Chaotic properties of dilute two- and three-dimensional random Lorentz gases. II. Open systems - art. no. 016312

We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e., the disordered Lorentz gas, in a generic nonequilibrium situation. In a large s ystem which is finite in at least some directions, and with absorbing bound ary conditions, the moving particle escapes the system with probability one . However, there is a set of zero Lebesgue measure of initial phase points for the moving particle, such that escape never occurs. Typically, this set of points forms a fractal repeller, and the Lyapunov spectrum is calculate d here for trajectories on this repeller. For this calculation, we need the solution of the recently introduced extended Boltzmann equation for the no nequilibrium distribution of the radius of curvature matrix and the solutio n of the standard Boltzmann equation. The escape-rate formalism then gives an explicit result for the Kolmogorov Sinai entropy on the repeller.