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9780195140187

Nonequilibrium Statistical Mechanics

by
  • ISBN13:

    9780195140187

  • ISBN10:

    0195140184

  • Format: Hardcover
  • Copyright: 2001-04-19
  • Publisher: Oxford University Press

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Summary

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

Brownian Motion and Langevin Equations
3(27)
Langevin Equation and the Fluctuation-Dissipation Theorem
3(4)
Time Correlation Functions
7(3)
Correlation Functions and Brownian Motion
10(4)
Brownian Motion of Other Variables
14(4)
Generalizations of Langevin Equations
18(3)
Brownian Motion in a Harmonic Oscillator Heat Bath
21(3)
Heavy Mass in a Harmonic Lattice
24(6)
Fokker-Planck Equations
30(18)
Liouville Equation in Classical Mechanics
30(6)
Fokker-Planck Equations
36(5)
About Fokker-Planck Equations
41(7)
Master Equations
48(19)
The Golden Rule
48(5)
Optical Absorption Coefficient
53(3)
Quantum Mechanical Master Equations
56(5)
Other Kinds of Master Equations
61(6)
Reaction Rates
67(16)
Transition State Theory
67(6)
The Kramers Problem and First Passage Times
73(5)
The Kramers Problem and Energy Diffusion
78(5)
Kinetic Models
83(18)
Kinetic Models
83(6)
Kinetic Models and Rotational Relaxation
89(4)
BGK Equation and the H-Theorem
93(3)
BGK Equation and Hydrodynamics
96(5)
Quantum Dynamics
101(26)
The Quantum Liouville Operator
101(5)
Electron Transfer Kinetics
106(4)
Two-Level System in a Heat Bath: Dephasing
110(5)
Two-Level System in a Heat Bath: Bloch Equations
115(6)
Master Equation Revisited
121(6)
Linear Response Theory
127(16)
Static Linear Response
127(3)
Dynamic Linear Response
130(6)
Applications of Linear Response Theory
136(7)
Projection Operators
143(26)
Projection Operators and Hilbert Space
143(6)
Derivation of Generalized Langevin Equations
149(2)
Noise in Generalized Langevin Equations
151(6)
Generalized Langevin Equations---Some Identities
157(3)
From Nonlinear to Linear---An Example
160(5)
Linear Langevin Equations for Slow Variables
165(4)
Nonlinear Problems
169(24)
Mode-Coupling Theory and Long Time Tails
169(5)
Derivation of Nonlinear Langevin Equations and Fokker-Planck Equations
174(7)
Nonlinear Langevin Equations and Fokker-Planck Equations for Slow Variables
181(4)
Kinds of Nonlinearity
185(3)
Nonlinear Transport Equations
188(5)
The Paradoxes of Irreversibility
193(5)
Appendixes 198(13)
1 First-Order Linear Differential Equations
198(2)
2 Gaussian Random Variables
200(3)
3 Laplace Transforms
203(2)
4 Continued Fractions
205(2)
5 Phenomenological Transport Equations
207(4)
References 211(2)
Index 213

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