Quantum evolution of a chaotic system in contact with its surroundings

Making use of appropriate quantum-classical correspondence we have examined the differential behavior of regular and chaotic trajectories in terms of quantum decoherence, the evolution of average quantities, and variances and entropy in a driven double-well oscillator in contact with the surroundings. Our numerical analysis has shown that even on a short time scale the decay of the average quantum coherence is multiexponential. While the onset of decoherence is much faster for a regular trajectory, the decay is faster asymptotically for a chaotic trajectory compared to a regular one. The coupling of the system to the environment turns chaotic in a regular evolution. The environment also affects the evolution of quantum variances for a regular trajectory almost from the beginning, while it has an insignificant effect on chaotic evolution up to a time after which, for both trajectories, noise in the quantum variances exhibits remarkable suppression, although fluctuations of the reservoir modes, in general, tend to increase the level of variances. We identify three stages of quantum evolution; a short decoherence regime followed by a Liouville flow, the latter regime being dominated by the classical curvature of the potential. This is the regime at which growth of entropy or quantum variances is exponential, the rate being determined by the classical largest Lyapunov exponent. The last stage is the irreversible flow dominated by diffusion which suppresses noises in the quantum variances.