Dynamical localisation for random Schrodinger operators

We show for a large class of random Schrodinger operators H-omega on l(2)(Z(v)) and on L-2(R-v) that dynamica localization holds, i.e. that, with probability one and for a suitable energy interval I, one has [GRAPHICS] Here psi is a function of sufficiently rapid decrease, psi(t) = e(-iH omega t)psi, P-I(H-omega) is the spectral projector of H-omega onto the interval I, and q is a positive real. The result covers all random Schrodinger operators for which exponential localization has been proved, including operators with Bernoulli potentials in dimension 1 and random Landau Hamiltonians. An application to the random dimer model is given.