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Cited by 6,154stochastic dynamics and bifurcationAdvanced Physical and Chemical Molecular InteractionsStatistical Mechanics and Entropy

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Reaction-rate theory: fifty years after Kramers

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Hänggi, Peter, Talkner, Peter, Borkovec, Michal·1990·Reviews of Modern Physics
DOI 10.1103/revmodphys.62.251
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Abstract

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

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Research works printed but not linked: 111

  1. Abraham, F. F., 1974, Homogeneous Nucleation
  2. Agarwal, G. S., 1974, Quantum Optics, Springer Tracts in Modern Physics Vol. 70
  3. Alberding, N., 1978, Hydrogen in Metals
  4. Alicki, R., 1987, Quantum Dynamical Semigroups and Applications, Lecture Notes in Physics Vol. 286
  5. Andronov, A. A., 1966, Theory of Oscillations
  6. Arrhenius, S., 1889, Z. Phys. Chem. (Leipzig), 4, 226, 10.1515/zpch-1889-0416 · DOI
  7. Bernasconi, J., 1985, Helv. Phys. Acta, 58, 597
  8. Berne, B. J., 1985, Multiple Time Scales
  9. Berne, B. J., 1970, Adv. Chem. Phys., 17, 63
  10. Bernoulli, D., 1732, Commentarii Academiae Scientiarum Imperialis Petropolitanae, 6, 108
  11. Bernoulli, D., 1734, Commentarii Academiae Scientiarum Imperials Petropolitanae, 7, 162
  12. Berry, R. S., 1980, Physical Chemistry
  13. Binder, K., 1986, Topics in Current Physics No. 7
  14. Bohr, A., 1969, Nuclear Structure
  15. Borkovec, M., 1990, J. Chem. Phys.
  16. Caldeira, A. O., Ann. Phys. (N.Y.), 153, 445
  17. Caldeira, A. O., Physica A (Utrecht), 130, 374
  18. Callear, A. B., 1983, Modern Methods in Kinetics, Comprehensive Chemical Kinetics
  19. Careri, G., 1989, Dissipative Quantum Tunneling of Protons on Hydrated Protein Powders
  20. Dmitrenko, I. M., 1985, Fiz. Nizk. Temp., 11, 146
  21. Dogonadze, R. R., 1970, Teor. Eksp. Khim., 6, 298
  22. Farina, J. D., 1981, Optical Bistability I
  23. Feller, W., 1966, Introduction to Probability and Its Application
  24. Fokker, A. D., 1914, Ann. Phys. (Leipzig), 43, 812
  25. Fonseca, T., 1985, Adv. Chem. Phys., 62, 389
  26. Forster, D., 1975, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions, Frontiers in Physics
  27. Glasstone, S., 1941, The Theory of Rate Processes
  28. Goldanskii, V. I., 1959, Dokl. Acad. Nauk SSSR, 124, 1261
  29. Goldanskii, V. I., 1959, Dokl. Acad. Nauk SSSR, 127, 1037
  30. Goldanskii, V. I., 1987, Sov. Sci. Rev. Chem. B, 9, 59
  31. Goldstein, H., 1980, Classical Mechanics
  32. Grabert, H., 1985, SQUID 85
  33. Grabert, H., 1986, Tunneling
  34. Grigolini, P., 1985, Adv. Chem. Phys., 62, 29
  35. Gross, D. H. E., 1980, Deep Inelastic and Fusion Reactions with Heavy Ions, Lecture Notes in Physics No. 117
  36. Haake, F., 1973, Statistical Treatment of Open Systems by Generalized Master Equations, Springer Tracts in Modern Physics Vol. 66
  37. Hynes, J. T., 1988, Discuss. Faraday Soc., 85, 353
  38. Iansiti, M., 1989, APS March Meeting, St. Louis
  39. Iansiti, M., Bull. Am. Phys. Soc., 562
  40. Iansiti, M., Bull. Am. Phys. Soc.
  41. Jauslin, H., 1986, Tunneling
  42. Klein, O., 1922, Ark. Mat. Astron. Fys., 16, 1
  43. Klyatskin, V. I., 1977, Radiofizika, 20, 562
  44. Korshunov, S. E., 1987, Zh. Eksp. Teor. Fiz., 92, 1828
  45. Kubo, R., 1959, Lectures in Theoretical Physics, Boulder
  46. Laidler, K. J., 1987, Chemical Kinetics
  47. Landau, L., 1932, Phys. Z. Sowjetunion, 1, 89
  48. Langer, J. S., 1980, Systems Far from Equilibrium, Lecture Notes in Physics Vol. 132
  49. Larkin, A. I., 1983, Pis'ma Zh. Eksp. Teor. Fiz., 37, 322
  50. Larkin, A. I., 1984, Zh. Eksp. Teor. Fiz., 86, 719
  51. Laue, M., 1918, Jahrb. Radiakt. Elektron., 15, 205
  52. Laue, M., Jahrb. Radiakt. Elektron., 15, 257
  53. Laue, M., Jahrb. Radiakt. Elektron., 15, 301
  54. Lefevre-Seguin, V., 1990, Thermally-Activated Escape of D.C. Squids at 4.2 K: A New Confirmation of the Kramers Theory in Two Dimensions
  55. Lett, P., 1986, Optical Instabilities, Cambridge Studies in Modern Optics Vol. 4
  56. Lewis, G. N., 1925, J. Am. Chem. Soc., 47, 1514
  57. Lichtenberg, A. J., 1983, Appl. Math. Sci.
  58. Mandel, L., 1981, Optical Bistability I
  59. Marchesoni, F., 1990, Pair Production in a φ4-String
  60. Melnikov, V. I., 1984, Zh. Eksp. Teor. Fiz., 87, 663
  61. Melnikov, V. I., 1983, Pis'ma Zh. Eksp. Teor. Fiz., 38, 111
  62. Montroll, E. W., 1958, Adv. Chem. Phys., 1, 361
  63. Moss, F., 1989, Noise in Nonlinear Dynamical Systems
  64. Nikitin, E. E., 1966, Theory of Thermally Induced Gas Phase Reactions
  65. Nikitin, E. E., 1974, Physical Chemistry: An Advanced Treatise
  66. Nitzan, A., 1988, Adv. Chem. Phys., 70, 489
  67. Oppenheimer, J. R., 1928, Phys. Rev., 31, 80
  68. Ornstein, L. S., 1917, Versl. Acad. Amst., 26, 1005
  69. Ornstein, L. S., 1919, Proc. Acad. Amst., 21, 96
  70. Petukhov, B. V., 1972, Zh. Eksp. Teor. Fiz., 63, 634
  71. Pfeifer, P., 1983, Symmetries and Properties of Nonrigid Molecules: A Comprehensive Survey
  72. Pirc, R., 1969, Phys. Kondens. Mater., 9, 377
  73. Planck, M., 1917, Sitzungsber. Preuss. Akad. Wiss., 324
  74. Pollak, E., 1985, Theory of Chemical Reaction Dynamics
  75. Pollak, E., 1990, J. Chem. Phys.
  76. Pontryagin, L. A., 1933, Zh. Eksp. Teor. Fiz., 3, 165
  77. J. B. Barbour, 1989, Noise in Nonlinear Dynamics
  78. Primas, H., 1978, Adv. Chem. Phys., 38, 1
  79. Rayleigh, Lord, 1902, Scientific Papers of Lord Rayleigh
  80. Reimann, P., 1989, Stationary Probability for one-dimensional Discrete Maps disturbed by weak Gaussian Noise
  81. Rice, O. K., 1930, Z. Phys. Chem. Abt. B, 7, 226
  82. Richardson, O. W., 1902, Proc. Cambridge Philos. Soc., 11, 286
  83. Richter, D., 1987, Quantum Aspects of Molecular Motion in Solids
  84. Rips, I., 1990, Phys. Rev. A
  85. Roy, R., 1989, Noise in Nonlinear Dynamical Systems
  86. Sargent, M., 1974, Laser Physics
  87. Sceats, M. G., 1988, Adv. Phys. Chem., 70, 357
  88. Schrödinger E., 1915, Phys. Z., 16, 289
  89. Seeger, A., 1966, Physical Acoustics
  90. Sinha, K., 1972, Helv, Phys. Acta, 45, 619
  91. Smoluchowski, M. V., 1914, Bull. Acad. Cracovie, Classe des sciences mathématiques et naturelles, Serie A, 418
  92. Smoluchowski, M. V., 1915, Ann. Phys. (Leipzig), 48, 1103
  93. Smoluchowski, M. V., 1917, Z. Phys. Chem. (Leipzig), 92, 129
  94. Stiller, W., 1989, Arrhenius Equation and Nonequilibrium Kinetics, Teubner Texte zur Physik Bd. 21
  95. Stillinger, F. H., 1978, Theor. Chem., 3, 178
  96. Stratonovich, R. L., 1963, Topics in the Theory of Random Noise
  97. Stückelberg, E. G. C., 1932, Helv. Phys. Acta, 5, 369
  98. Sussmann, J. A., 1971, Ann. Phys. (Paris), 6, 135
  99. Talkner, P., 1989, Helv. Phys. Acta, 62, 932
  100. Talkner, P., 1983, Noise in Physical Systems and 1f Noise
  101. Tikhonov, V. I., 1960, Avtomatika i Telemekhanika, 21, 301
  102. O. M. Blunn, 1965, Nonlinear Transformations of Stochastic Processes
  103. Troe, J., 1975, Physical Chemistry: An Advanced Treatise
  104. Uhlhorn, U., 1960, Ark. Fys., 17, 361
  105. Van Kampen, N. G., 1976, Adv. Chem. Phys., 34, 245
  106. Velsko, S. P., 1982, J. Chem. Phys., 65, 59
  107. Wardlaw, D. W., 1988, Adv. Chem. Phys., 70, 231
  108. Weiss, G. H., 1983, Adv. Chem. Phys., 32, 363
  109. Weiss, U., 1980, Functional Integration: Theory and Application
  110. Weiss, U., Phys. Lett. A, 104, 492
  111. Zeldovich, Ya. B., 1943, Acta Phys. Chim. USSR, 18, 1

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Metadata

Authors
Hänggi, P., Talkner, P., & Borkovec, M.
Affiliations
University of Augsburg (DE)
ORCID
Borkovec, Michal
Venue
Reviews of Modern Physics
Publisher
American Physical Society (APS)
Published
1990-04-01
Volume
62
Issue
2
Pages
251-341
ISSN
  • 0034-6861 (ISSN-L)
  • 1539-0756
DOI
10.1103/revmodphys.62.251
OpenAlex
W2092144432
Cited by
6,154
References
619
Citations by year
2026: 187 · 2025: 193 · 2024: 200 · 2023: 192 · 2022: 231 · 2021: 248 · 2020: 235 · 2019: 165 · 2018: 213 · 2017: 219 · 2016: 196 · 2015: 209 · 2014: 256 · 2013: 196 · 2012: 222
FWCI
71.83
Type
journal article
Language
en
Open access
Licence
Locations
  • Reviews of Modern Physics (publishedVersion)
  • DORA PSI (Paul Scherrer Institute) (submittedVersion, other-oa)
  • Publication Server of Goethe University Frankfurt am Main (Goethe University Frankfurt) (submittedVersion)
  • OPUS (Augsburg University) (submittedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
Keywords
metastable systems, transition state theory, turnover theory, mean first passage time, driven systems, quantum tunneling, rate constants

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