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# Steady-State Electrical Conduction in the Periodic Lorentz Gas

@inproceedings{Chernov1993SteadyStateEC, title={Steady-State Electrical Conduction in the Periodic Lorentz Gas}, author={Nikolai I. Chernov and Gregory L. Eyink and Joel L Lebowitz and Ya. G. Sinai}, year={1993} }

- Published 1993

We study nonequilibrium steady states in the Lorentz gas of periodic scatterers when an electric external field is applied and the particle kinetic energy is held fixed by a "thermostat" constructed according to Gauss' principle of least constraint (a model problem previously studied numerically by Moran and Hoover). The resulting dynamics is reversible and deterministic, but does not preserve Liouville measure. For a sufficiently small field, we prove the following results: (1) existence of aâ€¦Â CONTINUE READING