A general connection between the characteristic function of a L\'evy process
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 microphysical
models and recent experiments is considered, focusing on the recently observed
transition between a dynamics described by a compound Poisson process and a
Gaussian process.Comment: 10 pages, revtex, no figures, to appear in Phys. Rev. Let
