We investigate transport properties of an ensemble of particles moving inside an infinite periodic horizontal planar barrier billiard. A particle moves among bars and elastically reflects on them. The motion is a uniform translation along the bars’ axis. When the tangent of the incidence angle, α, is fixed and rational, the second moment of the displacement along the orthogonal axis at time n, <S>^2, is either bounded or asymptotic to K_n^2, when n→∞. For irrational α, the collision map is ergodic and has a family of weakly mixing observables, the transport is not ballistic, and autocorrelation functions decay only in time average, but may not decay for a family of irrational α’s. An exhaustive numerical computation shows that the transport may be superdiffusive or subdiffusive with various rates or bounded strongly depending on the values of α. The variety of transport behaviors sounds reminiscent of well-known behavior of conservative systems. Considering then an ensemble of particles with nonfixed α, the system is nonergodic and certainly not mixing and has anomalous diffusion with self-similar space-time properties. However, we verified that such a system decomposes into ergodic subdynamics breaking self-similarity.

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