Nonequilibrium Statistical Mechanics

✍ Scribed by Robert Zwanzig

• Publisher: Oxford Univ Pr
• Year: 2002
• Tongue: English
• Leaves: 233
• Edition: 3
• Category: Library

✦ Synopsis

This is a presentation of the main ideas and methods of modern nonequilibrium statistical mechanics. It is the perfect introduction for anyone in chemistry or physics who needs an update or background in this time-dependent field. Topics covered include fluctuation-dissipation theorem; linear response theory; time correlation functions, and projection operators. Theoretical models are illustrated by real-world examples and numerous applications such as chemical reaction rates and spectral line shapes are covered. The mathematical treatments are detailed and easily understandable and the appendices include useful mathematical methods like the Laplace transforms, Gaussian random variables and phenomenological transport equations.

✦ Table of Contents

Contents......Page 8
1.1 Langevin Equation and the Fluctuation-Dissipation Theorem......Page 14
1.2 Time Correlation Functions......Page 18
1.3 Correlation Functions and Brownian Motion......Page 21
1.4 Brownian Motion of Other Variables......Page 25
1.5 Generalizations of Langevin Equations......Page 29
1.6 Brownian Motion in a Harmonic Oscillator Heat Bath......Page 32
1.7 Heavy Mass in a Harmonic Lattice......Page 35
2.1 Liouville Equation in Classical Mechanics......Page 41
2.2 Fokker-Planck Equations......Page 47
2.3 About Fokker-Planck Equations......Page 52
3.1 The Golden Rule......Page 59
3.2 Optical Absorption Coefficient......Page 64
3.3 Quantum Mechanical Master Equations......Page 67
3.4 Other Kinds of Master Equations......Page 72
4.1 Transition State Theory......Page 78
4.2 The Kramers Problem and First Passage Times......Page 84
4.3 The Kramers Problem and Energy Diffusion......Page 89
5.1 Kinetic Models......Page 94
5.2 Kinetic Models and Rotational Relaxation......Page 100
5.3 BGK Equation and the H-Theorem......Page 104
5.4 BGK Equation and Hydrodynamics......Page 107
6.1 The Quantum Liouville Operator......Page 112
6.2 Electron Transfer Kinetics......Page 117
6.3 Two-Level System in a Heat Bath: Dephasing......Page 121
6.4 Two-Level System in a Heat Bath: Bloch Equations......Page 126
6.5 Master Equation Revisited......Page 132
7.1 Static Linear Response......Page 138
7.2 Dynamic Linear Response......Page 141
7.3 Applications of Linear Response Theory......Page 147
8.1 Projection Operators and Hilbert Space......Page 154
8.2 Derivation of Generalized Langevin Equations......Page 160
8.3 Noise in Generalized Langevin Equations......Page 162
8.4 Generalized Langevin Equations—Some Identities......Page 168
8.5 From Nonlinear to Linear—An Example......Page 171
8.6 Linear Langevin Equations for Slow Variables......Page 176
9.1 Mode-Coupling Theory and Long Time Tails......Page 180
9.2 Derivation of Nonlinear Langevin Equations and Fokker-Planck Equations......Page 185
9.3 Nonlinear Langevin Equations and Fokker-Planck Equations for Slow Variables......Page 192
9.4 Kinds of Nonlinearity......Page 196
9.5 Nonlinear Transport Equations......Page 199
10. The Paradoxes of Irreversibility......Page 204
1 First-Order Linear Differential Equations......Page 209
2 Gaussian Random Variables......Page 211
3 Laplace Transforms......Page 214
4 Continued Fractions......Page 216
5 Phenomenological Transport Equations......Page 218
References......Page 222
B......Page 224
E......Page 225
F......Page 226
I......Page 227
L......Page 228
N......Page 229
Q......Page 230
S......Page 231
T......Page 232
V......Page 233