Suppression of chaos, quantum resonance, and statistics of a nonintegrable system

The quantum motion of a periodically two-sided kicked rotator is studied. It is shown that while this system is classically chaotic, its quantized version is exactly periodic for a suitable choice of the relevant parameters, and thus not only the chaotic diffusion behavior is suppressed in the course of quantization, but also the sensitivity to initial conditions. The statistical properties of an ensemble of such systems are also investigated; the distribution of the probability density is shown to obey the Rayleigh statistics.