物理和化学中的随机过程

PREFACE TO THE FIRST EDITION

PREFACE TO THE SECOND EDITION

ABBREVIATED REFERENCES

PREFACE TO THE THIRD EDITION

1. STOCHASTIC VARIABLES

1. Definition

2. Averages

3. Multivariate distributions

4. Addition of stochastic variables

5. Transformation of variables

6. The Gaussian distribution

7. The central limit theorem

Ⅱ. RANDOM EVENTS

1. Definition

2. The Poisson distribution

3. Alternative description of random events

4. The inverse formula

5. The correlation functions

6. Waiting times

7. Factorial correlation functions

Ⅲ. STOCHASTIC PROCESSES

1. Definition

2. Stochastic processes in physics

3. Fourier transformation of stationary processes.

4. The hierarchy of distribution functions

5. The vibrating string and random fields

6. Branching processes

Ⅳ. MARKOV PROCESSES

1. The Markov property

2. The Chapman-Kolmogorov equation

3. Stationary Markov processes

4. The extraction of a subensemble

5. Markov chains

6. The decay process

Ⅴ. THE MASTER EQUATION

1. Derivation

2. The class of W-matrices

3. The long-time limit

4. Closed， isolated， physical systems

5. The increase of entropy

6. Proof of detailed balance

7. Expansion in eigenfunctions

8. The macroscopic equation

9. The adjoint equation

10. Other equations related to the master equation

Ⅵ. ONE-STEP PROCESSES

1. Definition; the Poisson process

2. Random walk with continuous time

3. General properties of one-step processes

4. Examples of linear one-step processes

5. Natural boundaries

6. Solution of linear one-step processes with natural boundaries

7. Artificial boundaries

8. Artificial boundaries and normal modes

9. Nonlinear one-step processes

Ⅶ. CHEMICAL REACTIONS

1. Kinematics of chemical reactions

2. Dynamics of chemical reactions.

3. The stationary solution

4. Open systems

5. Unimolecular reactions

6. Collective systems

7. Composite Markov processes

Ⅷ. THE FOKKER-PLANCK EQUATION

1. Introduction

2. Derivation of the Fokker-Planck equation

3. Brownian motion

4. The Rayleigh particle

5. Application to one-step processes

6. The multivariate Fokker-Planck equation

7. Kramers equation

Ⅸ. THE LANGEVIN APPROACH

1. Langevin treatment of Brownian motion

2. Applications

3. Relation to Fokker-Planck equation

4. The Langevin approach

5. Discussion of the It6——Stratonovich dilemma

6. Non-Gaussian white noise

7. Colored noise

Ⅹ. THE EXPANSION OF THE MASTER EQUATION

1. Introduction to the expansion

2. General formulation of the expansion method，

3. The emergence of the macroscopic law

4. The linear noise approximation

5. Expansion of a multivariate master equation..

6. Higher orders

Ⅺ. THE DIFFUSION TYPE

1. Master equations of diffusion type

2. Diffusion in an external field

3. Diffusion in an inhomogeneous medium

4. Multivariate diffusion equation

5. The limit of zero fluctuations

Ⅻ. FIRST-PASSAGE PROBLEMS

1. The absorbing boundary approach

2. The approach through the adjoint equation-Discrete case

3. The approach through the adjoint equation-Continuous case

4. The renewal approach

5. Boundaries of the Smoluchowski equation

6. First passage of non-Markov processes

7. Markov processes with large jumps

ⅩⅢ. UNSTABLE SYSTEMS

1. The bistable system

2. The escape time

3. Splitting probability

4. Diffusion in more dimensions

5. Critical fluctuations

6. Kramers escape problem

7. Limit cycles and fluctuations.

ⅩⅣ. FLUCTUATIONS IN CONTINUOUS SYSTEMS

1. Introduction

2. Diffusion noise

3. The method of compounding moments

4. Fluctuations in phase space density

5. Fluctuations and the Boltzmann equation

ⅩⅤ. THE STATISTICS OF JUMP EVENTS

1. Basic formulae and a simple example

2. Jump events in nonlinear systems

3. Effect of incident photon statistics

4. Effect of incident photon statistics - continued.

ⅩⅥ. STOCHASTIC DIFFERENTIAL EQUATIONS

1. Definitions

2. Heuristic treatment of multiplicative equations.

3. The cumulant expansion introduced

4. The general cumulant expansion

5. Nonlinear stochastic differential equations

6. Long correlation times

ⅩⅦ. STOCHASTIC BEHAVIOR OF QUANTUM SYSTEMS

1. Quantum probability

2. The damped harmonic oscillator

3. The elimination of the bath

4. The elimination of the bath-continued

5. The Schrodinger-Langevin equation and the quantum master equation

6. A new approach to noise

7. Internal noise

SUBJECT INDEX

Definition、Averages、Multivariate distributions、Addition of stochastic variables、Transformation of variables、The Gaussian distribution、The central limit theorem、Definition、The Poisson distribution、Alternative description of random events、The inverse formula、The correlation functions、Waiting times、Factorial correlation functions等等。