  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.
