This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, etc. The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles.
Historical Background and Introductory Concepts; Methods for Solving Langevin and Fokker-Planck Equations; Matrix Continued Fractions; Escape Rate Theory; Linear and Nonlinear Response Theory; Brownian Motion of a Free Particle and a Harmonic Oscillator; Rotational Brownian Motion about a Fixed Axis in a Periodic Potential; Brownian Motion in a Tilted Periodic Potential: Application to the Josephson Tunnelling Junction and Ring Lasers; Brownian Motion in a Double-Well Potential; Isotropic and Anisotropic Rotational Brownian Motion in Space in the Presence of an External Potential with Applications to Dielectric and Kerr Effect Relaxation in Fluids and Liquid Crystals; Brownian Motion of Classical Spins with Applications to Superparamagnetism; Magnetic Stochastic Resonance; Dynamic Hysteresis; Switching Field Surfaces; Inertial Langevin Equations with Applications to Orientational Relaxation in Liquids; Itinerant Oscillator Model; Anomalous Diffusion; Continuous Time Random Walks; Methods for the Solution of Fractional Fokker-Planck Equations.