Generalization of the classical Kramers rate for non-Markovian open systems out of equilibrium

Journal of Mathematical Physics

Volumn 49, Issue 1, 2008, Pages

  Bolivar, A O ^a  

^a Instituto Mário Schönberg   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38849195516     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2825841     Document Type: Article

References (23)

1. H. A. Kramers, Physica (Amsterdam) PHYSAG 0031-8914 10.1016/S0031- 8914(40)90098-2 7, 284 (1940); S. Chandrasekhar, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.15.1 15, 1 (1943).
2. T. Fonseca, J. A. N. F. Gomes, P. Grigolini, and F. Marchesoni, Adv. Chem. Phys. ADCPAA 0065-2385 10.1002/9780470142868.ch9 63, 389 (1985); P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.62.251 62, 251 (1990).
3. Ber. Bunsenges. Phys. Chem. BBPCAX 0005-9021 95 (3) (1991) special issue on rate processes in dissipative systems: 50 years after Kramers; Activated Barrier Crossing: Applications in Physics, Chemistry, and Biology, edited by, G. R. Fleming, and, P. Hänggi, (World Scientific, Singapore, 1993); New Trends in Kramers' Reaction Rate Theory, edited by, P. Talkner, and, P. Hänggi, (Kluwer, Dordrecht, 1995); K. L. Sebastian and A. K. R. Paul, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.927 62, 927 (2000); P. Reimann, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(01)00081-3 361, 57 (2002).
4. P. Hänggi and F. Marchesoni, Chaos CHAOEH 1054-1500 10.1063/1.1895505 15, 026101 (2005) and references therein.
5. A. O. Bolivar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94. 026807 94, 026807 (2005).
6. A. Adelman, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.431961 64, 124 (1976); R. M. Mazo, in Stochastic Processes in Nonequilibrium Systems, Lecture Notes in Physics Vol. 84, edited by, L. Garrido, P. Segler, and, P. J. Shepherd, (Springer-Verlag, Berlin, 1978); P. Hänggi and F. Mojtabai, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.26.1168 26, 1168 (1982); J. R. Chaudhuri, G. Gangopadhyay, and D. S. Ray, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.477174 109, 5565 (1998); S. K. Banik, J. R. Chaudhuri, and D. S. Ray, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.481439 112, 8330 (2000); J. R. Chaudhuri, S. K. Banik, B. C. Bag, and D. S. Ray, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.061111 63, 061111 (2001).
7. P. Hänggi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.26.2996 26, 2996 (1982); P. Hänggi, F. Marchesoni, and P. Grigolini, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01306642 56, 333 (1984).
8. B. Carmeli and A. Nitzan, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.445535 79, 393 (1983); P. Hänggi and U. Weiss, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.29.2265 29, 2265 (1984); T. Hesselroth, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.48.46 48, 46 (1993); P. Talkner and H.-B. Braun, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.454318 88, 7537 (1988); E. Gùrdia, F. Marchesoni, and M. San Miguel, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(84)90343-8 100A, 15 (1984); F. Marchesoni and P. Grigolini, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.444554 78, 6287 (1983); T. Fonseca, J. A. N. F. Gomes, P. Grigolini, and F. Marchesoni, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.446233 79, 3320 (1983).
9. R. F. Grote and J. T. Hynes, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.440485 73, 2715 (1980); J. E. Straub, M. Borkovec, and B. J. Berne, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.449172 83, 3172 (1985); J. E. Straub, M. Borkovec, and B. J. Berne, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.450425 84, 1788 (1986); F. A. Oliveira, Physica A PHYADX 0378-4371 10.1016/S0378-4371(98) 00134-4 257, 128 (1998).
10. M. Marchi, F. Marchesoni, L. Gammaitoni, E. Menichella-Saetta, and S. Santucci, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.3479 54, 3479 (1996); J. Lehmann, P. Reimann, and P. Hänggi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.6282 62, 6282 (2000).
11. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.223 70, 223 (1998).
12. E. Pollak and P. Talkner, Chaos CHAOEH 1054-1500 10.1063/1.1858782 15, 026116 (2005) and references therein.
13. P. Langevin, C. R. Hebd. Seances Acad. Sci. COREAF 0001-4036 146, 530 (1908).
14. R. Zwanzig, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01008729 9, 215 (1973).
15. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
16. H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications, 2nd ed. (Springer, Berlin, 1989).
17. C. W. Gardiner, Handbook of Stochastic Methods: For Physics, Chemistry, and the Natural Sciences (Springer, Berlin, 1985).
18. W. T. Coffey, Yu. P. Kalmikov, and J. T. Waldron, The Langevin Equation (World Scientific, Singapore, 2004).
19. A. O. Bolivar (unpublished).
20. A. O. Bolivar, Quantum-Classical Correspondence: Dynamical Quantization and the Classical Limit (Springer-Verlag, Berlin, 2004).
21. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1963), Vol. 1.
22. A. Kolmogorov, Math. Ann. MAANA3 0025-5831 104, 414 (1931).
23. R. F. Pawula, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.162.186 162, 186 (1967).