QUANTUM CHAOS IN THE CONFIGURATIONAL QUANTUM CAT MAP

The motion of a classical or quantum-mechanical charged particle in th e unit square (with periodic boundary conditions) is investigated unde r the influence of periodic electromagnetic fields. It is shown that t he external fields can be chosen in such a way that the configuration space of the particle is mapped periodically to itself according to Ar nold's cat map. The time evolution of the quantum system shows the sam e degree of irregularity as does the classical time evolution which is completely dominated by the properties of the hyperbolic map. In part icular, the eigenfunctions of the Floquet operator are determined anal ytically, and, as an immediate consequence, the spectrum of quasienerg ies in this system is seen to be absolutely continuous. Furthermore, s patial correlations decay exponentially. The observed features are in striking similarity to properties of classically chaotic systems; for example, long-time predictions of the future behavior of the system tu rn out to be extremely sensitive to the specification of the initial s tate. In other words, the time evolution of the quantum system is algo rithmically complex. These phenomena, based on the formation of arbitr arily fine structures in the two-dimensional configuration space, requ ire that the system absorb energy (provided by the external kicks) at an exponential rate.