Stochastic processes in physics and chemistry / / N.G. van Kampen

• Record Nr.: UNINA9910811350603321
• Autore: Kampen N. G. van
• Pubbl/distr/stampa: Amsterdam ; ; London, : Elsevier, 2007
• ISBN: 1-281-00388-3; 9786611003883; 0-08-047536-1
• Edizione: [3rd ed.]
• Descrizione fisica: 1 online resource (481 p.)
• Collana: North-Holland personal library
• Classificazione: 33.26; 35.05
• Disciplina: 519.202453
• Soggetti: Stochastic processes; Statistical physics; Chemistry, Physical and theoretical - Statistical methods
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Previous ed.: Amsterdam: North-Holland, 1992.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front Cover; Stochastic Processes in Physics and Chemistry; Copyright Page; PREFACE TO THE FIRST EDITION; PREFACE TO THE SECOND EDITION; ABBREVIATED REFERENCES; PREFACE TO THE THIRD EDITION; TABLE OF CONTENTS; Chapter I. STOCHASTIC VARIABLES; 1. Definition; 2. Averages; 3. Multivariate distributions; 4. Addition of stochastic variables; 5. Transformation of variables; 6. The Gaussian distribution; 7. The central limit theorem; Chapter II. RANDOM EVENTS; 1. Definition; 2. The Poisson distribution; 3. Alternative description of random events; 4. The inverse formula; 5. The correlation functions; 6. Waiting times7. Factorial correlation functions; Chapter III. STOCHASTIC PROCESSES; 1. Definition; 2. Stochastic processes in physics; 3. Fourier transformation of stationary processes; 4. The hierarchy of distribution functions; 5. The vibrating string and random fields; 6. Branching processes; Chapter IV. MARKOV PROCESSES; 1. The Markov property; 2. The Chapman-Kolmogorov equation; 3. Stationary Markov processes; 4. The extraction of a subensemble; 5. Markov chains; 6. The decay process; Chapter V. THE MASTER EQUATION; 1. Derivation; 2. The class of W-matrices; 3. The long-time limit; 4. Closed, isolated, physical systems5. The increase of entropy; 6. Proof ; of detailed balance; 7. Expansion in eigenfunctions; 8. The macroscopic equation; 9. The adjoint equation; 10. Other equations related to the master equation; Chapter VI. ONE-STEP PROCESSES; 1. Definition; the Poisson process; 2. Random walk with continuous time; 3. General properties of one-step processes; 4. Examples of linear one-step processes; 5. Natural boundaries; 6. Solution of linear one-step processes with natural boundaries; 7. Artificial boundaries; 8. Artificial boundaries and normal modes; 9. Nonlinear one-step processesChapter VII. CHEMICAL REACTIONS; 1. Kinematics of chemical reactions; 2. Dynamics of chemical reactions; 3. The stationary solution; 4. Open systems; 5. Unimolecular reactions; 6. Collective systems; 7. Composite Markov processes; Chapter VIII. THE FOKKER-PLANCK EQUATION; 1. Introduction; 2. Derivation of the Fokker-Planck equation; 3. Brownian motion; 4. The Rayleigh particle; 5. Application to one-step processes; 6. The multivariate Fokker-PIanck equation; 7. Kramers' equation; Chapter IX. THE LANGEVIN APPROACH; 1. Langevin treatment of Brownian motion; 2. Applications3. Relation to Fokker-Planck equation; 4. The Langevin approach; 5. Discussion of the Itô-Stratonovich dilemma; 6. Non-Gaussian white noise; 7. Colored noise; Chapter X. THE EXPANSION OF THE MASTER EQUATION; 1. Introduction to the expansion; 2. General formulation of the expansion method; 3. The emergence of the macroscopic law; 4. The linear noise approximation; 5. Expansion of a multivariate master equation; 6. Higher orders; Chapter XI. THE DIFFUSION TYPE; 1. Master equations of diffusion type; 2. Diffusion in an external field; 3. Diffusion in an inhomogeneous medium; 4. Muitivariate diffusion equation
• Sommario/riassunto: 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, Sa