  We study motion of a quantum wavepacket in a one-dimensional potential with
correlated disorder. Presence of long-range potential correlations allows for
existence of both localized and extended states. Weak time-dependent
perturbation in the form of a fluctuating plane wave is superimposed onto the
potential. This model can be realized in experiments with optically trapped
cold atoms. Time-dependent perturbation causes transitions between localized
and extended states. Owing to violation of space-time symmetries, there arises
atomic current which is codirectional with the wave-like perturbation. However,
it is shown that the perturbation can drag atoms only within some limited time
interval, and then the current changes its direction. Increasing of the
perturbation bandwidth and/or amplitude results in decreasing of the time of
current reversal. We argue that onset of the current reversal is associated
with inhomogeneity of diffusion in the momentum space.

Disordered Systems and Neural Networks;Quantum Gases;Quantum Physics