00-90 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) Feb 28, 00
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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.

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