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
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absorbing boundary approximation autocorrelation function average boundary condition Brownian particle characteristic function chemical reaction coefficients collision compute Consider constant cumulants defined density matrix Derive described detailed balance determined differential equation diffusion dots eigenvalues energy ensemble equilibrium example Exercise expansion explicitly expression factor Find finite fluctuations Fokker–Planck equation Gaussian given Hence independent initial condition initial value integral interval jump Langevin equation limit M-equation macroscopic equation macrostate Markov process Markovian master equation matrix mean first-passage molecules moments N.G. van Kampen nonlinear obeys obtained one-step process operator order Q oscillator photons Phys physical Poisson distribution possible potential probability density probability distribution problem properties Q-expansion quantity random walk result Show solved space stationary distribution stationary solution statistical mechanics stochastic differential equation stochastic process Suppose tion transformation transition probability vanishes variables vector velocity Wiener process write 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.