This 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.
Historical 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.