The Fokker-Planck Equation

Klappentext

This book deals with the derivation of the Fokker-Planck equation, methods of solving it and some of its applications. Various methods such as the simulation method, the eigenfunction expansion, numerical integration, the variational method, and the matrix continued-fraction method are discussed. This is the first time that this last method, which is very effective in dealing with simple Fokker-Planck equations having two variables, appears in a textbook. The methods of solution are applied to the statistics of a simple laser model and to Brownian motion in potentials. It is shown that the solution of the equation for Brownian motion in a variety of potentials can be expressed in terms suitable for evaluation on a computer. A supplement is included, containing a short review of new material together with some recent references. The book should be very useful to graduate students in physics, chemical physics, and electrical engineering, and also to research workers in these fields.

Inhalt
Contents: Introduction.- Probability Theory.- Langevin Equations.- Fokker-Planck Equation.- Fokker-Planck Equation for One Variable; Methods of Solution.- Fokker-Planck-Equation for Several Variables; Methods of Solution.- Linear Response and Correlation Functions.- Reduction of the Number of Variables.- Solutions of Tridiagonal Recurrence Relations, Application to Ordinary and Partial Differential Equations.- Solutions of the Kramers Equation.- Brownian Motion in Periodic Potentials.- Statistical Properties of Laser Light.- Appendices.- Supplement.- References.- Subject Index.