  The effective Lagrangian of a test particle, interacting with an ideal gas,
is calculated with in the closed time path formalism in the one-loop and the
leading order of the particle trajectory. The expansion in the time derivative
is available for slow enough motion and it uncovers diffusive effective forces
and decoherence for the coordinate and the momentum. A pure Newtonian friction
force and an anisotrop coordinate decoherence are found for zero temperature
ideal gas of fermions.
