D. Panja et al., Long-time-tail effects on Lyapunov exponents of a random, two-dimensional field-driven Lorentz gas, J STAT PHYS, 100(1-2), 2000, pp. 279-311
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.