Kicked quantum rotator with dynamic disorder: A diffusive behavior in momentum space

It is shown that diffusion, in momentum space, exists for the periodically kicked quantum rotator when dynamic disorder is considered on the external potential v() (the amplitude of the kick). This is opposite to the behavior without disorder (deterministic) where localization exists. Explicitly if v() is stochastic, then the diffusion coefficient is linked to the second derivative of the correlation function eiv(+cphi)e-iv() at cphi=0. Two examples are considered, the Gaussian process and the random linear case v()= (with a random parameter). In both cases, the diffusion coefficient was evaluated exactly. Finally, we conjecture that this diffusive behavior may be found in a great variety of kicked systems with static disorder.