DIFFUSION AND SUPERDIFFUSION OF A QUANTUM PARTICLE IN TIME-DEPENDENT RANDOM POTENTIALS

Using a density matrix description in momentum space, we study the evolution of a quantum particle in a one-dimensional time-dependent gaussian potential whose fluctuations are correlated over a small finite time interval tau. Two cases must be distinguished: the case of spatially correlated disorder and the case of spatially uncorrelated disorder. For spatially correlated disorder the mean square displacement from the origin of the initial wavepacket and the mean kinetic energy increase asymptotoically as t3 and as t, respectively, while for spatially uncorrelated disorder the mean square displacement increases linearly and the mean kinetic energy, is time-independent. These asymptotic time-dependences are the same as in the white-noise case (tau = 0): in first approximation a small correlation time has no effect in the case of spatially correlated disorder while changing only the diffusion constant in the case of uncorrelated disorder.