Entropy production, dynamical localization and criteria for quantum chaos in the open quantum kicked rotor

The von Neumann entropy production for a quantum mechanical kicked rotor coupled to a thermal environment is calculated. This rate of entropy increase is shown to be a good criterion to distinguish between quantum mechanical counterparts of chaotic and regular classical motion. We show that for high temperatures the entropy production rate increases linearly with the Kolmogorov-Sinai entropy of the classical system. However, for lower temperatures we also show that there are fluctuations in this linear behaviour due to dynamical localization.