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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

Author

Coffey, William T; Kalmykov, Yuri P

Publisher

World Scientific Publishing Co. Pte Ltd

Published

2017

Language

EN

ISBN

9789813222007