Transitions between wells and escape by diffusion in a one-dimensional potential landscape

The time-dependence of the occupation probabilities of neighboring wells due to diffusion in one dimension is formulated in terms of a set of generalized rate equations describing transitions between neighboring wells and escape across a final barrier. The equations contain rate coefficients, memory coefficients, and a long-time coefficient characterizing the amplitude of long-time decay. On a more microscopic level the stochastic process is described by a Smoluchowski equation for the one-dimensional probability distribution. A numerical procedure is presented which allows calculation of the transport coefficients in the set of generalized rate equations on the basis of the Smoluchowski equation.