Anomalous diffusion and dynamical localization in a parabolic map

Abstract

We study numerically classical and quantum dynamics of a piecewise parabolic area preserving map on a cylinder which emerges from the bounce map of elongated triangular billiards. The classical map exhibits anomalous diffusion. Quantization of the same map results in a system with dynamical localization and pure point spectrum.

4 pages in RevTeX (4 ps-figures included)