The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering by William T Coffey

The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and…

byWilliam T Coffey, Yuri P Kalmykov

Kobo ebook | March 22, 2017

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Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle — the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion — first formulated by Langevin in 1908 — so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker–Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject.


  • Historical Background and Introductory Concepts
  • Langevin Equations and Methods of Solution
  • Brownian Motion of a Free Particle and a Harmonic Oscillator
  • Rotational Brownian Motion About a Fixed Axis in N-Fold Cosine Potentials
  • Brownian Motion in a Tilted Periodic Potential: Application to the Josephson Junction
  • Translational Brownian Motion in a Double-Well Potential
  • Non-inertial Rotational Diffusion in External Potentials: Applications to Orientational Relaxation of Molecules in Fluids and Liquid Crystals
  • Anisotropic Rotational Diffusion in an External Potential: Application to Kerr Effect and Dielectric Relaxation
  • Brownian Motion of Classical Spins: Application to Magnetization Relaxation in Nanomagnets
  • Inertial Effects in Rotational and Translational Brownian Motion
  • Inertial Effects in Rotational Diffusion in Molecular Liquids and Ferrofluids
  • Anomalous Diffusion and Relaxation

Readership: Advanced undergraduates, postgraduates, academics and researchers in statistical physics, condensed matter physics and magnetism, chemical physics, theoretical chemistry and applied mathematics.
Key Features:

  • This volume is the fourth edition of the first elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion in a potential with particular emphasis on modern applications in the natural sciences, electrical engineering, etc.
  • It has been extensively enlarged to cover in a reasonably succinct manner using a synergetic approach a number of new topics such as anomalous diffusion, continuous time random walks, stochastic resonance, nanomagnetism, magnetic resonance imaging, spintronics, etc. which are of major current interest in view of the large number of disparate systems which exhibit these phenomena
  • The book is written in a manner such that all the material should be accessible to an advanced undergraduate or beginning graduate student
Title:The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and…Format:Kobo ebookPublished:March 22, 2017Publisher:World Scientific Publishing CompanyLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9813222018

ISBN - 13:9789813222014

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