two-Level System in a Heat Bath: Dephasing......Page 118
6.4 Two-Level System in a Heat Bath: Bloch Equations......Page 123
6.5 Master Equation Revisited......Page 129
7.1 Static Linear Response......Page 135
7.2 Dynamic Linear Response......Page 138
7.3 Applications of Linear Response Theory......Page 144
8.1 Projection Operators and Hilbert Space......Page 151
8.2 Derivation of Generalized Langevin Equations......Page 157
8.3 Noise in Generalized Langevin Equations......Page 159
8.4 Generalized Langevin Equations—Some Identities......Page 165
8.5 From Nonlinear to Linear—An Example......Page 168
8.6 Linear Langevin Equations for Slow Variables......Page 173
9.1 Mode-Coupling Theory and Long Time Tails......Page 177
9.2 Derivation of Nonlinear Langevin Equations and Fokker-Planck Equations......Page 182
9.3 Nonlinear Langevin Equations and Fokker-Planck Equations for Slow Variables......Page 189
9.4 Kinds of Nonlinearity......Page 193
9.5 Nonlinear Transport Equations......Page 196
10. The Paradoxes of Irreversibility......Page 201
1 First-Order Linear Differential Equations......Page 206
2 Gaussian Random Variables......Page 208
3 Laplace Transforms......Page 211
4 Continued Fractions......Page 213
5 Phenomenological Transport Equations......Page 215
References......Page 219
B......Page 221
E......Page 222
F......Page 223
I......Page 224
L......Page 225
N......Page 226
Q......Page 227
S......Page 228
T......Page 229
V......Page 230