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Prigogine I., Rice S.A. — Advances in chemical physics. Volume 117
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Íàçâàíèå: Advances in chemical physics. Volume 117Àâòîðû: Prigogine I., Rice S.A. Àííîòàöèÿ: Providing the chemical physics field with a forum for critical, authoritative evaluations in every area of the discipline, the latest volume of Advances in Chemical Physics continues to provide significant, up-to-date chapters written by internationally recognized researchers.
This volume is essentially devoted to helping the reader obtain general information about a wide variety of topics in chemical physics. Advances in Chemical Physics, Volume 117 includes chapters addressing laser photoelectron spectroscopy, nonadiabatic transitions due to curve crossings, multidimensional raman spectroscopy, birefringence and dielectric relaxation in strong electric fields, and crossover formulae for Kramers Theory of thermally activated escape rates.
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Integral representation, relaxation time, linear response 465—468 Interaction-induced scattering, coherent anti-Stokes Raman scattering (CARS), intermolecular vibrations 245—246 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, axial/nonaxial symmetric potentials, escape rates 675 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, axial/nonaxial symmetric potentials, escape rates, nonaxial formula divergence for small axial symmetry departures 681—690 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, double well potential bridging formula 650—655 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, double well potential bridging formula, population proof 672—674 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, double well potential bridging formula, Wiener — Hopf Fourier transforms 669—672 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, energy variance proof 663—664 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, ERFC proof 668—669 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, escape rate prefactor, TST expression 632—634 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, Fokker — Planck equation, energy-action, right-hand energy diffusion operator 657—658 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, Fokker — Planck equation, energy-action, variables 634—637 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, Green's function, energy diffusion, proof 659—663 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, Green's function, energy diffusion, variables 638—639 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, integral formula for prefactor A 646—650 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, integral formula for prefactor A, radial convergence proof 665—667 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, integral formula for prefactor A, series expression of convergence 667—668 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, magnetic relaxation applications 656—657 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, metastable decay rate, whole damping range 655—656 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, particle crossover 631—632 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, single oscillation expression 658—659 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, Wiener — Hopf solution, energy distribution function distribution equation 639—646 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, crossover functions, Wiener — Hopf solution, energy distribution function distribution equation, Fourier transform proofs 664—665 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, escape rate, validity 497—501 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, extension to 579—581 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation 522—531 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, linearized solution 524—527 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, potential barrier summit, linearization near 523—524 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, range of validity 549—561 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, range of validity, alternative derivation 552—555 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, range of validity, damping regimes 550—551 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, range of validity, linearized solution 527 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, range of validity, numerical interpretation 551 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, range of validity, small viscosity alternative 556—561 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, range of validity, Smoluchowski equation derivation 555—556 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, range of validity, vanishing friction limit 549 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Klein — Kramers equation, reaction rate calculations 529—531 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Langer's method 581—588 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, Langer's method, Kramers' formula by 588—593 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, magnetic spins 593—598 Intermediate-to-high damping (IHD) regimes, Kramers reaction rate theory, rotational Brownian motion, axial symmetry, magnetocrystalline anisotropy 570—575 Intermediate-to-high damping (IHD) regimes, reaction rate theory 489—490 Intermolecular vibrations, coherent anti-Stokes Raman scattering (CARS) 243—246 Intermolecular vibrations, fifth-order Raman spectroscopy 261—264 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, axial symmetry calculation 715—716 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, crossover function proof 717—718 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, divergence of escape rates 706—709 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, crossover high damping formulas 690—694 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, IHD divergence for small departures 681—690 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, notation 675—681 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, theoretical background 674—675 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, VLD limit applications 694—706 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, VLD limit applications, energy diffusion method 695—698 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, VLD limit applications, uniaxial perturbations 703—706 725—740 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, VLD limit applications, uniaxial/LD crossovers 698—703 718—725 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, kinetic equation derivations 710—712 Interpolation formulas, Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, partition function, steepest descent evaluation 712—715 Intramolecular vibrations, coherent anti-Stokes Raman scattering (CARS) 237—243 Intramolecular vibrations, fifth-order Raman spectroscopy 264—265 Intramolecular vibrations, Raman-echo spectroscopy, liquid molecules 252—256 Intuitive derivation, Klein — Kramers equation, heat-bath systems 510—511 Ion internal energies, molecular excited states, resonance-enhanced multiphoton ionization (REMP1) spectroscopy 5—8 Ionization threshold, molecular excited states, resonance-enhanced multiphoton ionization (REMPI) spectroscopy 4—8 Isavnin, A.G. 448(128) 481 Ischenko, V.V. 578(107) 759(107) 765 Isotropic correlation function, coherent anti-Stokes Raman scattering (CARS), intramolecular vibrations 242—243 Isserlis's theorem, Kramers reaction rate theory, Klein — Kramers derivation, Langevin equation 510 Isserlis's theorem, Kramers reaction rate theory, Klein — Kramers equation, Kramers' derivation 512—513 Isserlis's theorem, Kramers reaction rate theory, Langevin/Fokker — Planck equations 494—497 Ito, K. 32(106) 120 Ito, M. 36(120—121) 38(120—121) 120 Ivanecky, J.H. 257(92) 264(92) 273 Iwata, S. 6(33) 109(33) 113(33) 117 J diffusion model, inertial effects, dielectric and birefringence relaxation 417 J diffusion model, inertial effects, dielectric and birefringence relaxation, dielectric response 425—428 J diffusion model, inertial effects, dielectric and birefringence relaxation, extended rotational diffusion 418—425 J diffusion model, inertial effects, dielectric and birefringence relaxation, spectra and relaxation times 436—439 Jacobian function, Fourier transform calculations 470—472 Jacobian function, inertial effects, dielectric and birefringence relaxation, dielectric response 426—428 Jacobian function, inertial effects, dielectric and birefringence relaxation, free rotational motion 421—425 Jacobian function, Kramers reaction rate theory, intermediate-to-high damping (IHD) limit, particle current calculations 587 602—606 Jadray, R. 125 Jadzyn, J. 289(43—44) 373(43—44) 462(43—44 136—137) 478 481 Janssen, M.H.M. 83(204) 123 Jeans, H.J. 490(9) 762 Jedju, T.M. 251(31) 271 Jefferson, A. 72(198) 79(198) 122 Jennings, D.E. 59(149) 121 Jet-cooling techniques, ammonia molecules 99—105 Joens, J.A. 94(255) 124 Johnson, D.R. 71(189) 122 Johnson, R.D. III 59(155 158) 66(155) 101(283) 121 125 Joly, A.G. 257(50) 272 Jonathan, N. 43(141—142) 71(166) 74(166) 76(200) 81(166) 121—123 Jones, W.E. 71—72(184) 77(184) 122 Joo, T. 236(4—5) 270 Joos, G. 490(11) 505(11) 510(11) 762 Jordanides, X.J. 257(69) 261(69) 272 Julienne, P.S. 158(83) 233 Jung, P. 374(81) 396(81) 399(81) 401(81) 479 761—762(97) 765 Jungen, C. 42(134) 84(210—212) 121 123 Jungen, M. 93(249) 124 Jurza, A.S. 86(232) 94(232) 123 Kabler, M.N. 132(54) 232 Kac, M. 759(94) 765 Kachachi, H. 674(86) 764 Kachru, R. 10(69 81—82) 119 260(93) 273 Kaellberg, A. 10(63) 119 Kai, Y. 244(14) 271 Kakar, R.K. 71—72(183) 122 Kalmykov, Yu.P. 277(7—8) 278(8) 283(31—33) 286—287(1) 288(40) 295(8 31) 296(55—56) 297(8) 299(59) 300(8 56) 301—302(59) 304—307(8) 309(31—32) 311(31) 316(31 33) 318(55) 319(64) 321(55 65—66) 327(32) 328(64) 331(8 31) 333(31) 337(8 31) 338(8) 340(31) 347(70) 349—352(70) 353(8 70) 355(70) 358(73) 360(75—76) 367(75—76) 373(77—78) 383(82—83) 405(95) 408(95) 416(8) 417(99 107—108) 420—421(108) 424(108) 426—427(108) 433—434(108) 437(40) 438(108) 439(7 113) 440—442(121) 444—445(121) 446(7—8 121) 448(130—133) 449(132) 451—452(130) 454(32) 455(65) 459(64—65 134—135) 460(8) 463(8) 473(121) 475(121) 477—481 488—489(5) 491(5) 492(36) 493—495(5) 501(36) 502(39) 505(5) 509—512(5) 515(39) 521—522(5) 528(5) 547(5) 554(5) 563(5) 565(5 39) 566(5 51 57) 568(36) 569(36 39) 571(5 53) 578(5 57 60) 579(5 39 67) 612(5) 622(5) 626(36) 629(5) 742—743(5) 745(5) 749—750(5) 752(5 67) 753(5 54) 754(5) 755(5 54) 760(95) 761(5 36) 762—765 Kalpouzos, C. 257(56) 272 Kameta, K. 32(105—106) 120 Kami, Y. 133(70) 232 Kang, T.J. 252(40) 271 Karlsson, L. 84(205) 123 125 Kasprowicz-Kielich, B. 286(38) 309(38) 402(91) 478 480 Katayama, I. 10(61) 119 Katsumata, S. 6(33) 109(33) 113(33) 117 Kaufman, L.J. 257(70) 262(70 98) 263(98) 265—266(98) 272—273 Kawaguchi, K. 93(238) 124 Kawasaki, M. 72(192) 96—97(260) 122 124 Kayanuma, Y. 132(55) 232 Kedziora, P. 289(43—44) 373(43—44) 462(43—44 136—137) 478 481 Kendall, D.J.W. 35(112) 120 Kennedy, E.C. 489(59 70) 503(70) 566(52) 574(59) 613(70) 624—626(70) 656(70) 674(52 86) 675—676(70) 678(70) 684(70) 690(70) 694—695(70) 702(70) 707(52) 763—764 Kenney-Wallace, G.A. 257(56) 272 Kenyon, G.L. 125 Keogh, G. 257(61) 261(61) 272 Kerr effect relaxation, dynamic Kerr effect, linear response theory, weak ac electric field steady-state response superimposed on dc bias field 349 Kerr effect relaxation, inertial effects, dielectric and birefringence relaxation, linear response 428—429 468—472 Kerr effect relaxation, molecular hyperpolarizability, linear ac response and aftereffect solution 412—416 Kerr effect relaxation, molecular hyperpolarizability, nonlinear step-on responses 401—412 Kerr effect relaxation, nonlinear Brownian relaxation, strong electric fields, superimposed ac/dc electric fields, polar and polarizable molecules 383—394 Keyes, T. 245(15 20) 257(88) 260(20 94—95) 271 273 Khidekel, V. 257(72) 272 Kielich, S. 401(86) 402(91) 480 Kikuchi, K. 282—283(20) 289(20) 346—347(20) 478 Kilson — Storer model, inertial effects, dielectric and birefringence relaxation 416—417 Kim, D. 283(34) 403(34) 478 Kim, S.K. 257(57) 272 Kimura, K. 3(7—8) 6(33) 109(33) 113(33) 117 Kinematic relation, Kramers reaction rate theory, rotational Brownian motion, dielectric relaxation 566—569 King, G.W. 84(217) 89(217) 123 Kinoshita, S. 244(14) 271 Kirkwood, J.C. 261(96) 266(96 106—107 111 113—114) 273 Kitchenham, R. 257(55) 272 Kivelson, D. 245(15 21) 254(45) 271 Klee, S. 40(131) 121 Klein — Kramers equation, Kramers reaction rate theory 505—512 Klein — Kramers equation, Kramers reaction rate theory, axial/nonaxial symmetric potentials, escape rates 680—681 Klein — Kramers equation, Kramers reaction rate theory, drift and diffusion coefficients 511—512 Klein — Kramers equation, Kramers reaction rate theory, escape rate validity 498—501 Klein — Kramers equation, Kramers reaction rate theory, heat bath effect 510—511 Klein — Kramers equation, Kramers reaction rate theory, IHD limit 522—531 Klein — Kramers equation, Kramers reaction rate theory, IHD limit, linearized solution 524—527 Klein — Kramers equation, Kramers reaction rate theory, IHD limit, potential barrier summit, linearization near 523—524 Klein — Kramers equation, Kramers reaction rate theory, IHD/VLD validity ranges 549—561 Klein — Kramers equation, Kramers reaction rate theory, IHD/VLD validity ranges, alternative Klein — Kramers derivation 552—555 Klein — Kramers equation, Kramers reaction rate theory, IHD/VLD validity ranges, numerical verification 551 Klein — Kramers equation, Kramers reaction rate theory, IHD/VLD validity ranges, small viscosity treatment 556—561 Klein — Kramers equation, Kramers reaction rate theory, IHD/VLD validity ranges, Smoluchowski equation 555—556 Klein — Kramers equation, Kramers reaction rate theory, IHD/VLD validity ranges, vanishing friction limit 549 Klein — Kramers equation, Kramers' derivation 512—522 Klein — Kramers equation, Kramers' derivation, Maxwellian velocity distribution 520—522 Klein — Kramers equation, Kramers' derivation, mean and mean square changes, Brownian momentum 513—516 Klein — Kramers equation, Kramers' derivation, state space probability density 516—520 Klein — Kramers equation, Langevin equation, single degree of freedom 509—510 Klein — Kramers equation, Langevin/Fokker — Planck equations 495—497 Klein — Kramers equation, large viscosity case 543—548 Klein — Kramers equation, large viscosity case, Smoluchowski equation 544—549 Klein — Kramers equation, large viscosity case, very high damping regime 543—544 Klein — Kramers equation, Liouville equation 505—508 Klein — Kramers equation, Liouville equation, reduction and generalization 508—509 Klein — Kramers equation, small viscosity case 531—543 Klein — Kramers equation, small viscosity case, energy-phase variables 532—535 Klein — Kramers equation, small viscosity case, first passage time approach 541—543 Klein — Kramers equation, small viscosity case, low-damping regime 531 Klein — Kramers equation, small viscosity case, phase variable averaging 535—538 Klein — Kramers equation, small viscosity case, very low damping escape rate 538—541 Klein, O. 491(20) 762 Kleman, B. 84(209) 97(209) 123 Kleppner, D. 182(96) 233 Klik, I. 604(64) 580—581(64 72) 593—594(64 72) 595(64) 596(64 72) 613—614(64 72) 615(64) 617—618(64 72) 622(64 76) 626(64 72) 629(64) 694(64 72) 764 Knapp, E.W. 254(48) 272 Knoll, L. 10(60) 19(60) 21(60) 119 Knowles, P.J. 93(245) 124 Koenders, B.G. 5(16) 8(16) 117 Kohler, B. 257(50 52) 272 Kollman, P.A. 125 Kolmogorov equation, Kramers reaction rate theory, low-damping (LD) regime, escape rate calculations, adjoint Fokker — Planck operator, differential equation 613—617 Kolmogorov equation, Kramers reaction rate theory, rigid Brownian rotator escape times, bistable potential, Green function time evolution, integral escape time expression 743—745 Kolmogorov equation, Kramers reaction rate theory, rotational Brownian motion, axial symmetry, magnetocrystalline anisotropy 575 Kolmogorov equation, Kramers reaction rate theory, rotational Brownian motion, mean first passage times (MFPT) escape rate calculation 575—578 Koningstein, J.A. 236(6) 243(6) 270 Kono, M. 99(273) 125 Konstantaki, M. 84(225) 89(225) 92(225) 123 Koopmans, M.P. 36—37(118) 39—40(118) 120 Kopp, I. 94(256) 124 Korenblit, I.Ya. 211(97) 233 Kotlar, A.J. 59(147) 121 Kouchi, N. 30(100) 32(105—106) 120 Kovac, B. 94(251) 124 Kozich, V. 266(116—117) 273 Kramers flux over barrier method, rotational Brownian motion, axial symmetry, magnetocrystalline anisotropy 575 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, axial symmetry calculation 715—716 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, crossover function proof 717—718 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, divergence of escape rates 706—709 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, crossover high damping formulas 690—694 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, IHD divergence for small departures 681—690 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, notation 675—681 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, theoretical background 674—675 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, VLD limit applications 694—706 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, VLD limit applications, energy diffusion method 695—698 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, VLD limit applications, uniaxial perturbations 703—706 725—740 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, interpolation formulas, VLD limit applications, uniaxial/LD crossovers 698—703 718—725 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, kinetic equation derivations 710—712 Kramers reaction rate theory, axial/nonaxial symmetric potential escape rates, single domain ferromagnetic particles, partition function, steepest descent evaluation 712—715 Kramers reaction rate theory, Brownian motion 490—493 Kramers reaction rate theory, Brownian motion, rotational Brownian motion 501—504 Kramers reaction rate theory, Brownian motion, rotational Brownian motion, dielectric relaxation 566—569 Kramers reaction rate theory, Brownian motion, rotational Brownian motion, integral relaxation time 578—579 Kramers reaction rate theory, Brownian motion, rotational Brownian motion, magnetic relaxation, single-domain ferromagnetic particles 561—566 Kramers reaction rate theory, Brownian motion, rotational Brownian motion, magnetocrystalline anisotropy, axially symmetric potentials 570—575 Kramers reaction rate theory, Brownian motion, rotational Brownian motion, mean first passage time escape rate calculation 575—578 Kramers reaction rate theory, crossover of VLD/IHD regimes, double well potential bridging formula 650—655 Kramers reaction rate theory, crossover of VLD/IHD regimes, double well potential bridging formula, population proof 672—674 Kramers reaction rate theory, crossover of VLD/IHD regimes, double well potential bridging formula, Wiener — Hopf Fourier transforms 669—672 Kramers reaction rate theory, crossover of VLD/IHD regimes, energy variance proof 663—664 Kramers reaction rate theory, crossover of VLD/IHD regimes, ERFC proof 668—669 Kramers reaction rate theory, crossover of VLD/IHD regimes, escape rate prefactor, TST expression 632—634 Kramers reaction rate theory, crossover of VLD/IHD regimes, Fokker — Planck equation, energy-action variable, right-hand energy diffusion operator 657—658 Kramers reaction rate theory, crossover of VLD/IHD regimes, Fokker — Planck equation, energy-action variables 634—637 Kramers reaction rate theory, crossover of VLD/IHD regimes, Green's function, energy diffusion, proof 659—663 Kramers reaction rate theory, crossover of VLD/IHD regimes, Green's function, energy diffusion, variables 638—639 Kramers reaction rate theory, crossover of VLD/IHD regimes, integral formula for prefactor A 646—650 Kramers reaction rate theory, crossover of VLD/IHD regimes, integral formula for prefactor A, radial convergence proof 665—667 Kramers reaction rate theory, crossover of VLD/IHD regimes, integral formula for prefactor A, series expression of convergence 667—668 Kramers reaction rate theory, crossover of VLD/IHD regimes, magnetic relaxation applications 656—657 Kramers reaction rate theory, crossover of VLD/IHD regimes, metastable decay rate, whole damping range 655—656 Kramers reaction rate theory, crossover of VLD/IHD regimes, particle crossover 631—632 Kramers reaction rate theory, crossover of VLD/IHD regimes, single oscillation expression 658—659 Kramers reaction rate theory, crossover of VLD/IHD regimes, Wiener — Hopf solution, energy distribution function distribution equation 639—646 Kramers reaction rate theory, crossover of VLD/IHD regimes, Wiener — Hopf solution, energy distribution function distribution equation, Fourier transform proofs 664—665 Kramers reaction rate theory, current of particles, proof for 600—606 Kramers reaction rate theory, eigenvalue problem, proof and matrix 598—600 Kramers reaction rate theory, escape rate formulas, validity range 497—501 Kramers reaction rate theory, Fokker — Planck equation 493—497 Kramers reaction rate theory, inertial effects, dielectric and birefringence relaxation, spectra and relaxation times 435—439 Kramers reaction rate theory, integral over current density, proof of evaluation 607—608 Kramers reaction rate theory, intermediate-to-high damping (IHD) limit, extension to 579—581 Kramers reaction rate theory, intermediate-to-high damping (IHD) limit, extension to, Kramers' formula by Langer's method 588—593 Kramers reaction rate theory, intermediate-to-high damping (IHD) limit, extension to, Langer's treatment of 581—588 Kramers reaction rate theory, intermediate-to-high damping (IHD) limit, extension to, magnetic spins 593—598 Kramers reaction rate theory, Klein — Kramers equation, derivation 505—512 Kramers reaction rate theory, Klein — Kramers equation, derivation, drift and diffusion coefficients 511—512 Kramers reaction rate theory, Klein — Kramers equation, derivation, heat bath effect 510—511 Kramers reaction rate theory, Klein — Kramers equation, derivation, IHD limit 522—531 Kramers reaction rate theory, Klein — Kramers equation, derivation, IHD limit, linearized solution 524—527 Kramers reaction rate theory, Klein — Kramers equation, derivation, IHD limit, potential barrier summit, linearization near 523—524 Kramers reaction rate theory, Klein — Kramers equation, derivation, IHD/VLD validity ranges 549—561 Kramers reaction rate theory, Klein — Kramers equation, derivation, IHD/VLD validity ranges, alternative Klein — Kramers derivation 552—555 Kramers reaction rate theory, Klein — Kramers equation, derivation, IHD/VLD validity ranges, numerical verification 551 Kramers reaction rate theory, Klein — Kramers equation, derivation, IHD/VLD validity ranges, small viscosity treatment 556—561 Kramers reaction rate theory, Klein — Kramers equation, derivation, IHD/VLD validity ranges, Smoluchowski equation 555—556 Kramers reaction rate theory, Klein — Kramers equation, derivation, IHD/VLD validity ranges, vanishing friction limit 549 Kramers reaction rate theory, Klein — Kramers equation, derivation, Kramers' derivation 512—522 Kramers reaction rate theory, Klein — Kramers equation, derivation, Kramers' derivation, Maxwellian velocity distribution 520—522 Kramers reaction rate theory, Klein — Kramers equation, derivation, Kramers' derivation, mean and mean square changes, Brownian momentum 513—516 Kramers reaction rate theory, Klein — Kramers equation, derivation, Kramers' derivation, state space probability density 516—520 Kramers reaction rate theory, Klein — Kramers equation, derivation, Langevin equation, single degree of freedom 509—510 Kramers reaction rate theory, Klein — Kramers equation, derivation, large viscosity case 543—548 Kramers reaction rate theory, Klein — Kramers equation, derivation, large viscosity case, Smoluchowski equation 544—549 Kramers reaction rate theory, Klein — Kramers equation, derivation, large viscosity case, very high damping regime 543—544 Kramers reaction rate theory, Klein — Kramers equation, derivation, Liouville equation 505—508 Kramers reaction rate theory, Klein — Kramers equation, derivation, Liouville equation, reduction and generalization 508—509 Kramers reaction rate theory, Klein — Kramers equation, derivation, small viscosity case 531—543 Kramers reaction rate theory, Klein — Kramers equation, derivation, small viscosity case, energy-phase variables 532—535 Kramers reaction rate theory, Klein — Kramers equation, derivation, small viscosity case, first passage time approach 541—543 Kramers reaction rate theory, Klein — Kramers equation, derivation, small viscosity case, low-damping regime 531 Kramers reaction rate theory, Klein — Kramers equation, derivation, small viscosity case, phase variable averaging 535—538 Kramers reaction rate theory, Klein — Kramers equation, derivation, small viscosity case, very low damping escape rate 538—541 Kramers reaction rate theory, Langevin equation 493—497 Kramers reaction rate theory, low-damping escape rates, first passage time method 610—626 Kramers reaction rate theory, low-damping escape rates, first passage time method, adjoint Fokker — Planck operator and differential equation 613—617 Kramers reaction rate theory, low-damping escape rates, first passage time method, boundary layer approximation 629—630 Kramers reaction rate theory, low-damping escape rates, first passage time method, boundary layer derivation and solution 630—631 Kramers reaction rate theory, low-damping escape rates, first passage time method, line integral, Stokes' expression 619—620 Kramers reaction rate theory, low-damping escape rates, first passage time method, line integral, Stokes' expression, derivation 627—628 Kramers reaction rate theory, low-damping escape rates, first passage time method, stretching transformation 620—623 Kramers reaction rate theory, low-damping escape rates, first passage time method, uniform asymptotic expression 617—619 Kramers reaction rate theory, low-damping escape rates, first passage time method, weak transverse field rate, evaluation 624—625 Kramers reaction rate theory, mean first passage times (MFPT) 504—505 Kramers reaction rate theory, origins and equations 487—490 Kramers reaction rate theory, rigid Brownian rotator escape rates, bistable potential Green function time evolution, Fokker — Planck equation, zero-frequency limit, delta function orientation distribution 745—749 Kramers reaction rate theory, rigid Brownian rotator escape rates, bistable potential Green function time evolution, Fokker — Planck equation, zero-frequency limit, delta function orientation distribution, integral expression of escape time 743—745 Kramers reaction rate theory, rigid Brownian rotator escape rates, bistable potential Green function time evolution, Fokker — Planck equation, zero-frequency limit, delta function orientation distribution, Kramers reaction rate theory, rigid Brownian rotator escape rates, bistable potential Green function time evolution, Fokker — Planck equation, zero-frequency limit, delta function orientation distribution, uniaxial anisotropy explicit expression 753—758 Kramers reaction rate theory, rigid Brownian rotator escape rates, bistable potential Green function time evolution, Fokker — Planck equation, zero-frequency limit, delta function orientation distribution, principles 741—743 Kramers reaction rate theory, rigid Brownian rotator escape rates, bistable potential Green function time evolution, Fokker — Planck equation, zero-frequency limit, delta function orientation distribution, series expression for summit time 752—753 Kramers reaction rate theory, rigid Brownian rotator escape rates, bistable potential Green function time evolution, Fokker — Planck equation, zero-frequency limit, delta function orientation distribution, zero-frequency limit recurrence relations 749—752
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