Separation of time scales in rate problems at very low barriers

Abstract

The separation of time scales for jump rate problems in periodic potentials is investigated down to barriers as low as the thermal energy in the spatial diffusion regime. The jump rate and the time of flight between nearest wells are obtained by comparing the exact numerical result for the dynamic structure factor with the proper expression deriving from jump diffusion theory. The method is applied to the example of a cosine potential; the possibility of defining the rate at very low barriers is quantitatively discussed.