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.