Effect of a uniform bias force on the Brownian movement in double-well potentials

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Abstract
A general property of the Brownian motion in a bistable potential with the asymmetry arising from the imposition of a bias force is described. The property is that, at values of the bias force far less than the critical value required to destroy the bistable nature of the potential, the relaxation process may come to be dominated by fast intrawell modes rather than the slow overbarrier relaxation mode. The effect manifests itself in the pronounced departure of the inverse of the smallest eigenvalue of the Fokker-Planck equation from the relaxation time. The phenomenon is illustrated by two examples.