ABSTRACT
The classical motion of a rotator under an external time-periodic, δ-like perturbation has been studied in great detail in the last two decades. Indeed this system, as the external perturbation is increased, displays the great variety and complexity of generic, non integrable, classical systems. The simplicity and richness of this model makes it a good candidate to investigate the manifestation of classical chaotic motion in quantum mechanics. In this paper we discuss the quantum behaviour of such system. The analytical and numerical results so far obtained indicate that quantum mechanics places strong limitations to classical chaotic motion. This is the main feature of quantum motion and, even if some statistical behaviour is present, a satisfactory classification of its statistical properties, as we have in classical mechanics, is here lacking.
Moreover, as for the classical case, the qualitative properties of the quantum motion appear to depend also on some fine details such as the number theoretic properties of the ratio between the frequency of the unperturbed motion and the frequency of the external perturbation.
We also discuss the relation between the quantum limitation of classical chaos and the Anderson localization in static potentials which is due to quantum interference effects.
