ar X iv : h ep - t h / 95 01 05 4 v 1 1 3 Ja n 19 95 Environment - Induced Effects on Quantum Chaos : Decoherence , Delocalization and Irreversibility ∗

Decoherence in quantum systems which are classically chaotic is studied. It is wellknown that a classically chaotic system when quantized loses many prominent chaotic traits. We show that interaction of the quantum system with an environment can under general circumstances quickly diminish quantum coherence and reenact some characteristic classical chaotic behavior. We use the Feynman-Vernon influence functional formalism to study the effect of an ohmic environment at high temperature on two classically-chaotic systems: The linear Arnold cat map (QCM) and the nonlinear quantum kicked rotor (QKR). Features of quantum chaos such as recurrence in QCM and diffusion suppression leading to localization in QKR are destroyed in a short time due to environment-induced decoherence. Decoherence also undermines localization and induces an apparent transition from reversible to irreversible dynamics in quantum chaotic systems. 1 Decoherence and Disappearance of Recurrence in the Quantum Cat Map Arnold’s cat map is a linear area-preserving map T on a torus in phase space formed by identifying the boundaries of the interval [0, 2π] in both the coordinate Q and the momentum P directions [1]. (Because of this the area of the torus is characterized by Planck’s constant which takes on the values h̄ = 2π/N , where N is the number of sites in both the coordinate and the momentum directions in the phase space.) From time step j to j + 1 it is given by