Abstract
For certain parameters the motion of particles in an inclined cosine potential is bistable, i.e. particles are either in a locked or a running state. Fluctuations will cause transitions between these two states. First the connection of the transition rates with the lowest non-zero eigenvalue and the stationary solution of the Fokker-Planck equation is given. Then the eigenvalues of the Fokker-Planck equation for this Brownian motion problem are calculated using the matrix continued fraction method. Finally explicit results for these (generally complex) eigenvalues as a function of the averaged angle of inclination are shown for three typical friction constants and various temperatures.
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Vollmer, H.D., Risken, H. Eigenvalues and their connection to transition rates for the Brownian motion in an inclined cosine potential. Z. Physik B - Condensed Matter 52, 259–266 (1983). https://doi.org/10.1007/BF01307378
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DOI: https://doi.org/10.1007/BF01307378