Numerical solution for diffusion in periodic potentials: A comparison with the theory of activated processes

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Abstract
A numerical algorithm is implemented to explore Brownian particle diffusion in a periodic potential for the full viscosity range. The predictions of the theory of activated processes are checked. In particular, a recent refinement of the vanishingly small viscosity limit of the Kramers approach by Grote and Hynes [J. Chem. Phys. 77, 3736 (1982)] and Büttiker, Harris, and Landauer [Phys. Rev. B 28, 1268 (1983)] is found to fit our numerical results better.