  We consider a system of particles subjected to a uniform external force E and
undergoing random collisions with "virtual" fixed obstacles, as in the Drude
model of conductivity. The system is maintained in a nonequilibrium stationary
state by a Gaussian thermostat. In a suitable limit the system is described by
a self consistent Boltzmann equation for the one particle distribution function
f. We find that after a long time f(v,t) approaches a stationary velocity
distribution f(v) which vanishes for large speeds, i.e. f(v)=0 for |v|>vmax(E),
with vmax(E)~1/|E| as |E| -> 0. In that limit f(v)~exp(-c|v|^3) for fixed v,
where c depends on mean free path of the particle. f(v) is computed explicitly
in one dimension.
