Quantum manifestations of chaotic scattering in the presence of KAM tori

¹ Physik-Department E13, Technische Universität München, D-85747 Garching, Germany
² Institut für Physik, Universität Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

Received: 5 July 1996
Accepted: 23 October 1996

Abstract

We investigate the semiclassical scattering amplitude for systems, where the classical dynamics is non-hyperbolic, i.e. where islands of KAM trajectories exist in an otherwise chaotic phase space. With the help of semiclassical calculations for the three-disk billiard in an external magnetic field, in which a hyperbolic–non-hyperbolic transition is observed as a function of the field strength, we show that the "stickiness” of the KAM tori leads to a much slower decrease of the survival probability, as compared with the hyperbolic case. This is reflected by a much narrower shape of the energy correlation function. However, we also find that the algebraic asymptotic decay of the survival probability in the non-hyperbolic case is not important for the quantum fluctuations.