Abstract
In the stationary state the equation of motion for particles moving in a periodic potential has two solutions, a locked one and a running one, for low and intermediate damping constants and for suitable external forces. The effect of an additional Langevin force to this bistable behaviour is investigated. For finite noise strength, the mobility depends continuously on the external force, whereas in the limit of vanishing strength of the noise force one gets a sharp transition between the locked and the running solution at a critical external force. This critical force is calculated exactly in the low friction limit and approximately for intermediate friction constants. Furthermore the temperature dependence for various forces including the critical one is shown in the low friction limit.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ivanchenko, Yu.M., Zil'berman, L.A.: Sov. Phys. JETP28, 1272 (1969)
Ambegaokar, V., Halperin, B.I.: Phys. Rev. Lett.22, 1364 (1969)
Kurkijärvi, K., Ambegaokar, V.: Phys. Lett. A31, 314 (1970)
Lee, P.A.: J. Appl. Phys.42, 325 (1971)
Fulde, P., Pietronero, L., Schneider, W.R., Strässler, S.: Phys. Rev. Lett.35, 1776 (1975)
Dieterich, W., Peschel, I., Schneider, W.R.: Z. Physik B27, 177 (1977)
Risken, H., Vollmer, H.D.: Z. Physik B31, 209 (1978)
Schneider, T., Stoll, E.P., Morf, R.: Phys. Rev. B18, 1417 (1978)
Geisel, T. In: Physics of Superionic Conduction. Salamon, M.B. (ed.) p. 201. Berlin, Heidelberg, New York: Springer 1979
Stratonovich, R.L.: Topics in the Theory of Random Noise. Vol. II. New York: Gordon and Breach 1967
Viterbi, A.J.: Principles of Coherent Communication. New York: McGraw Hill 1966
Lindsey, W.C.: Synchronization Systems in Communication and Control. Englewood Cliffs, N.J.: Prentice Hall 1972
Ryter, D.: Statistics of the Cycle Slips of Second Order Phase Locked Loops, preprint, Bern 1978
Coffey, W.T.: Molecular Physics37, 473 (1979)
Risken, H., Vollmer, H.D.: Z. Physik B33, 297 (1979)
Vollmer, H.D., Risken, H.: Z. Physik B34, 313 (1979)
Risken, H., Vollmer, H.D.: Z. Physik B35, 177 (1979)
McCumber, D.E.: J. Appl. Phys.39, 3113 (1968)
Matkowsky, B.J., Schuss, Z.: J. Appl. Math.33, 365 (1977)
Lefever, R., Horsthemke, W.: In: Synergetics far from Equilibrium. Pacault, A., Vidal, C. (eds.) p. 57. Berlin, Heidelberg, New York: Springer 1979
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. New York: Dover Publications Inc. 1965
Cohen, J.K., Lewis, R.M.: J. Inst. Maths. Applics.3, 266 (1967)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vollmer, H.D., Risken, H. Bistability effects of the brownian motion in periodic potentials. Z Physik B 37, 343–349 (1980). https://doi.org/10.1007/BF01352745
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01352745