Description
About the Authors

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.
William T Coffey is Professor of Electrical Engineering at the University of Dublin, Trinity College. He is a Fellow of the American Physical Society, a Member of the Royal Irish Academy, Holder of an Honorary Doctorate from the University of Perpignan, and a member of the Editorial Board of the famous series Advances in Chemical Physics. His main research interest is relaxation phenomena in condensed matter. He has published over 200 research papers, three books, and several book chapters.

Yuri P Kalmykov is Professor of Physics at the Université de Perpignan Via Domitia. Professor Kalmykov received his MSc and PhD degrees in physics from the Moscow Institute of Physics and Technology in 1978 and 1981, respectively. He is a Fellow of the Institute of Physics and Honorary Fellow of Trinity College Dublin. Professor Kalmykov has published more than 250 research papers, reviews, and book chapters. His main research interests are in the fields of the statistical and condensed matter physics.

Physics

The Langevin Equation