Environment-Induced Effects on Quantum Chaos: Decoherence, Delocalization and Irreversibility

TL;DR

This paper investigates how environmental interactions cause decoherence in quantum chaotic systems, leading to the loss of quantum traits and a transition towards classical chaotic behavior, including irreversibility.

Contribution

It demonstrates that environment-induced decoherence can quickly suppress quantum chaos features in systems like QCM and QKR, bridging quantum and classical chaos.

Findings

Decoherence destroys recurrence in QCM.

Decoherence suppresses diffusion and causes localization in QKR.

Environment induces a transition from reversible to irreversible dynamics.

Abstract

Decoherence in quantum systems which are classically chaotic is studied. It is well-known 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.