  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.
