FM 2000-10       mp_arc@math.utexas.edu \# 00-90
                 nonlin.CD@xxx.lanl.gov \# 0002052 

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

Title: Properties of Stationary Nonequilibrium States in the Thermostatted Lorentz Gas I: the One Particle System

Abstract: We study numerically and analytically the properties of the
stationary state of a particle moving under the influence of an
electric field $\bE$ in a two dimensional periodic Lorentz gas with
the energy kept constant by a Gaussian thermostat. Numerically the
current appears to be a continuous function of $\bE$ whose derivative
varies very irregularly, possibly in a discontinuous manner. We argue
for the non differentibility of the current as a function of $\bE$
utilizing a symbolic description of the dynamics based on the
discontinuities of the collision map. The decay of correlations and
the behavior of the diffusion constant are also investigated.

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

Addresses:
F.B.: IHES, 75 route de Chartres, 91440 Bures sur Yvette, France
D.D.: Department of Mathematics, Rutgers University,
        110 Frelinghuysen Road, Piscataway NJ 08854.
J.L.L.: Department of Mathematics and Physics, Rutgers University,
        110 Frelinghuysen Road, Piscataway NJ 08854.


e-mail: bonetto@ihes.fr
        ddaems@cenoli.ulb.ac.be
        lebowitz@math.rutgers.edu