Brownian motion in a periodic potential under an applied bias : the transition from hopping to free conduction

We consider particles in an arbitrary large bias, subject to a periodic potential ; the friction is such that the oscillation in the potential wells is underdamped. We develop a stochastic formulation based on the assumption that the friction is Markovian from one well to the next. The relevant parameter is the mean energy δ lost in crossing one well, compared to either T or to the drop in bias energy y. We show that a rapid change of regime occurs at y = δ. When δ >> y, T, we recover the old results of Frenkel. When δ > y, T, nous retrouvons les résultats classiques de Frenkel. Dans la limite opposée δ << T, la mobilité augmente; nous donnons dans ce cas une solution détaillée pour y quelconque. Nous généralisons ainsi les résultats obtenus par Ambegaokar et Halperin [2] dans le cas suramorti