Non-equilibrium Lorentz gas on a curved space

Details Non-equilibrium Lorentz gas on a curved space Non-equilibrium Lorentz gas on a curved space

2007-01-12

arxiv.org/abs/nlin/0701024v1

J. Stat. Mech. 7 (2007) L01003

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1088/1742-5468/2007/01/L01003

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 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 where phase-space contraction occurs in the bulk, the phase-space contraction rate here takes place at the periodic boundaries.

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