Brownian motion model of activated transitions in a periodic potential

Abstract

The effects of the boundary conditions on the kinetics of activated processes are investigated by means of the nonstationary solutions of the Fokker–Planck equation for a particle moving in a bistable potential and coupled to a heat bath. The transition rate constant in a first-order rate equation is determined as a function of the damping constant, which describes the strength of coupling to the heat bath, for a periodic bistable potential and compared to the corresponding results for a bounded bistable potential previously obtained in Ref. 1. The mechanisms underlying the differences observed are discussed. The dependence of the rate constant on the potential barrier height is studied for both periodic and bounded potentials. Transient processes occurring after a nonequilibrium initial state are also investigated and proposed to be useful to extract information on the potential from time-resolved experiments. The transition rates determined are compared to those observed in trajectories simulated from the Langevin equation.