Description
Book SynopsisThis volume is the second edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the Brownian motion in a potential, with emphasis on modern applications in the natural sciences, electrical engineering and so on. It has been substantially enlarged to cover in a succinct manner a number of new topics, such as anomalous diffusion, continuous time random walks, stochastic resonance etc, which are of major current interest in view of the large number of disparate physical systems exhibiting these phenomena. The book has been written in such a way that all the material should be accessible to an advanced undergraduate or beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of research papers or scattered review articles.
Trade Review"This enlarged and updated second edition of the book: 'The Langevin equation' presents an extremely useful source for the practitioners of stochastic processes and its applications to physics, chemistry, engineering and biological physics, both for the experts and the beginners. It gives a valuable survey of solvable paradigms that rule many diverse stochastic phenomena. As such, it belongs onto the desk of all engaged in doing research and teaching in this area."Peter HanggiUniversity of Augsburg"... this enlarged and updated second edition constitutes an excellent and quite useful contribution to this important subject of relevance in physics, chemistry and several branches of engineering."Mathematical Reviews"This is a timely update of the theory and applications of the Langevin equation, which skillfully combines the elementary approaches with most recent developments such as anomalous diffusion and fractional kinetics. Both experts and beginners will benefit from this well-written textbook."J KlafterHeinemann Chair of Physical ChemistryTel Aviv University"This book has been written in such a way that all the materials should be accessible to an advanced undergraduate or beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of research papers or scattered review articles."Zentralblatt MATH
Table of ContentsHistorical Background and Introductory Concepts; Langevin Equations and Methods of Solution; Matrix Continued Fraction Method for the Solution of Langevin and Fokker-Planck Equations; Linear and Nonlinear Response Theory; Brownian Motion of a Free Particle and a Harmonic Oscillator; One-Dimensional Rotational Brownian Motion in a Potential; Brownian Motion in a Tilted Cosine Potential: Application to the Josephson Tunnelling Junction; Rotational Brownian Motion in an External Potential with Applications to Dielectric and Magnetic Relaxation; Non-Axially Symmetric Problems in Rotational Brownian Motion: Applications to the Theory of Superparamagnetism; Inertial Langevin Equations: Application to Orientational Relaxation in Liquids; Itinerant Oscillator Model; Anomalous Diffusion; Methods for the Solution of Fractional Fokker-Planck Equations.
