  We investigate the decoherence of a small quantum system weakly coupled to a
complex, chaotic environment when the dynamics is not Gaussian but Levy
anomalous. By studying the time dependence of the linear entropy and the
damping of the interference of two Gaussian wave packets in the Wigner
representation, we show that the decoherence time for a quantum Levy stable
process is always smaller than for Gaussian diffusion.
