Nonequilibrium Stationary Solutions of Thermostated Boltzmann Equation in a Field

Details Nonequilibrium Stationary Solutions of Thermostated Boltzmann Equation in a Field Nonequilibrium Stationary Solutions of Thermostated Boltzmann Equation in a Field

2009-09-27

arxiv.org/abs/0909.4958v1

Nonlinear Sciences

Chaotic Dynamics

pdf, 10 pages

Scientific paper

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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