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.