The Nose-Hoover thermostated Lorentz gas

We apply the Nose-Hoover thermostat and three variations of it, which contr ol different combinations of velocity moments, to the periodic Lorentz gas. Switching on an external electric field leads to nonequilibrium steady sta tes for the four models. By performing computer simulations we study the pr obability density, the conductivity and the attractor in nonequilibrium. Th e results are compared to the Gaussian thermostated Lorentz gas and to the Lorentz gas as thermostated by deterministic scattering. We find that sligh t modifications of the Nose-Hoover thermostat lead to different dynamical p roperties of our models. However, in all cases the attractor appears to be multifractal.