The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant.
C.W.Gardiner, Quantum Optics (Springer, Berlin 1991)
D.T. Gillespie, Markov Processes (Academic Press, San Diego 1992)
W.T. Coffey, Yu.P.Kalmykov, and J.T.Waldron, The Langevin Equation (2nd edition, World Scientific, 2004)
* Comprehensive coverage of fluctuations and stochastic methods for describing them
* A must for students and researchers in applied mathematics, physics and physical chemistry
Author(s): Kampen, N G Van
Series: North-Holland personal library
Edition: 3
Publisher: North-Holland; Elsevier Science
Year: 2007;2011
Language: English
Pages: 481
City: Burlington
Preface to the first edition
Preface to the second edition
Preface to the second edition
Table of Contents
I. 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 process
4. The hierarchy of distribution functions
5. The vibrating strings 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 subenesemle
5. Markov Chains
6. The Decay Process
V. The master equation
1. Derivation
2. 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 eigen functions
8. The Macroscopic Equation
9. The Adjoint Equation
10. Other equations related to master equation
VI. One-step processes
1. Definition; The Poisson Process
2. Random Walk with Continuous Time
3. General Properties of One-Step Process
4. Examples of linear one-step process
5. Natural Boundaries
6. Solution of linear one-step processes with natural boundaries
7. Artificial Boundaries
8. Artificial boundaries and normal modes
9. Non linear one-step processes
VII. Chemical reactions
1. Kinematics of chemical reactions
2. Dynamics of chemical reactions
3. The stationary solution
4. Open Systems
5. Unimoleculear Solutions
6. Collective Systems
7. Composite Markov Processes
VIII. The Fokker-Planck equation
1. Introduction
2. Derivation of Fokker-Plank Equation
3. Brownian Motion
4. The Rayleigh particle
5. Application to one-step process
6. The multivariate Fokker-Plank equation
7. Kramer's Equation
IX. The Langevin approach
1. Langevin treatment of Brownian Motion
2. Applications
3. Relation to Fokker-Plank equation
4. The Langevin approach
5. Discussion of Itô-Stratonovich dilema
6. Non-Gaussian white Noise
7. Colored noise
X. The expansion of the master equation
1. Introduction to expansion
2. General formulation of the expansion method
3. The emergence of 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 inhomogenous 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. The Boundaries of the Smouluchowski 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 formule and a simple example
2. Jump events in non linear equations
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
