Diffusion in a class of exactly solvable non-harmonic potentials. Intrinsic effects induced by non-linearities

Abstract

This paper deals with the problem of a particle that diffuses in a potential with a reflecting barrier and has a point of stable equilibrium and a point of unstable equilibrium. Based on the exact solutions obtained earlier for the Fokker-Planck equation of a class of these models, we analyze the behavior of the probability density, the mean path and the onset time which determines the transition from unimodal to bimodal probability densities. The study is made over different initial positions, two of them very close to the unstable point, which permits a clear comparison among the subsequent evolutions, and the observation of some intrinsic effects induced by non-linearities.