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物理和化学中的随机过程 第3版 英文版PDF|Epub|txt|kindle电子书版本网盘下载
- （荷）范卡梅伦著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：9787510005695
- 出版时间：2010
- 标注页数：463页
- 文件大小：15MB
- 文件页数：477页
- 主题词：物理学－随机过程－英文；化学－随机过程－英文
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图书目录
Ⅰ．STOCHASTIC VARIABLES1
1．Definition1
2．Averages5
3．Multivariate distributions10
4．Addition of stochastic variables14
5．Transformation of variables17
6．The Gaussian distribution23
7．The central limit theorem26
Ⅱ．RANDOM EVENTS30
1．Definition30
2．The Poisson distribution33
3．Alternative description of random events35
4．The inverse formula40
5．The correlation functions41
6．Waiting times44
7．Factorial correlation functions47
Ⅲ．STOCHASTIC PROCESSES52
1．Definition52
2．Stochastic processes in physics55
3．Fourier transformation of stationary processes58
4．The hierarchy of distribution functions61
5．The vibrating string and random fields64
6．Branching processes69
Ⅳ．MARKOV PROCESSES73
1．The Markov property73
2．The Chapman-Kolmogorov equation78
3．Stationary Markov processes81
4．The extraction of a subensemble86
5．Markov chains89
6．The decay process93
Ⅴ．THE MASTER EQUATION96
1．Derivation96
2．The class of W-matrices100
3．The long-time limit104
4．Closed,isolated,physical systems108
5．The increase of entropy111
6．Proof of detailed balance114
7．Expansion in eigenfunctions117
8．The macroscopic equation122
9．The adjoint equation127
10．Other equations related to the master equation129
Ⅵ．ONE-STEP PROCESSES134
1．Definition;the Poisson process134
2．Random walk with continuous time136
3．General properties of one-step processes139
4．Examples of linear one-step processes143
5．Natural boundaries147
6．Solution of linear one-step processes with natural boundaries149
7．Artificial boundaries153
8．Artificial boundaries and normal modes157
9．Nonlinear one-step processes161
Ⅶ．CHEMICAL REACTIONS166
1．Kinematics of chemical reactions166
2．Dynamics of chemical reactions171
3．The stationary solution173
4．Open systems176
5．Unimolecular reactions178
6．Collective systems182
7．Composite Markov processes186
Ⅷ．THE FOKKER-PLANCK EQUATION1．Introduction193
2．Deritvation of the Fokker-Planck equation197
3．Brownian motion200
4．The Rayleigh particle204
5．Application to one-step processes207
6．The multivariate Fokker-Planck equation210
7．Kramers' equation215
Ⅸ．THE LANGEVIN APPROACH219
1．Langevin treatment of Brownian motion219
2．Applications221
3．Relation to Fokker-Planck equation224
4．The Langevin approach227
5．Discussion of the It？-Stratonovich dilemma232
6．Non-Gaussian white noise237
7．Colored noise240
Ⅹ．THE EXPANSION OF THE MASTER EQUATION1．Introduction to the expansion244
2．General formulation of the expansion method248
3．The emergence of the macroscopic law254
4．The linear noise approximation258
5．Expansion of a multivariate master equation263
6．Higher orders267
Ⅺ．THE DIFFUSION TYPE273
1．Master equations of diffusion type273
2．Diffusion in an external field276
3．Diffusion in an inhomogeneous medium279
4．Multivariate diffusion equation282
5．The limit of zero fluctuations287
Ⅻ．FIRST-PASSAGE PROBLEMS292
1．The absorbing boundary approach292
2．The approach through the adjoint equation-Discrete case298
3．The approach through the adjoint equation-Continuous case303
4．The renewal approach307
5．Boundaries of the Smoluchowski equation312
6．First passage of non-Markov processes319
7．Markov processes with large jumps322
ⅩⅢ．UNSTABLE SYSTEMS326
1．The bistable system326
2．The escape time333
3．Splitting probability337
4．Diffusion in more dimensions341
5．Critical fluctuations344
6．Kramers' escape problem347
7．Limit cycles and fluctuations355
ⅩⅣ．FLUCTUATIONS IN CONTINUOUS SYSTEMS1．Introduction363
2．Diffusion noise365
3．The method of compounding moments367
4．Fluctuations in phase space density371
5．Fluctuations and the Boltzmann equation374
ⅩⅤ．THE STATISTICS OF JUMP EVENTS1．Basic formulae and a simple example383
2．Jump events in nonlinear systems386
3．Effect of incident photon statistics388
4．Effect of incident photon statistics-continued392
ⅩⅥ．STOCHASTIC DIFFERENTIAL EQUATIONS1．Deftnitions396
2．Heuristic treatment of multiplicative equations399
3．The cumulant expansion introduced405
4．The general cumulant expansion407
5．Nonlinear stochastic differential equations410
6．Long correlation times416
ⅩⅦ．STOCHASTIC BEHAVIOR OF QUANTUM SYSTEMS1．Quantum probability422
2．The damped harmonic oscillator428
3．The elimination of the bath436
4．The elimination of the bath-continued440
5．The Schr？dinger-Langevin equation and the quantum master equation444
6．A new approach to noise449
7．Internal noise451
SUBJECT INDEX457