Nonequilibrium stationary solutions of thermostated boltzmann equation in a field

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.1 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. (formula presented) for fixed v, where c depends on mean free path of the particle. f(v) is computed explicitly in one dimension.