Description

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)

Key Features

* Comprehensive coverage of fluctuations and stochastic methods for describing them * A must for students and researchers in applied mathematics, physics and physical chemistry

Readership

Students and researchers in applied mathematics, physics and physical chemistry

Table of Contents

Dedication

PREFACE TO THE FIRST EDITION

PREFACE TO THE SECOND EDITION

ABBREVIATED REFERENCES

PREFACE TO THE THIRD EDITION

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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 A

Details

No. of pages:
464
Language:
English
Copyright:
© 2007
Published:
Imprint:
North Holland
Electronic ISBN:
9780080475363
Print ISBN:
9780444529657

About the author