Kicked quantum rotator with dynamic disorder: A diffusive behavior in momentum space
Juan Cesar Flores · Physical Review A · 1991
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(\ensuremath{\theta}) (the amplitude of the kick). This is opposite to the behavior without disorder (deterministic) where localization exists. Explicitly if v(\ensuremath{\theta}) is stochastic, then the diffusion coefficient is linked to the second derivative of the correlation function 〈${\mathit{e}}^{\mathit{i}\mathit{v}(\mathrm{\ensuremath{\theta}}+\mathit{c}\mathit{p}\mathit{h}\mathit{i})}$${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathit{i}\mathit{v}(\mathrm{\ensuremath{\theta}})}$〉 at cphi=0. Two examples are considered, the Gaussian process and the random linear case v(\ensuremath{\theta})=\ensuremath{\eta}\ensuremath{\theta} (with \ensuremath{\eta} 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.