The Fokker-Planck equation. Methods of solutions and applications.
2nd ed. 1989. 3rd print.

*(English)*Zbl 0866.60071
Springer Series in Synergetics. 18. Berlin: Springer-Verlag. xiv, 474 p. (1996).

[For the first (1984) and second editions (1989) see Zbl 0546.60084 and Zbl 0665.60084, respectively.]

This book is devoted to the Fokker-Planck equation which is an equation of motion for the distribution function of stochastically fluctuating macroscopic variables. This equation plays an important role in problems from different fields such as solid-state physics, chemical physics, quantum optics, biology and electrical engineering. The book starts with a discussion of the Fokker-Planck equation and its special forms. Chapter 2 gives the basic ideas and concepts of the probability theory in a simplified form. Chapter 3 presents the Langevin equation. The next chapter discusses the Kramers-Moyal expansion and its applications to derivation of the Fokker-Planck equation. Chapters 5 and 6 present the Fokker-Planck equation with time-independent drift and diffusion coefficients. Various methods of solution for the Fokker-Planck and the Kramers equations such as analytical methods, eigenfunction expansion, adiabatic elimination of variables, variational method, numerical integration, simulation method, matrix continued-fraction method are discussed in Chapters 5-10. The last chapters 11 and 12 demonstrate how the methods developed in this book can be applied to investigate the Brownian motion in periodic potentials and statistical properties of the laser light. The appendices give some examples of practical usage of the methods of solutions. This edition contains also a supplement which gives a short review of some new developed materials. A rich and comprehensive list of references completes this book which will be useful for graduate students and research workers in physics, chemical physics and electrical engineering.

This book is devoted to the Fokker-Planck equation which is an equation of motion for the distribution function of stochastically fluctuating macroscopic variables. This equation plays an important role in problems from different fields such as solid-state physics, chemical physics, quantum optics, biology and electrical engineering. The book starts with a discussion of the Fokker-Planck equation and its special forms. Chapter 2 gives the basic ideas and concepts of the probability theory in a simplified form. Chapter 3 presents the Langevin equation. The next chapter discusses the Kramers-Moyal expansion and its applications to derivation of the Fokker-Planck equation. Chapters 5 and 6 present the Fokker-Planck equation with time-independent drift and diffusion coefficients. Various methods of solution for the Fokker-Planck and the Kramers equations such as analytical methods, eigenfunction expansion, adiabatic elimination of variables, variational method, numerical integration, simulation method, matrix continued-fraction method are discussed in Chapters 5-10. The last chapters 11 and 12 demonstrate how the methods developed in this book can be applied to investigate the Brownian motion in periodic potentials and statistical properties of the laser light. The appendices give some examples of practical usage of the methods of solutions. This edition contains also a supplement which gives a short review of some new developed materials. A rich and comprehensive list of references completes this book which will be useful for graduate students and research workers in physics, chemical physics and electrical engineering.

Reviewer: S.Poghosyan (Erevan)

##### MSC:

60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

82-02 | Research exposition (monographs, survey articles) pertaining to statistical mechanics |

82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |

60J65 | Brownian motion |