Cp. Dettmann et al., CONJUGATE PAIRING IN THE 3-DIMENSIONAL PERIODIC LORENTZ GAS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(6), 1995, pp. 5746-5748
We numerically evaluate the Lyapunov exponents for the three-dimension
al periodic Lorentz gas in an electric field, with a Gaussian thermost
at. For small values of the field, the dynamics appears to be ergodic.
For larger fields there are chaotic and periodic windows. The Lyapuno
v exponents are found to obey the conjugate pairing rule in both chaot
ic and stable regions, indicating that conjugate pairing can occur for
small systems, and is not restricted to the large N limit.