BROWNIAN-MOTION IN A PERIODIC POTENTIAL UNDER AN APPLIED BIAS - TRANSITION FROM HOPPING TO FREE CONDUCTION

Particles in an arbitrary large bias, subject to a periodic potential, are considered; the friction is such that the oscillation in the potential wells is underdamped. A stochastic formulation based on the assumption that the friction is Markovian from one well to the next is developed. The relevant parameter is the mean energy delta lost in crossing one well, compared to either T or to the drop in bias energy y. It is shown that a rapid change of regime occurs at y equals delta . The old results of Frenkel are recovered when delta greater than y, T. When delta less than T, the mobility is increased: a detailed solution in this limit is given for arbitrary bias. Thus, the results obtained by Ambegaokar and Halperin in the overdamped case are extended.