Abstract

The periodic Lorentz gas with external field and iso-kinetic thermostat is equivalent, by conformal transformation, to a billiard with expanding phase space and slightly distorted scatterers, for which the trajectories are straight lines. A further time rescaling allows one to keep the speed constant in that new geometry. In the hyperbolic regime, the stationary state of this billiard is characterized by a phase-space contraction rate, equal to that of the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas case where phase-space contraction occurs in the bulk, the phase-space contraction rate here takes place at the periodic boundaries. © IOP Publishing Ltd.