TUNNELING VERSUS CHAOS IN THE KICKED HARPER MODEL

We study the interplay between tunneling and chaos in a quantum system which classically would be weakly chaotic. We show that the tunneling rate between two stable islands is exponential and regular when the characteristic size of the chaotic region separating the islands is much larger or much smaller than Planck's constant. When the chaotic region and Planck's constant are of the same size the tunneling rate is shown to be irregular. This result is obtained by means of a numerical analysis of the quantum kicked Harper model, but we argue this to be a generic effect of classical chaos on tunneling.