Asymptotic quantum behavior of classically anomalous maps

In the framework of quantum chaos, the theory of dynamical localization plays an outstanding role, both for its conceptual relevance and physical import. Theoretical arguments, confirmed by a large amount of numerical simulations, have shown in the case of complete classical chaos, that the localization length is related to the classical diffusion constant and the effective Planck's constant h. We investigate the quantum behavior when classical dynamics exhibits anomalous diffusion (so that the diffusion constant is not defined): we show that dynamical localization still takes place, and that the scaling with the quantum parameter is the same as the, classically diffusive case.