Properties of Stationary Nonequilibrium States in the Thermostatted   Lorentz Gas I: the One Particle System
  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. 
F. Bonetto, D. Daems and J.L. Lebowitz