09-176 Federico Bonetto, Joel L. Lebowitz
Nonequilibrium Stationary Solutions of Thermostated Boltzmann Equation in a Field (266K, pdf) Sep 27, 09
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Abstract. We consider a system of particles subjected to a uniform external force E and undergoing random collisions with virtual fixed obstacles, as in the Drude model of conductivity. The system is maintained in a nonequilibrium stationary state by a Gaussian thermostat. In a suitable limit the system is described by a self consistent Boltzmann equation for the one particle distribution function f . We find that after a long time f(v,t) approaches a stationary velocity distribution f(v) which vanishes for large speeds, i.e. f(v) = 0 for |v| > vmax(E), with vmax(E)~1/|E| as |E| → 0. In that limit f(v)~exp(−c|v|3 ) for fixed v, where c depends on mean free path of the particle. f(v) is computed explicitly in one dimension.

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