Fokker-plank dynamic in a general periodic potential shape

Abstract

A general theory for diffusion mechanism of Brownian particle submitted to a bistable and metastable periodic potential is presented. It is based on the description of the kinetics in the framework of Fokker-Planck equation (F.P.E). A formal solution of the F.P.E is obtained using the Matrix Continued Fraction Method (M.C.F.M), which gives an expression for the relevant correlation function. In particular, the half width of the quasi-elastic peak of the dynamical structure factor S(q, w) and the diffusion coefficient are fully studied in a wide range of physical parameters. A comparison between the results of system in a bistable and those in a metastable potential is presented and analysed.