FM 02-02

Authors: Federico Bonetto, D. Daems, Joel L. Lebowitz and V. Ricci

Title: Properties of Stationary Nonequilibrium States in the Thermostatted Lorentz Gas I: the Many Point Particle System
Abstract: 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 $|\bE|$ 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 when N goes to infinity.

Keywords: thermostatted Lorentz gas, steady state current, smoothness, regularity, symbolic dynamics