物理和化學中的隨機過程（第3版） [Stochastic Processes in Physics and Chemistry(Third edition)] epub pdf mobi txt 電子書 下載 2024

物理和化學中的隨機過程（第3版） [Stochastic Processes in Physics and Chemistry(Third edition)] epub pdf mobi txt 電子書 下載 2024

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物理和化學中的隨機過程（第3版） [Stochastic Processes in Physics and Chemistry(Third edition)] epub pdf mobi txt 電子書 下載 2024

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內容簡介

　　Definition、Averages、Multivariate distributions、Addition of stochastic variables、Transformation of variables、The Gaussian distribution、The central limit theorem、Definition、The Poisson distribution、Alternative description of random events、The inverse formula、The correlation functions、Waiting times、Factorial correlation functions等等。

內頁插圖

目錄

PREFACE TO THE FIRST EDITION
PREFACE TO THE SECOND EDITION
ABBREVIATED REFERENCES
PREFACE TO THE THIRD EDITION
1. 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

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 times
7. Factorial correlation functions

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

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

Ⅴ. THE MASTER EQUATION
1. Derivation
2. The class of W-matrices
3. The long-time limit
4. Closed， isolated， physical systems
5. 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

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 processes

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

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-Planck equation
7. Kramers equation

Ⅸ. THE LANGEVIN APPROACH
1. Langevin treatment of Brownian motion
2. Applications
3. Relation to Fokker-Planck equation
4. The Langevin approach
5. Discussion of the It6——Stratonovich dilemma
6. Non-Gaussian white noise
7. Colored noise

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

Ⅺ. THE DIFFUSION TYPE
1. Master equations of diffusion type
2. Diffusion in an external field
3. Diffusion in an inhomogeneous medium
4. Multivariate diffusion equation
5. The limit of zero fluctuations

Ⅻ. FIRST-PASSAGE PROBLEMS
1. The absorbing boundary approach
2. The approach through the adjoint equation-Discrete case
3. The approach through the adjoint equation-Continuous case
4. The renewal approach
5. Boundaries of the Smoluchowski equation
6. First passage of non-Markov processes
7. Markov processes with large jumps

ⅩⅢ. UNSTABLE SYSTEMS
1. The bistable system
2. The escape time
3. Splitting probability
4. Diffusion in more dimensions
5. Critical fluctuations
6. Kramers escape problem
7. Limit cycles and fluctuations.

ⅩⅣ. FLUCTUATIONS IN CONTINUOUS SYSTEMS
1. Introduction
2. Diffusion noise
3. The method of compounding moments
4. Fluctuations in phase space density
5. Fluctuations and the Boltzmann equation
ⅩⅤ. THE STATISTICS OF JUMP EVENTS
1. Basic formulae and a simple example
2. Jump events in nonlinear systems
3. Effect of incident photon statistics
4. Effect of incident photon statistics - continued.

ⅩⅥ. STOCHASTIC DIFFERENTIAL EQUATIONS
1. Definitions
2. Heuristic treatment of multiplicative equations.
3. The cumulant expansion introduced
4. The general cumulant expansion
5. Nonlinear stochastic differential equations
6. Long correlation times

ⅩⅦ. STOCHASTIC BEHAVIOR OF QUANTUM SYSTEMS
1. Quantum probability
2. The damped harmonic oscillator
3. The elimination of the bath
4. The elimination of the bath-continued
5. The Schrodinger-Langevin equation and the quantum master equation
6. A new approach to noise
7. Internal noise
SUBJECT INDEX

精彩書摘

　　A "random number" or "stochastic variable" is an object X defined by
　　a. a set of possible values （called "range", "set of states", "sample space"or "phase space"）;
　　b. a probability distribution over this set.
　　Ad a. The set may be discrete, e.g.: heads or tails; the number of electronsin the conduction band of a semiconductor; the number of molecules of acertain component in a reacting mixture. Or the set may be continuous in agiven interval: one velocity component of a Brownian particle （interval-∞+∞）; the kinetic energy of that particle （0,∞）; the potential differencebetween the end points of an electrical resistance （-∞, +∞）. Finally the setmay be partly discrete, partly continuous, e.g., the energy of an electron inthe presence of binding centers. Moreover the set of states may be multidimen-sional; in this case X is often conveniently written as a vector X. Examples:X may stand for the three velocity components of a Brownian particle; orfor the collection of all numbers of molecules of the various components ina reacting mixture; or the numbers of electrons trapped in the various speciesof impurities in a semiconductor.
　　For simplicity we shall often use the notation for discrete states or for acontinuous one-dimensional range and leave it to the reader to adapt thenotation to other cases.

前言/序言

　　The interest in fluctuations and in the stochastic methods for describing themhas grown enormously in the last few decades.The number of articles scatteredin the literature of various disciplines must run to thousands，and special journalsare devoted to the subject.Yet the physicist or chemist who wants to becomeacquainted with the field cannot easily find a suitable introduction.He reads theseminal articles of Wang and Uhlenbeck and Of Chandrasekhar.which are almostforty years old，and he culls some useful information from the books ofFeller，Bharucha.Reid.Stratonovich，and a few others.Apart from that he is confrontedwith a forbidding mass of mathematical literature.much of which is of littlerelevance to his needs.Tllis book is an attempt to fill this gap in the literature.
　　The first part covets the main points of the classical material.Its aim is to provide physicists and chemists with a coherent and sufficiently complete frame-work，in a language that is familiar to them.A thorough intuitive understandingofthe material is held to be a more important tool for research than mathemat-ical rigor and generality.A physical system at best only approximately flulfillsthe mathematical conditions on which rigorous proofs are built，and a physicistshould be constantly aware of the approximate nature of his calculations.（Forinstance.Kolmogorovs derivation of the Fokke蔔.Planck equation does not tellhim for which actual systems this equation may be used.）Nor is he interestedin the most generai formulations，but a thorough insight in special cases willenablehimto extendthetheorytoother caseswhentheneed arises.Accordinglythe theory is here developed in close connection with numerous applications andexamples.
　　The second part，starting with chapter IX『now chapter Xl，is concerned wimfluctuations in nonlinear systems.This subject involves a number of conceptualdimculties.first pointed out bv D.K.C.MacDonald.They are of a Physical ratherthan a mathematical nature.Much confusion is caused by the still prevailing viewthat nonlinear fluctuations can be approached from the same physical starting point as linear ones and merely require more elaborate mathematics.In actuaifact.what is needed is a firmer physical basis and a more detailed knowledge ofthe physical system than required for the study oflinear noi

物理和化學中的隨機過程（第3版） [Stochastic Processes in Physics and Chemistry(Third edition)] epub pdf mobi txt 電子書 下載 2024

物理和化學中的隨機過程（第3版） [Stochastic Processes in Physics and Chemistry(Third edition)] 下載 epub mobi pdf txt 電子書

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