Journal of Statistical Physics, Vol. 101, Nos. 1/2, 2000. p. 61-77.
We apply the Nose-Hoover thermostat and three variations of it, which control different combinations of velocity moments, to the periodic Lorentz gas. Switching on an external electric field leads to nonequilibrium steady states for the four models. By performing computer simulations we study the probability density, the conductivity and the attractor in nonequilibrium. The results are compared to the Gaussian thermostated Lorentz gas and to the Lorentz gas as thermo-stated by deterministic scattering. We find that slight modifications of the Nose-Hoover thermostat lead to different dynamical properties of our models. However, in all cases the attractor appears to be multifractal.