The Fokker-Planck Equation: Methods of Solution and Applications

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Springer Science & Business Media, 06.12.2012 - 472 Seiten
One of the central problems synergetics is concerned with consists in the study of macroscopic qualitative changes of systems belonging to various disciplines such as physics, chemistry, or electrical engineering. When such transitions from one state to another take place, fluctuations, i.e., random processes, may play an im portant role. Over the past decades it has turned out that the Fokker-Planck equation pro vides a powerful tool with which the effects of fluctuations close to transition points can be adequately treated and that the approaches based on the Fokker Planck equation are superior to other approaches, e.g., based on Langevin equa tions. Quite generally, the Fokker-Planck equation plays an important role in problems which involve noise, e.g., in electrical circuits. For these reasons I am sure that this book will find a broad audience. It pro vides the reader with a sound basis for the study of the Fokker-Planck equation and gives an excellent survey of the methods of its solution. The author of this book, Hannes Risken, has made substantial contributions to the development and application of such methods, e.g., to laser physics, diffusion in periodic potentials, and other problems. Therefore this book is written by an experienced practitioner, who has had in mind explicit applications to important problems in the natural sciences and electrical engineering.
 

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Inhalt

Introduction
1
Probability Theory
13
Langevin Equations
32
FokkerPlanck Equation
63
FokkerPlanck Equation for One Variable Methods of Solution
96
FokkerPlanck Equation for Several Variables Methods of Solution
133
Linear Response and Correlation Functions
163
Reduction of the Number of Variables
179
Solutions of the Kramers Equation
229
Brownian Motion in Periodic Potentials
276
Statistical Properties of Laser Light
374
Appendices
414
S Supplement to the Second Edition
436
References
448
Subject Index
463
Urheberrecht

Solutions of Tridiagonal Recurrence Relations Application to Ordinary
196

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