Asymptotic quantum behavior of classically anomalous maps - art. no. 015204

In the framework of quantum chaos, the theory of dynamical localization pla ys an outstanding role, both for its conceptual relevance and physical impo rt. Theoretical arguments, confirmed by a large amount of numerical simulat ions, have shown in the case of complete classical chaos, that the localiza tion length is related to the classical diffusion constant and the effectiv e Planck's constant h. We investigate the quantum behavior when classical d ynamics 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 diff usive case.