  In this paper we constructed a special family of semidispersing billiards
bounded on a rectangle with a few dispersing scatters. We assume there exists a
pair of flat points (with zero curvature) on the boundary of these scatters,
whose tangent lines form a channel in the billiard table that is perpendicular
to the vertical sides of the rectangle. The billiard can be induced to a Lorenz
gas with infinite horizon when replacing the rectangle by a torus. We study the
mixing rates of the one-parameter family of the semi-dispersing billiards and
the Lorenz gas on a torus; and show that the correlation functions of both maps
decay polynomially.
