Abstract
A new integral representation of the transition rate holds for any friction and is shown to allow a feasible evaluation in a wide friction range. Analytic approximations include the (high-friction) Kramers result with the leading correction, as well as a low-friction case. The method is complementary to a recent one of Melnikov and Meshkov.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. B. Dynkin,Markov Processes (Springer, New York, 1965).
D. Ryter,Physica 142A:103 (1987).
D. Ryter and H. Meyr,Physica 142A:122 (1987).
H. Risken,The Fokker-Planck Equation (Springer, Berlin, 1983).
H. Dekker,Physica 135A:80 (1986).
B. J. Matkovsky, Z. Schuss, and C. Tier,J. Stat. Phys. 35:443 (1984).
V. I. Mel'nikov and S. V. Meshkov,J. Chem. Phys. 85:1018 (1986).
G. H. Weiss,J. Stat. Phys. 42:3 (1986).
P. Hänggi,J. Stat. Phys. 42:105 (1986).
H. A. Kramers,Physica 7:284 (1940).
P. Talkner and D. Ryter, inNoise in Physical Systems and 1/f Noise (North-Holiand, Amsterdam, 1983).
D. Ryter,Physica 130A:205 (1985).
M. Büttiker, E. Harris, and R. Landauer,Phys. Rev. B 28:1268 (1983); H. Risken and K. Voigtlaender,J. Stat. Phys. 41:825 (1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ryter, D. Noise-induced transitions in a double-well potential at low friction. J Stat Phys 49, 751–765 (1987). https://doi.org/10.1007/BF01009355
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01009355