Stochastic Processes in Physics and Chemistry
The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant.
C.W.Gardiner, Quantum Optics (Springer, Berlin 1991)
D.T. Gillespie, Markov Processes (Academic Press, San Diego 1992)
W.T. Coffey, Yu.P.Kalmykov, and J.T.Waldron, The Langevin Equation (2nd edition, World Scientific, 2004)
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Chapter XI THE DIFFUSION TYPE
Chapter XII FIRSTPASSAGE PROBLEMS
Chapter XIII UNSTABLE SYSTEMS
Chapter XIV FLUCTUATIONS IN CONTINUOUS SYSTEMS
Chapter XV THE STATISTICS OF JUMP EVENTS
Chapter XVI STOCHASTIC DIFFERENTIAL EQUATIONS
Chapter XVII STOCHASTIC BEHAVIOR OF QUANTUM SYSTEMS
Chapter IX THE LANGEVIN APPROACH
Chapter X THE EXPANSION OF THE MASTER EQUATION
according additional applies approximation average boundary called chapter coefficients compute condition Consider constant corresponding course defined definition density depends Derive described determined diffusion distribution energy equal equilibrium example Exercise expansion expression fact factor Find fluctuations Fokker–Planck equation function Gaussian given gives Hence higher identity independent initial integral interval jump limit linear M-equation macroscopic Markov process master equation matrix mean mechanics method molecules moments needed noise nonlinear obeys obtained occur operator particle Phys physical positive possible potential probability probability distribution problem properties Prove quantity quantum quantum mechanics random reaction reduces relation result Show solution solved space stationary stationary solution Statist step stochastic stochastic differential equation Suppose theory tion transformation transition unit vanishes variables write written zero
Page vii - Que nous sert-il d'avoir la panse pleine de viande, si elle ne se digère? si elle ne se trans-forme en nous? si elle ne nous augmente et fortifie...
Page vii - The interest in fluctuations and in the stochastic method for describing them has grown enormously in the last few decades. The number of articles scattered in the literature of various disciplines must run to thousands and special journals are devoted to the subject. Yet the physicist or chemist who wants to become acquainted with the field cannot easily find a suitable introduction. This book is an attempt to fill this gap in the literature. The first part consists of an introductory exposition...
Page vii - ... enormously in the last few decades. The number of articles scattered in the literature of various disciplines must run to thousands and special journals are devoted to the subject. Yet the physicist or chemist who wants to become acquainted with the field cannot easily find a suitable introduction. This book is an attempt to fill this gap in the literature. The first part consists of an introductory exposition of probability, random events, and stochastic processes as they occur in physics, chemistry...
Page x - An Introduction to Probability Theory and its Applications. Vol. I, 2nd Edition. Wiley, New York.