Long-time-tail effects on Lyapunov exponents of a random, two-dimensional field-driven Lorentz gas

We study the Lyapunov exponents for a moving, charged particle in a two-dim ensional Lorentz gas with randomly placed, nonoverlapping hard-disk scatter ers in a thermostatted electric field, (E) over bar The low-density values of thr Lyapunov exponents have been calculated with the use of an extended Lorentz-Boltzmann equation. In this paper we develop a method to extend the ses results to higher density, using the BBGKY hierarchy equations and exte nding them to include the additional variables needed for calculation of th e Lyapunov exponents. We then consider the effects of correlated collision sequences, due to the so-called ring events, on the Lyapunov exponents. For small values of the applied electric field, the ring terms lead to nonanal ytic, field-dependent contributions to both the positive and negative Lyapu nov exponents which are of the form <(epsilon)over tilde> ln <(epsilon)over tilde, where <(epsilon)over tilde is a dimensionless parameter proportiona l to the strength of the applied field. We show that these nonanalytic term s can be understood as resulting from the change in the collision frequency from its equilibrium value due to the presence of the thermostatted field. and that the collision frequency also contains such nonanalytic terms.