Properties of stationary nonequilibrium states in the thermostatted periodic Lorentz gas: The multiparticle system

We study the stationary nonequilibrium states of N-point particles moving under the influence of an electric field E among fixed obstacles (disk) in a two-dimensional torus. The total kinetic energy. of the system is kept constant through a Gaussian thermostat that 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 N-->infinity limit.