QUANTUM TRANSPORT IN A TIME-DEPENDENT RANDOM POTENTIAL WITH A FINITE CORRELATION TIME

Using an earlier density matrix formalism in momentum space we study t he motion of a particle in a time-dependent random potential with a fi nite correlation time tau, for 0 < t much less than tau. Within this d omain we consider two subdomains bounded by kinetic time scales (t(c2) = 2mHBAR(-1)c(2), c(2) = sigma(2), xi(2), sigma xi, with 2 sigma the width of an initial wavepacket and xi the correlation length of the ga ussian potential fluctuations), where we obtain power law scaling laws for the effect of the random potential in the mean squared displaceme nt [x(2)] and in the mean kinetic energy [E(kin)]. At short times, t m uch less than min (t(sigma 2), 1/2t(xi 2)), [x(2)] and [E(kin)] scale classically as t(4) and t(2), respectively. At intermediate times, t(s igma xi) much less than t much less than 2t(sigma 2) and 1/2t(xi 2) mu ch less than t much less than t(sigma xi), these quantities scale quan tum mechanically as t(3/2) and as root t, respectively. These results lie in the perspective of recent studies of the existence of (fraction al) power law behavior of [x(2)] and [E(kin)] at intermediate times. W e also briefly discuss the scaling laws for [x(2)] and [E(kin)] at sho rt times in the case of spatially uncorrelated potential.