Diffusion and superdiffusion of a quantum particle in time-dependent random potentials

Abstract

Using a density matrix description in momentum space, we study the evolution of a quantum particle in a onedimensional time-dependent gaussian potential whose fluctuations are correlated over a small finite time interval τ. Two cases must be distinguished: the case of spatially correlated disorder and the case of spatially uncorelated disorder. For spatially correlated disorder the mean square displacement from the origin of the initial wavepacket and the mean kinetic energy increase asymptotoically ast3 and ast, 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 (τ=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.