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Electrical current in Sinai billiards under general small forces
The Lorentz gas of -periodic scatterers (or the so called Sinai
billiards) can be used to model motion of electrons on an ionized medal. We
investigate the linear response for the system under various external forces
(during both the flight and the collision). We give some characterizations
under which the forced system is time-reversible, and derive an estimate of the
electrical current generated by the forced system. Moreover, applying Pesin
entropy formula and Young dimension formula, we get several characterizations
of the non-equilibrium steady state of the forced system.Comment: 19 page
On another edge of defocusing: hyperbolicity of asymmetric lemon billiards
Defocusing mechanism provides a way to construct chaotic (hyperbolic)
billiards with focusing components by separating all regular components of the
boundary of a billiard table sufficiently far away from each focusing
component. If all focusing components of the boundary of the billiard table are
circular arcs, then the above separation requirement reduces to that all
circles obtained by completion of focusing components are contained in the
billiard table. In the present paper we demonstrate that a class of convex
tables--asymmetric lemons, whose boundary consists of two circular arcs,
generate hyperbolic billiards. This result is quite surprising because the
focusing components of the asymmetric lemon table are extremely close to each
other, and because these tables are perturbations of the first convex ergodic
billiard constructed more than forty years ago
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