DIFFUSION AND SUPERDIFFUSION OF A PARTICLE IN A RANDOM POTENTIAL WITH FINITE CORRELATION TIME

We study theoretically the long time asymptotic of a quantum particle moving in a random time-dependent potential with finite correlation time, in d=1. By applying a new unitary numerical scheme we first show the minor importance of quantum interference and then derive an effective Langevin-type equation for the corresponding clasical problem in the limit of weak potential. We find that on intermediate time scales Ekin(t)t2/5, while the true long time asymptotic is determined by a new friction term, which gives rise to a stationary power law velocity distribution, multifractality of the velocity moments, and a slowing down of the superdiffusive behavior. © 1995 The American Physical Society.