Current in Periodic Lorentz Gases with Twists

We study electrical current in two-dimensional periodic Lorentz gas in the presence of a twist force on the scatterers. In this deterministic system, billiard orbits are still geodesics between collisions, but do not reflect elastically when reaching the boundary. When the horizon is finite, i.e. the free flights between collisions are bounded, the resulting current J is proportional to the strength of the twist force measured by ε. We also prove the existence of a unique SRB measure, for which the Pesin entropy formula and Young’s expression for the fractal dimension are valid.