#### Thermostating by deterministic scattering

K. Rateitschak, R. Klages, G. Nicolis, P. Gaspard,
Center for Nonlinear Phenomena and Complex Systems,
Universit'e Libre de Bruxelles,
Campus Plaine CP 231, Blvd du Triomphe

B-1050 Brussels, Belgium
We consider an elementary cell of a periodic Lorentz gas where a point
particle is scattered elastically at a hard disk. We modify the
microscopic scattering rules of this system by including a mechanism
for energy transfer between the particle and the disk, which is
equipped with arbitrarily many dynamical degrees of freedom. The
collision rules are chosen such that the full system (particle and
disk) is deterministic, time-reversible, and approaches a
microcanonical phase space density in equilibrium. By applying an
external electric field we find that in the limit of infinitely many
dynamical degrees of freedom of the disk our system goes into a
nonequilibrium steady state where the average current and the average
kinetic energy of the moving particle are constant in time.