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Coffey W.T., Kalmykov Yu.P., Waldron J.T. — The Langevin equation
Coffey W.T., Kalmykov Yu.P., Waldron J.T. — The Langevin equation



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Название: The Langevin equation

Авторы: Coffey W.T., Kalmykov Yu.P., Waldron J.T.

Аннотация:

This volume is the second edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the Brownian motion in a potential, with emphasis on modern applications in the natural sciences, electrical engineering and so on. It has been substantially enlarged to cover in a succinct manner a number of new topics, such as anomalous diffusion, continuous time random walks, stochastic resonance etc, which are of major current interest in view of the large number of disparate physical systems exhibiting these phenomena. The book has been written in such a way that all the material should be accessible to an advanced undergraduate or beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of research papers or scattered review articles.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2004

Количество страниц: 704

Добавлена в каталог: 24.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action-angle variables      524
Additive noise      76
After-effect function      163 207
Angular momentum operator      341 379
Anisotropy constant      122 407 490
Anomalous dielectric relaxation      160
Anomalous diffusion      152 617 620 654
Anomalous relaxation      156 601 631
Arrhenius law      86
Associated Legendre functions      381 531
Asymmetric top      378 388
Asymptotic expansion      268 317 255
Autocorrelation function      13 59 206 224 245 270 303
Avogadro's number      16
Axially symmetric potential      397 582
Birefringence      437 443
Blocking temperature      125
Brinkman equations      517 518
Brown's asymptotic formula      136 357 580
Brown's Fokker — Planck equation      131
Brownian fluctuation of a suspended mirror      16
Brownian motion      3 236
Brownian motion in a tilted periodic potential      282
Brownian motion of a free particle      236
Brownian particles      3 4
Cage model      558
Central limit theorem      56
Centred random variable      47 245
Chapman — Kolmogorov equation      69 605
Characteristic function      52
Clebsch — Gordan coefficients      331 332 384 470
Cole — Cole equation      156 651 663
Cole — Cole plots      362 394 652
Complex polarisability      203
Confluent hypergeometric (Kummer) function      246 351 529 635
Continued fractions      201 266 268 291 313 350 351 358 368 372 537 596
Continuity equation      8 31 116 130 624
Continuous time random walk (CTRW)      156 158 600 602 608 609
Correlation coefficient      48 51
Correlation function      59 312 333 346 454 536 563
Correlation time      207 264 268 316 349
Covariance      47
Covariance matrix      51
Crosscorrelation function      59
Cubic anisotropy      132 490
Curie point      126
Current-voltage characteristics      112 290
Debye relaxation time      116 160 331 399 524 581 611
Debye theory of dielectric relaxation      117
Depletion effect      143
Deterministic drift      180 330 381
Dielectric relaxation      113 230 243 436 443
Differential-recurrence relations      177
Diffusion coefficient      19 72 75 601
Diffusion equation      19 92
Dipole moment      121 327 367 437 513
Discrete orientation model      127 500
Discrete time random walk      600
Distribution function      46
Doob's interpretation      171
Drift coefficient      72 76
Dynamic Kerr-effect      112 230
Effective eigenvalue      221 258 293 320 430
Effective eigenvalue method      221 371 429 458
Effective relaxation time      222 256 354 360 373 416 502 617 620
Egg model      577
Einstein's formula      14
Einstein's method      17
EINSTEIN's summation convention      180
Electric polarisation      388 439 655
Energy control diffusion      44
Ensemble average      25 26
Equipartition theorem      25 285
Ergodic hypothesis      26
Error function      214 317 353
Error function of imaginary argument      231 276 353
Escape rate      95
Euler angles      378
Euler — Langevin equation      184 327 378 531 545
Far-infrared absorption      558
Fast Fourier Transform      528
Ferrofluids      141 576 587
Ferromagnetic resonance (FMR)      131 481 487
Fluctuation-dissipation theorem      15 205 665
Fokker — Planck equation      6 68 79 80 116 210 214 229 311 336 343 388 518 544 556 622
Fokker — Planck operator      210 616 623
Forward Kolmogorov equation      9
Fourier — Hermite series      518 634
Fractal      5 670
Fractal dimension      602 670
Fractional derivative      158
Fractional diffusion equation      603
Fractional Klein — Kramers equation      633 641 649 656
Fractional Langevin equation      665
Fundamental solution      85 601 611
Gamma function      158
Gaussian distribution      48 50 608
Gaussian random variable(s)      54 55 245 593
Generalised Langevin equation      665 668
Generalised Mittag-Lefler function      628 666
Gilbert's equation      124 335 337 578
Gordon sum rule      638 651
harmonic oscillator      241
Hermite polynomials      514 518 531
High damping limit      37
Hypergeometric functions      246 270 351
Hysteresis      128
Impedance of the Josephson junction      299
Incoherent scattering of slow neutrons      112
Indicator function      67
Inertial effects      21 244 507 631
Integral exponential function      542 651
Integral relaxation time      207 417 616 620
Intermediate to high damping (IHD)      37 88 91 99
Intertrapping time      160
Isserlis's theorem      13 55 72 591
Itinerant oscillator      557
Ito and Stratonovich rules      171
Ito calculus      175
Ito equation      175
Joint probability distribution      49
Josephson junction      177 282
Josephson radiation      302
Jump length variance      603
Kerr-effect relaxation      112 436
Kinetic theory      4
Klein — Kramers equation      9 35 41 79 633
Koch curve      670
Kramers escape rate theory      85
Kramers transition state theory      86
Kramers — Kronig relations      203
Kramers — Moyal expansion      72 74
Kubo relation      206
Kummer transformation      352 355
Landau — Lifshiftz equation      578
Langer formula      109
Langer's treatment      104
Langevin equation      10 11 60 114 183 186 236 244 253 286 337 509 561 590
Langevin function      121 369
Laplace operator      116 131 330
Legendre polynomials      334 387
Levy distribution      607 611
Levy flight      603 608
Linear impedance      292 298
Linear response theory      201 210
Liouville equation      29 31 34
Locked region      306
Longitudinal correlation time      256 271 349 352 401 410
Longitudinal response      368 407
Longitudinal susceptibility      352 369 401 472 493 582
Low damping (LD)      37 90 99
Magnetic after-effect      121
Magnetic domains      122
Magnetic viscosity      124
Marginal distribution function      50
Markov process      58 63
Mathematica program      290 330 332 417 470
Matrix continued fractions      196 397 401 412 429 439 446 457 476 497 521 541 553 570
Matrix diagonalisation method      191
Matrix recurrence relations      196 397
Maxwell — Boltzmann distribution      25 105 229
Maxwell — Boltzmann law      27
Mean first passage time (MFPT)      622 624 627
Mean square displacements      13 20 36 236
Mean waiting time      603
Method of steepest descents      350
Mittag-Lefler function      161 610 615 622 628 637
Mobility of superionic conductors      112 282
Modified Bessel functions      195 264 289 355 369 403 521 657
Moment generating function      52
Mori theory      566
Multiplicative noise      76 172
Multiplicative noise term      76 287 311 328 381
N-fold cosine potential      252
Neel relaxation      124 128
Neel relaxation time      125 133
Nematic liquid crystals      333 347 450
Noise-induced drift      78 180 186 329 381
Non-axially symmetric potentials      468
Noninertial limit      285
Nonlinear Langevin equation      172 179
Nonlinear response      226 229 436 443 527
Nyquist's Theorem      23 62
Omstein — Fuerth formula      238
Omstein — Uhlenbeck process      82
Omstein — Uhlenbeck theory      236
Onsager model      558 561
Orientational space gradient operator      339 379
Paleomagnetism      126
Parabolic cylinder function      314 518
Partition function      28 146
Phase space      25
Poley absorption      119 557 558 663
Probability density function      47
Probability theory      44
Quantum noise in ring laser gyroscopes      112
Random fractal      5 671
Random process      57
Random variable      46
Random walk      152 600
Realisations      8
Recurrence relations      196
Relaxation      2
Representative point      26
Rice's method      241
Riemann — Liouville definition      160 610
Riemann — Zeta function      269 625 630
Ring laser gyroscope      282 307
Robert Brown      1
Rocard equation      246 538 636 645 651
Rotational Brownian motion      20 113 252 397 530 544
Rotational diffusion      326 378
Saddle point      97 483
Self-similarity      5 608 671
Sharp values      76 173 311 331 382
Single domain particle      121 141
Smallest novanishing eigenvalue      214 224 269 317 354 480 485
Smoluchowski equation      9 83 116 262 441
Smoluchowski integral equation      69 152
Spectral density      60
Spherical harmonics      331
Standard deviation      47 41
Standard normal distribution      48
Stationary process      58 59
Stationary solution      9
Stieltjes integral      67
Stochastic differential equation      13 328
Stochastic process      57
Stochastic resonance      149 421
Stokes's law      20
Stosszahlansatz      7 19 33 153
Stratonovich calculus      183 533 547
Stratonovich definition      174 328 338
Stratonovich equation      175
Sturm — Liouville equation      262 613 614
Subdiffusion      158 602 611 632
Superdiffusion      158 602 608
Superparamagnetism      121
susceptibility      223 352 423 429 472 493 615 618
Symmetric top      383 544
Telegraph equation      639
Theory of angular momentum      341
Time average      27
Torsional oscillator model      247
Trajectory of a Brownian particle      5
Transition probability      69
Transition state theory      85 86
Transverse polarisability      274
Transverse relaxation time      256 274 360
Transverse response      372
Transverse susceptibility      359 373 429 582
Uniaxial potential      136 334 347 407 457
Unlocked region      306
Variance      47
Variance of the Wiener process      64
Weierstrass random walks      608 672
White noise      12
White noise torque      114 243 327 378 531
Wiener integral      66 247
Wiener process      63
Wiener — Khinchine theorem      59 238
Wigner D functions      59 238
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