The nonequilibrium Ehrenfest gas: A chaotic model with flat obstacles?

It is known that the nonequilibrium version of the Lorentz gas (a billiard with dispersing obstacles [Ya. G. Sinai, Russ. Math. Surv. 25, 137 (1970)], electric field, and Gaussian thermostat) is hyperbolic if the field is small [N. I. Chernov, Ann. Henri Poincare 2, 197 (2001)]. Differently the hyperbolicity of the nonequilibrium Ehrenfest gas constitutes an open problem since its obstacles are rhombi and the techniques so far developed rely on the dispersing nature of the obstacles [M. P. Wojtkowski, J. Math. Pures Appl. 79, 953 (2000)]. We have developed analytical and numerical investigations that support the idea that this model of transport of matter has both chaotic (positive Lyapunov exponent) and nonchaotic steady states with a quite peculiar sensitive dependence on the field and on the geometry, not observed before. The associated transport behavior is correspondingly highly irregular, with features whose understanding is of both theoretical and technological interests.