  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.
