CHAOTIC QUANTUM MOTION IN A SPACE-TIME PERIODIC POTENTIAL - AN EXACTLY SOLVABLE MODEL

We study the quantum mechanical motion of a particle in a space-time p eriodic potential of the Chirikov-Taylor type, V(x, t) = (K/4 pi(2)) c os(2 pi x) Sigma(n=-infinity)(infinity) delta(t - n). It is well known that the classical mechanical motion can be chaotic, where the chaoti c character of the motion manifests itself by a macroscopic momentum d iffusion (Brownian motion): [(p(t) - p(0))(2)] similar to t. We here s how that the quantum mechanical version of this system, under certain conditions, is exactly solvable. It turns out that the momentum diffus ion occurs also in the quantum system. This is remarkable, as it seems to contradict the widespread belief that ''quantum chaos is impossibl e''.