Federico Bonetto, Joel L. Lebowitz
Nonequilibrium Stationary Solutions of Thermostated
Boltzmann Equation in a Field
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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.