Abstract
The Brownian motion of particles in a periodic potential in response to a constant external force is investigated in the low-friction-limit. By introducing an energy and a space variable and by making a proper self consistent ansatz, the Fokker-Planck equation is solved in the stationary state for small friction constants. We found out that, for fixed force to friction ratios, the mobility times the friction constant is a linear function of the square root of the friction constant if the damping is small enough. Explicit results for this linear function are presented for a cosine potential and compared to previous results.
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Risken, H., Vollmer, H.D.: Z. Physik B33, 297 (1979)
Vollmer, H.D., Risken, H.: Z. Physik B34, 313 (1979)
Viterbi, A.: Principles of Coherent Communication, New York: McGraw-Hill Book Company 1966
Stratonovich, R.L.: Topics in the Theory of Random Noise, Vol. II, New York: Gordon and Breach 1967
Haken, H., Sauermann, H., Schmid, Ch., Vollmer, H.D.: Z. Physik206, 369 (1967)
Ivanchenko, Yu.M., Zil'berman, L.A.: Sov. Phys. JETP28, 1272 (1969)
Ambegaokar, V., Halperin, B.I.: Phys. Rev. Lett.22, 1364 (1969)
Haken, H.: Synergetics, Berlin, Heidelberg, New York: Springer 1977
Risken, H., Vollmer, H.D.: Physics Letters69 A, 387 (1979)
Stratonovich, R.L.: Topics in the Theory of Random Noise, Vol. I, p. 115 New York: Gordon and Breach 1963
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions, New York: Dover Publications Inc. 1965
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Risken, H., Vollmer, H.D. Brownian motion in periodic potentials in the low-friction-limit; nonlinear response to an external force. Z Physik B 35, 177–184 (1979). https://doi.org/10.1007/BF01321244
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DOI: https://doi.org/10.1007/BF01321244