Influence of the periodic potential shape on the Fokker–Planck dynamics

The influence of the periodic potential structure on the diffusion mechanism of a Brownian particle is studied using the Fokker–Planck equation. The equation is solved numerically by the matrix continued fraction method in order to calculate relevant correlation functions. In particular, jump length probability, diffusion coefficient and the half-width of the quasi-elastic peak of the dynamical structure factor S(q,ω) are fully studied in a wide range of physical parameters for two forms of periodic potential (bistable and metastable potential). There is some difference between results provided by these two potential models, indicating that dynamical properties are very sensitive to the structure of the periodic potential, especially in the low friction regime.