**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

**email**

bonetto@ias.fr

ddaems@cenoli.ulb.ac.be

lebowitz@math.rutgers.edu

Valeria.Ricci@roma1.infn.it