  We introduce a measure of decoherence for a class of density operators. For
Gaussian density operators in dimension one it coincides with an index used by
Morikawa (1990). Spatial decoherence rates are derived for three large classes
of the Galilean covariant quantum semigroups introduced by Holevo. We also
characterize the relaxation to a Gaussian state for these dynamics and give a
theorem for the convergence of the Wigner function to the probability
distribution of the classical analog of the process.
