Abstract
We solve analytically the Fokker-Planck equation for a one-parameter family of symmetric, attractive, nonharmonic potentials which include double-well situations. The exact knowledge of the eigenfunctions and eigenvalues allows us to fully discuss the transient behavior of the probability density. In particular, for the bistable potentials, we can give analytical expressions for the probability current over the working barrier and for the onset time which characterizes the transition from uni- to bimodal probability densities.
Similar content being viewed by others
References
M. Suzuki,Adv. Chem. Phys. 46:195 (1981).
F. de Pasquale, P. Tartaglia, and P. Tombesi, preprint (1982).
B. Cardi, C. Cardi, B. Roulet, and D. Saint-James,Physica 108A:233 (1981).
N. G. van Kampen,J. Stat. Phys. 17:71 (1977).
M. San Miguel,Z. Phys. B33:307 (1979).
L. Brenig and N. Banai, to appear inPhysica. 5D, No. 2 (1982).
E. Wong,Am. Math. Soc. Proceedings of the 16th Symposium on Appl. Math., 264 (1964).
M. Mörsch, H. Risken, and H. D. Vollmer,Z. Phys. B32:245 (1979).
A. Schenzle and H. Brandt,Phys. Rev. A20:1628 (1979).
L. E. Reichl, to appear inJ. Chem. Phys.
P. Hänggi,Z. Phys. B30:85 (1978).
S. Chandrasekhar,Rev. Mod. Phys. 15:1 (1943).
M. Abramovitz and I. Segun,Handbook of Mathematical Functions, Dover, New York (1964).
M. O. Hongler,Physica 2D:353 (1981).
M. O. Hongler and N. D. Quach, preprint (1982).
M. O. Hongler, preprint (1982).
H. Haken,Synergetics, Springer-Verlag, New York (1977).
W. Horsthemke, private communication and to be published.
W. M. Zheng, preprint (1982).
Author information
Authors and Affiliations
Additional information
On leave from the Department of Theoretical Physics, Université de Genève, CH-1211, Genève 4, Switzerland.
Supported by the Swiss National Fund for Scientific Research.
On leave from the Institute of Theoretical Physics, Academia Sinica, Beijing, China.
Supported in part by the Robert A. Welch Foundation.
Rights and permissions
About this article
Cite this article
Hongler, M.O., Zheng, W.M. Exact solution for the diffusion in bistable potentials. J Stat Phys 29, 317–327 (1982). https://doi.org/10.1007/BF01020789
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01020789