Rates of quantum decoherence in regular and chaotic systems

We initiate a study of rates of quantum decoherence in regular and chaotic systems. The system of interest investigated is quite general, and the interaction with the surroundings is via a particular quantum-nondemolition coupling. We find that the averaged coherence, as measured by Tr${\mathrm{\rho }}^2$(t), decays faster asymptotically in chaotic than in regular systems; this is a direct result of the repulsion of energy levels in the former case. We also investigate the phenomenon of self-averaging, providing general conditions that ensure that averaged and unaveraged quantities, such as Tr${\mathrm{\rho }}^2$(t), coincide. We find good agreement between our analytic results and those obtained numerically for the circle and stadium billiards.