  We study the stationary nonequilibrium states of N point particles moving
under the influence of an electric field E among fixed obstacles (discs) in a
two dimensional torus. The total kinetic energy of the system is kept constant
through a Gaussian thermostat which produces a velocity dependent mean field
interaction between the particles. The current and the particle distribution
functions are obtained numerically and compared for small E with analytic
solutions of a Boltzmann type equation obtained by treating the collisions with
the obstacles as random independent scatterings. The agreement is surprisingly
good for both small and large N. The latter system in turn agrees with a self
consistent one particle evolution expected to hold in the limit of N going to
infinity.
