Diffusion in a multiwell potential with spatially varying viscosity

摘要

The problem of relaxation of a Brownian particle in a multiwell potential and in a medium with a viscosity which is piecewise constant, but which varies discontinuously in space, is studied using the Smoluchowski equation. Exact solutions are obtained. We find that when one barrier dominates the system the long time relaxation is determined by one eigenvalue, which may be computed using Kramersrsquo; rule applied to the dominant barrier. However, when all barriers are of comparable height, several eigenvalues compete in determining the long time behavior and these eigenvalues depend on the structure and distribution of viscosities of the entire system.