Abstract
Considered is the motion of a Brownian particle in a bistable potential exposed to an external periodic field. Our analysis is based on a systematic Fokker-Planck description of the non-stationary stochastic process. Besides general characteristics, such as the nonmixing property, we present full numerical solutions for probability distributions and the modulation induced rate enhancement. Moreover, approximation schemes for small and large frequencies are considered and their results are compared to the numerical data.
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References
Kramers, H.A.: Physica7, 284 (1940)
For a overview, see: Hänggi, P.: J. Stat. Phys.42, 105 (1986)
Hänggi, P., riseborough, P.: Am. J. Phys.51, 347 (1983);
Ryter, D., Talkner, P., Hänggi, P.: Phys. Lett.93 A, 447 (1983)
Arecchi, F.T., Califano, A.: Phys. Lett.101 A, 443 (1984);
Beasly, M.R., D'Humieres, D., Hubermann, B.A.: Phys. Rev. Lett.50, 1328 (1983)
Crutchfield, J.P., Hubermann, B.A.: Phys. Lett.77 A, 407 (1980)
Carmeli, B., Nitzan, A.: Phys. Rev. A32, 2435 (1985)
Munakata, T., Kawakatsu, T.: Progr. Theor. Phys.74, 262 (1985);
Munakata, T.: Progr. Theor. Phys.75, 747 (1986)
Larkin, A.I., Ovchinikov, Yu. N.: J. Low Temp. Phys.36, 317 (1986)
Chow, K.S., Ambegaokar, V.: Phys. Rev. B38, 11168 (1988)
Devoret, H.M., Esteve, D., Martinis, J.M., Cleland, A., Clarke, J.: Phys. Rev. B36, 58 (1987);
Devoret, M.H., Martinis, J.M., Esteve, D., Clark, J.: Phys. Rev. Lett.53, 1260 (1984)
Mc Namara, B., Wiesenfeld, K., Roy, R.: Phys. Rev. Lett.60, 2626 (1988);
Gammaitoni, L., Marchesoni, F., Menichella-Saetta, E., Santucci, S.: Phys. Rev. Lett.62, 349 (1989);
R. Fox: Phys. Rev. A.39, 4/48 (1989)
Jung, P., Hänggi, P.: Europhys. Lett.8, 505 (1989)
Risken, H.: The Fokker-Planck equation. Springer Series in Synergertics, Vol. 18. Berlin, Heidelberg, New York: Springer 1984
Zeldovich, Yu.B.: Sov. Phys. JETP24, 1006 (1967) [Zh. Eksp. Teor. Fiz.51, 1492 (1966)];
—: Sov. Phys. Usp.16, 427 (1973) [Usp. Fiz. Nauk.110 (1973) 139];
—: V.I. Ritus, Sov. Phys. JETP24, 1041 (1967) [Zh. Eksp. Teor. Fiz.51, 1544 (1966)]
Hänggi, P., Thomas, H.: Phys. Rep.88 C, 207 (1982)
For the case of a non-uniform distribution for the initial phases, see the footnotes in [12]
Debnath, G., Zhoo, T., Moss, F.: Phys. Rev. A39, 4323 (1989)
By a simple modification of the MCF expansion technique (see Chap. 9 of [13]) the eigenvalues λ0n =inω0 can also be found
Mc Namara, B., Wiesenfeld, K.: Phys. Rev. A39, 4854 (1989)
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Jung, P. Thermal activation in bistable systems under external periodic forces. Z. Physik B - Condensed Matter 76, 521–535 (1989). https://doi.org/10.1007/BF01307904
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DOI: https://doi.org/10.1007/BF01307904