F. Bonetto, D. Daems and J.L. Lebowitz
Properties of Stationary Nonequilibrium States in the Thermostatted
Periodic Lorentz Gas I: The One Particle System
(1232K, postscript)
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.