Nonequilibrium Statistical Mechanics

✍ Scribed by Robert Zwanzig

• Publisher: Oxford University Press
• Year: 2001
• Tongue: English
• Leaves: 233
• Edition: 1
• 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
1. Brownian Motion and Langevin Equations
1.1 Langevin Equation and the Fluctuation-Dissipation Theorem
1.2 Time Correlation Functions
1.3 Correlation Functions and Brownian Motion
1.4 Brownian Motion of Other Variables
1.5 Generalizations of Langevin Equations
1.6 Brownian Motion in a Harmonic Oscillator Heat Bath
1.7 Heavy Mass in a Harmonic Lattice
2. Fokker-Planck Equations
2.1 Liouville Equation in Classical Mechanics
2.2 Fokker-Planck Equations
2.3 About Fokker-Planck Equations
3. Master Equations
3.1 The Golden Rule
3.2 Optical Absorption Coefficient
3.3 Quantum Mechanical Master Equations
3.4 Other Kinds of Master Equations
4. Reaction Rates
4.1 Transition State Theory
4.2 The Kramers Problem and First Passage Times
4.3 The Kramers Problem and Energy Diffusion
5. Kinetic Models
5.1 Kinetic Models
5.2 Kinetic Models and Rotational Relaxation
5.3 BGK Equation and the H-Theorem
5.4 BGK Equation and Hydrodynamics
6. Quantum Dynamics
6.1 The Quantum Liouville Operator
6.2 Electron Transfer Kinetics
6.3 Two-Level System in a Heat Bath: Dephasing
6.4 Two-Level System in a Heat Bath: Bloch Equations
6.5 Master Equation Revisited
7. Linear Response Theory
7.1 Static Linear Response
7.2 Dynamic Linear Response
7.3 Applications of Linear Response Theory
8. Projection Operators
8.1 Projection Operators and Hilbert Space
8.2 Derivation of Generalized Langevin Equations
8.3 Noise in Generalized Langevin Equations
8.4 Generalized Langevin Equations—Some Identities
8.5 From Nonlinear to Linear—An Example
8.6 Linear Langevin Equations for Slow Variables
9. Nonlinear Problems
9.1 Mode-Coupling Theory and Long Time Tails
9.2 Derivation of Nonlinear Langevin Equations and Fokker-Planck Equations
9.3 Nonlinear Langevin Equations and Fokker-Planck Equations for Slow Variables
9.4 Kinds of Nonlinearity
9.5 Nonlinear Transport Equations
10. The Paradoxes of Irreversibility
Appendixes
1 First-Order Linear Differential Equations
2 Gaussian Random Variables
3 Laplace Transforms
4 Continued Fractions
5 Phenomenological Transport Equations
References
Index
A
B
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V