  We consider the evolution of a quantum particle hopping on a cubic lattice in
any dimension and subject to a potential consisting of a periodic part and a
random part that fluctuates stochastically in time. If the random potential
evolves according to a stationary Markov process, we obtain diffusive scaling
for moments of the position displacement, with a diffusion constant that grows
as the inverse square of the disorder strength at weak coupling. More
generally, we show that a central limit theorem holds such that the square
amplitude of the wave packet converges, after diffusive rescaling, to a
solution of a heat equation.
