Lyapunov Decoherence Rate in Classically Chaotic Systems

TL;DR

This paper demonstrates that in classically chaotic quantum systems, the decoherence rate caused by a heat bath equals the Lyapunov exponent, linking chaos theory with quantum decoherence.

Contribution

It provides a path integral and semiclassical analysis showing the decoherence rate matches the Lyapunov exponent in chaotic systems, under specific approximations.

Findings

Decoherence rate equals Lyapunov exponent in chaotic systems.

Semiclassical calculation of purity for Gaussian wave packets.

Results valid for short times and weak dissipation.

Abstract

We provide a path integral treatment of the decoherence process induced by a heat bath on a single particle whose dynamics is classically chaotic and show that the decoherence rate is given by the Lyapunov exponent. The loss of coherence is charaterized by the purity, which is calculated semiclassically within diagonal approximation, when the particle initial state is a single gaussian wave packet. The calculation is performed for weak dissipation and in the high temperature limit. This situation allows us to simplify the heat bath description to a single random potential. Although the dissipative term is neglected in such approach, the fluctuating one can be treated phenomenologically to fit with the above regime. Our results are therefore valid for times shorter than the inverse of the dissipation rate.