DECOHERENCE, DELOCALIZATION, AND IRREVERSIBILITY IN QUANTUM CHAOTIC SYSTEMS

Decoherence in quantum systems which are classically chaotic is studie d. The Arnold cat map and the quantum kicked rotor are chosen as examp les of linear and nonlinear chaotic systems. The Feynman-Vernon influe nce functional formalism is used to study the effect of the environmen t on the system. It is well known that quantum coherence can obliterat e chaotic behavior in the corresponding classical system. But interact ion with an environment can under general circumstances quickly dimini sh quantum coherence and reenact classical chaotic behavior. How effec tively decoherence works to sustain chaos, and how the resultant behav ior qualitatively differs from the quantum picture, depend on the coup ling of the system with the environment and the spectral density and t emperature of the environment: We show how recurrence in the quantum c at map is lost and classical ergodicity is recovered due to the effect of the environment. Quantum coherence and diffusion suppression are i nstrumental to dynamical localization for the kicked rotor. We show ho w environment-induced effects can destroy this localization. Such effe cts can also be understood as resulting from external noises driving t he system. Peculiar to decohering chaotic systems is the apparent tran sition from reversible to irreversible dynamics. We show such transiti ons in the quantum cat map and the quantum kicked rotor and distinguis h them from apparent irreversibility originating from dynamical instab ility and imprecise measurements. By performing a time reversal on and following the quantum kicked rotor dynamics numerically, we show how the otherwise reversible quantum dynamics acquires an arrow of time up on the introduction of noise or interaction with an environment.