Abstract
The eigenvalues for the Brownian motion in a periodic potential with an additive constant force are investigated in the low friction limit. First the Fokker-Planck equation for the distribution function in velocity and position space is transformed to energy and position coordinates. By a proper averaging process over the position coordinate a differential equation for the distribution function depending on the energy only is obtained. Next the eigenvalues and eigenfunctions are calculated from this equation by a Runge-Kutta method. Finally the problem is formulated in terms of an integral equation from which the lowest non-zero eigenvalue is obtained analytically in the bistability region in the zero temperature limit.
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