  Translation-covariant Markovian master equations used in the description of
decoherence and dissipation are considered in the general framework of Holevo's
results on the characterization of generators of covariant quantum dynamical
semigroups. A general connection between the characteristic function of
classical L\'evy processes and loss of coherence of the statistical operator
describing the center of mass degrees of freedom of a quantum system
interacting through momentum transfer events with an environment is
established. The relationship with both microphysical models and experimental
realizations is considered, focusing in particular on recent interferometric
experiments exploring the boundaries between classical and quantum world.
