Lyapunov exponents from kinetic theory for a dilute, field-driven Lorentz gas

Positive and negative Lyapunov exponents for a dilute, random, two-dimensional Lorentz gas in an applied field, (E) over right arrow, in a steady state at constant energy are computed to order E(2). The results are lambda(+/-) = lambda(+/-)(0) - a(+/-) (qE/mv)(2)t(0) where lambda(+/-)(0) are the exponents for the field-free Lorentz gas, a(+) = 11/48, a(-) =7/48, t(0) is the mean free time between collisions, q is the charge, m is the mass, and lv is the speed of the particle. The calculation is based on an extended Boltzmann equation in which a radius of curvature, characterizing the separation of two nearby trajectories, is one of the variables in the distribution function. The analytical results an in excellent agreement with computer simulations.