Quantum transport in a time-dependent random potential with a finite correlation time

Using an earlier density matrix formalism in momentum space we study the motion of a particle in a time-dependent random potential with a finite correlation time tau, for 0 < t much less than tau. Within this domain 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 gaussian potential fluctuations), where we obtain power law scaling laws for the effect of the random potential in the mean squared displacement [x(2)] and in the mean kinetic energy [E(kin)]. At short times, t much 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(sigma xi) much less than t much less than 2t(sigma 2) and 1/2t(xi 2) much less than t much less than t(sigma xi), these quantities scale quantum mechanically as t(3/2) and as root t, respectively. These results lie in the perspective of recent studies of the existence of (fractional) power law behavior of [x(2)] and [E(kin)] at intermediate times. We also briefly discuss the scaling laws for [x(2)] and [E(kin)] at short times in the case of spatially uncorrelated potential.