Thermally activated escape rate for the Brownian motion of a fixed axis rotator in a double well potential for all values of the dissipation

Journal of Chemical Physics

Volumn 120, Issue 19, 2004, Pages 9199-9211

  Coffey, William T ^a   Kalmykov, Yuri P ^b   Titov, Sergey V ^c  

^a TRINITY COLLEGE DUBLIN   (Ireland)

^b UNIVERSITÉ DE PERPIGNAN   (France)

^c INST OF RADIO ENG AND ELECTRONICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; DAMPING; EIGENVALUES AND EIGENFUNCTIONS; EXTRAPOLATION; FERROMAGNETIC MATERIALS; HAMILTONIANS; LIQUID CRYSTALS; MAGNETIC RELAXATION; MATRIX ALGEBRA; OPTICAL KERR EFFECT; ORDINARY DIFFERENTIAL EQUATIONS; OSCILLATORS (MECHANICAL); PROBABILITY DENSITY FUNCTION; QUANTUM THEORY; ROTATION;

FOKKER-PLANCK EQUATIONS (FPE); TRANSITION STATE THEORY (TST); VERY HIGH DAMPING (VHD); VERY LOW DAMPING (VLD);

BROWNIAN MOVEMENT;

EID: 2942560571     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1703525     Document Type: Article

References (51)

1. H. Risken, The Fokker-Planck Equation, 2nd Ed. (Springer, Berlin, 1989).
2. W. T. Coffey, Yu. P. Kalmykov, and J. T. Waldron, The Langevin Equation, 2nd Ed. (World Scientific, Singapore, 2004).
3. G. Barone and A. Paterno, Physics and Applications of the Josephson Effect (Wiley, New York, 1982).
4. Yu. P. Kalmykov, Phys. Rev. E 61, 6320 (2000); 62, 227 (2000).
5. Yu. P. Kalmykov, Phys. Rev. E 61, 6320 (2000); 62, 227 (2000).
6. H. A. Kramers, Physica (Utrecht) 7, 284 (1940).
7. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
8. W. T. Coffey, D. A. Garanin, and D. McCarthy, Adv. Chem. Phys. 117, 528 (2001).
9. V. I. Mel'nikov, Physica A 130, 606 (1985); Phys. Rep. 209, 1 (1991).
10. V. I. Mel'nikov, Physica A 130, 606 (1985); Phys. Rep. 209, 1 (1991).
11. V. I. Mel'nikov and S. V. Meshkov, J. Chem. Phys. 85, 1018 (1986).
12. H. Graben, Phys. Rev. Lett. 61, 1683 (1988).
13. E. Pollak, H. Graben, and P. Hänggi, J. Chem. Phys. 91, 4073 (1989).
14. I. Rips and E. Pollak, Phys. Rev. A 41, 5366 (1990).
15. M. Topaler and N. Makri, J. Chem. Phys. 101, 7500 (1994).
16. A. N. Drozdov and P. Talkner, J. Chem. Phys. 109, 2080 (1998).
17. R. Ferrando, R. Spadacini, and G. E. Tommei, Phys. Rev. A 46, R699 (1992).
18. R. Ferrando, R. Spadacini, and G. E. Tommei, Phys. Rev. E 48, 2437 (1993).
19. E. Pollak, J. Bader, B. J. Berne, and P. Talkner, Phys. Rev. Lett. 70, 3299 (1993).
20. Yu. Georgievskii and E. Pollak, Phys. Rev. Lett. 70, 5098 (1994).
21. E. Hershkovitz, P. Talkner, E. Pollak, and Yu. Georgievskii, Surf. Sci. 421, 73 (1999).
22. R. W. Pastor and A. Szabo, J. Chem. Phys. 97, 5098 (1992).
23. P. M. Déjardin, D. S. F. Crothers, W. T. Coffey, and D. J. McCarthy, Phys. Rev. E 63, 021102 (2001).
24. J. I. Lauritzen and R. Zwanzig, Jr., Adv. Mol. Relax. Interact. Processes 5, 339 (1973).
25. W. T. Coffey, Yu. P. Kalmykov, E. S. Massawé, and J. T. Waldron, J. Chem. Phys. 99, 4011 (1993).
26. C. J. Reid, Mol. Phys. 49, 331 (1983).
27. F. Marchesoni and J. K. Vij, Z. Phys. B: Condens. Matter 58, 187 (1985); F. Marchesoni, Phys. Rev. B 32, 1827 (1985).
28. F. Marchesoni and J. K. Vij, Z. Phys. B: Condens. Matter 58, 187 (1985); F. Marchesoni, Phys. Rev. B 32, 1827 (1985).
29. E. Praestgaard and N. G. van Kampen, Mol. Phys. 43, 33 (1981).
30. W. T. Coffey, M. W. Evans, and P. Grigolini, Molecular Diffusion and Spectra (Wiley, New York, 1984; Russian translation: Mir, Moscow, 1987).
31. W. T. Coffey, Yu. P. Kalmykov, and S. V. Titov, J. Chem. Phys. 115, 9895 (2001).
32. W. T. Coffey, Yu. P. Kalmykov, and S. V. Titov, Phys. Rev. E 67, 061115 (2003).
33. H. Goldstein, Classical Mechanics, 2nd Ed. (Addison-Wesley, Reading, MA, 1980).
34. Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (Dover, New York, 1964).
35. R. A. Sack, Proc. R. Soc. London, Ser. B 70, 402 (1957).
36. V. I. Mel'nikov, Phys. Rev. E 48, 3271 (1993); 50, 627 (1994).
37. V. I. Mel'nikov, Phys. Rev. E 48, 3271 (1993); 50, 627 (1994).
38. P. Talkner and E. Pollak, Phys. Rev. E 47, R21 (1993).
39. R. Ferrando, R. Spadacini, G. E. Tommei, and V. I. Mel'nikov, Phys. Rev. E 51, R1645 (1995).
40. A. Szabo, J. Chem. Phys. 72, 4620 (1980).
41. C. P. Bean and J. D. Livingston, J. Appl. Phys. 30, 120S (1959).
42. A. O. Caldeira and A. J, Leggett, Physica A 121, 587 (1983).
43. C. Anastopoulos and J. J. Halliwell, Phys. Rev. D 51, 6870 (1995).
44. J. L. Garcia-Palacios, Europhys. Lett. 65, 735 (2004).
45. U. Weiss, Quantum Dissipative Systems, 2nd Ed. (World Scientific, Singapore, 1999).
46. J. S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969).
47. R. Becker and W. Döring, Ann. Phys. (Leipzig) 24, 719 (1935).
48. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Oxford University Press, London, 1937).
49. Yu. P. Kalmykov, Khim. Fiz. 6, 745 (1987) [Sov. J. Chem. Phys. 6, 1427 (1990)].
50. Yu. P. Kalmykov, Khim. Fiz. 6, 745 (1987) [Sov. J. Chem. Phys. 6, 1427 (1990)].
51. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th Ed. (Cambridge University Press, Cambridge, England, 1927).