  We study the decoherence of a one-particle system, whose classical
correpondent is chaotic, when it evolves coupled to a weak quenched
environment. This is done by analytical evaluation of the Loschmidt Echo, (i.e.
the revival of a localized density excitation upon reversal of its time
evolution), in presence of the perturbation. We predict an exponential decay
for the Loschmidt Echo with a (decoherence) rate which is asymptotically given
by the mean Lyapunov exponent of the classical system, and therefore
independent of the perturbation strength, within a given range of strengths.
Our results are consistent with recent experiments of Polarization Echoes in
nuclear magnetic resonance and preliminary numerical simulations.
