SEPARATION OF TIME SCALES IN RATE PROBLEMS AT VERY-LOW BARRIERS

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