Gardiner C.W.W., Haken H. — Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences :: Электронная библиотека попечительского совета мехмата МГУ

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Gardiner C.W.W., Haken H. — Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences

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Название: Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences

Авторы: Gardiner C.W.W., Haken H.

Аннотация:

Handbook of Stochastic Methods covers the foundations of Markov systems, stochastic differential equations, Fokker-Planck equations, approximation methods, chemical master equations, and quantum-mechanical Markov processes. From the reviews: "Extremely well written and informative... clear, complete, and fairly rigorous treatment of a larger number of very basic concepts in stochastic theory." Journal of Quantum Electronics "A first class book." Optica Acta In this second edition extra material has been added with recent progress in stochastic methods taken into account.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Издание: 2nd edition

Год издания: 1997

Количество страниц: 442

Добавлена в каталог: 12.02.2008

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Предметный указатель

Metastability      342
Microscopic reversibility      159
moment      30
Moment generating function      32
Moments and characteristic function      32
Multitime averages in quantum systems      394
Multivariate master equation      303
Multivariate master equation for diffusing system      307 308
Natural boundary for FPE      122
Noise      11
Nonanticipating function, defined      86
Nonlinear absorber      415
Nyquist’s formula      163
Nyquist’s theorem      18 20
Omstein — Uhlenbeck process      74—77
Omstein — Uhlenbeck process and Onsager relations      160
Omstein — Uhlenbeck process and quantum harmonic oscillator      396
Omstein — Uhlenbeck process in small noise expansion of SDE      181
Omstein — Uhlenbeck process, complex, defined      410
Omstein — Uhlenbeck process, eigenfunctions      134
Omstein — Uhlenbeck process, existence theorems for      411—415
Omstein — Uhlenbeck process, exit time from a circle      171
Omstein — Uhlenbeck process, FPE from      396 415
Omstein — Uhlenbeck process, generalised      408 419
Omstein — Uhlenbeck process, generalised, defined      409
Omstein — Uhlenbeck process, multivariate      109 111
Omstein — Uhlenbeck process, Oscillator, noisy      105
Omstein — Uhlenbeck process, spectrum matrix      111
Omstein — Uhlenbeck process, stationary distribution      126
Omstein — Uhlenbeck process, stationary variance      110
Omstein — Uhlenbeck process, stationary variance in two dimensions      110
Omstein — Uhlenbeck process, time correlation function      76
Omstein — Uhlenbeck process, time correlation matrix in stationary state      111
Omstein — Uhlenbeck process, time dependent      115
Onsager relations      160—165
Operator correspondences in Glauber — Sudarshan P-representation      383
Operator identities for complex P-representation      414
Operator identities for positive P-representation      414—415
Ornstein — Uhlenbeck process (SDE)      106—107
Pauli matrices, defined      399
Phase space master equation      331 341
Phase transition, second order in reaction diffusion system      324
Phenomenological flux      162
Phenomenological force      161
Poisson distribution      13 14 38—39
Poisson distribution and coherent states      379
Poisson distribution relaxation in reaction diffusion system      316—318
Poisson process      13 72—75
Poisson representation      235 277— 301
Poisson representation and Boltzmann master equation      338 341
Poisson representation and time correlation functions      289—294
Poisson representation and unimolecular reactions      279
Poisson representation and unimolecular reactions in reaction diffusion system      314—315
Poisson representation and unimolecular reactions positive, defined      285—289
Poisson representation and unimolecular reactions real, defined      282
Poisson representation and unimolecular reactions, complex, defined      282
Poisson representation and unimolecular reactions, relation to generalised P-representation      413
Poissonian time dependent solutions of certain master equations      241
Positive P-representation, defined      410
Positive P-representation, FPE from      416—418
Positive P-representation, operator identities for      414—415
Potential barrier, escape over      138— 141
Potential conditions for FPE in complex P-representation      418—419
Potential conditions for many-variable FPE      146
Potential solution of one-variable FPE      124
Prey-predator system      8
Prey-predator system, chemical FPE for      268 273
probability      22
Probability a priori      23
Probability axioms      22
Probability current; defined      119
probability density      28
Probability, conditional      25
Probability, joint      24
Projection operator in adiabatic elimination      198
q-representation      409
Quantum characteristic function      386—388
Quantum Liouville equation      382
Quantum Markov process, derivation of      388—394
Quantum Markov process, time correlation functions in      402 408
Quantum master equation defined      394
Quantum master for harmonic oscillator      395 399
Quantum master, derivation of      390—394
Quantum mechanics of harmonic oscillator      373
Quantum regression theorem      404 405
Quantum regression theorem, P-representation      409
Random telegraph process      77 79
Random telegraph process and driven atom      402
Random variable      24
Random variable, Gaussian      36
Random variables independent      27
Random walk      70—73
Random walk, approximation by FPE      247
Rayleigh process      144 147
Rayleigh process, eigenfunctions      135
Reaction diffusion chemical equation      305
Reaction diffusion master equation; defined      313

Reaction diffusion system      303
Reaction diffusion system in Poisson representation      314
Reaction diffusion system, fluctuating partial differential equations      313
Reaction diffusion systems, divergence problems      327
Reflecting boundary condition for backward FPE      129
Regression theorem      65
Regression theorem, quantum      404 405
Relaxation time, dependence on peak populations      352
Sample path, continuous      5 45—47
Scaling assumption in approximation of master equation      246
Schrodinger’s equation      374
SDE      (see “Stochastic differential equation”)
Separatrix      361 372
Set of events      21
Sets of probability zero      29
Shot noise      12
Sigma algebra      22
Slave noisy      226
Slave noisy, silent      225
Slaving principle      197
Small noise expansion for SDE      180—187
Small noise expansion of FPE      187—194
Smoluchowski equation      197
Smoluchowski equation and escape problem      369
Smoluchowski equation for diffusion in a double well      349
Smoluchowski equation, boundary conditions      205
Smoluchowski equation, corrected      209
Smoluchowski equation, corrections to      206—210
Smoluchowski equation, defined      197 203
Spatial correlations      315—328
Spectrum      16
Spectrum matrix and eigenfunctions      169
Spectrum matrix with detailed balance      150
Spectrum of Omstein — Uhlenbeck process      111
Spectrum, flat      19
Splitting probability in double well potential      345
Standard deviation      30
Stationary      18
Stationary distribution of FPE, asymptotic method for      194
Stationary Markov process, defined      56
Stationary process, approach to      61 63
Stationary solutions, many-variable FPE      146—148
Stationary systems      17
Statistical mechanics      6
Stochastic differential equation      5 7 14 15 80—115
Stochastic differential equation and positive Poisson re      287 289
Stochastic differential equation as limit of nonwhite process      210—218
Stochastic differential equation, connection with FPE      96
Stochastic differential equation, definition and properties of      92—102
Stochastic differential equation, dependence of solutions on initial conditions      101
Stochastic differential equation, dependence of solutions on parameters      101
Stochastic differential equation, partial      305
Stochastic differential equation, small noise expansion for      180—187
Stochastic integral, defined      83
Stochastic partial differential equation      305
Stochastic process, defined      42
Stochastic process, separable      42
Stratonovich      86
Stratonovich SDE as limit of nonwhite process      210—218
Stratonovich stochastic integral      86
System size      235
System size expansion and critical fluctuations      255
System size expansion and critical fluctuations and Kramers — Moyal expansion      251
System size expansion and critical fluctuations and Kurtz’s theorem      254
System size expansion and critical fluctuations in birth-death master equation      266
System size expansion and critical fluctuations in Boltzmann master equation      337 340
System size expansion and critical fluctuations of master equation      250—257
Third-order noise      295
Third-order noise, defined      299—300
Time correlation function      (see “Autocorrelation function”)
Time correlation functions and P-representation      405 408
Time correlation functions and quantum harmonic oscillator      405 408
Time correlation functions for two-level atom      408
Time correlation functions in quantum Markov processes      402 408
Time reversal invariance      150
Transition probability      10
Trimolecular reaction as a limit of bimolecular reaction      294 299
Two-level atom driven      399 402
Two-level atom driven, time correlations      408
Unimolecular reactions in Poisson representation      279
Unstable state, decay from      347
Van Kampen’s system size expansion      250
Variance      30
Variational principle for eigenfunctions of FPE      168
viscosity      6
Volterra-Lotka system      (see also “Prey-predator system”)
von Neumann’s equation      382
White noise      19—20 80—83
White noise as limit of nonwhite process      210—218
Wiener process      46 47 67—70
Wiener process as limit of random walk      72
Wiener process, autocorrelation function      70
Wiener process, eigenfunctions      132
Wiener process, independence of increments      69
Wiener process, irregularity of sample paths      68
Wiener process, nondifferentiability of sample paths      68
Wiener — Khinchin theorem      17
Wigner representation      409

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