BREAKDOWN OF ERGODIC BEHAVIOR IN THE LORENTZ GAS

Applying an external field to the Lorentz gas model, and thermostating it to maintain a constant kinetic energy, we study the conductivity as a function of the field. For small fields the system is ergodic and the diffusion coefficient is well defined. At larger values of the field, ergodic behavior disappears and we observe a variety of possible dynamics, including the existence of a single stable trajectory for the largest fields. At intermediate values of field a series of transitions between ergodic, periodic, and nonergodic behavior appears. We present a detailed dynamical study of the breakdown in ergodic behavior. © 1994 The American Physical Society.