title: Transport in the barrier billiard.
abstract: 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_{n}^{2}〉, is either bounded or asymptotic to Kn^{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.
authors.affiliation: Department of Physics, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran.
authors.forename: S M
authors.initials: SM
authors.lastname: Saberi Fathi
authors.affiliation: Laboratoire de Physique des Plasmas, CNRS-Ecole Polytechnique, 91128 Palaiseau Cedex, France.
authors.forename: W
authors.initials: W
authors.lastname: Ettoumi
authors.affiliation: Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS et Université Paris 7-Denis Diderot, Case 7056, Bâtiment Condorcet, 10, rue Alice Domon et Léonie Duquet 75205 Paris Cedex 13, France.
authors.forename: M
authors.initials: M
authors.lastname: Courbage