Lyapunov Decoherence Rate in Classically Chaotic Systems

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.