THE NONEQUILIBRIUM LORENTZ GAS

We study the conductivity of a Lorentz gas system, composed of a regul ar array of fixed scatterers and a point-like moving particle, as a fu nction of the strength of an applied external field. In order to obtai n a nonequilibrium stationary state, the speed of the point particle i s fixed by the action of a Gaussian thermostat. For small fields the s ystem is ergodic and the diffusion coefficient is well defined. We sho w that in this range the Periodic Orbit Expansion can be successfully applied to compute the values of the thermodynamic variables. At large r values of the field we observe a variety of possible dynamics, inclu ding the breakdown of erqodic behavior, and later the existence of a s ingle stable trajectory for the largest fields. We also study the beha vior of the system as a function of the orientation of the array of sc atterers with respect to the external field. Finally, we present a det ailed dynamical study of the transitions in the bifurcation sequence i n both the elementary cell and the fundamental domain. The consequence s of this behavior for the ergodicity of the system are explored. (C) 1995 American Institute of Physics.