title: Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards.
abstract: We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of superdiffusion, in the sense that there is a logarithmic correction to the linear growth in time of the mean-squared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time range accessible to numerical simulations. We compare our simulations to analytical results for the variance of the anomalously rescaled limiting normal distributions.
authors.affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy.
authors.forename: Giampaolo
authors.initials: G
authors.lastname: Cristadoro
authors.affiliation: Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, C. P. 231, Campus Plaine, B-1050 Brussels, Belgium.
authors.forename: Thomas
authors.initials: T
authors.lastname: Gilbert
authors.affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy.
authors.forename: Marco
authors.initials: M
authors.lastname: Lenci
authors.affiliation: Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510 México D.F., Mexico.
authors.forename: David P
authors.initials: DP
authors.lastname: Sanders
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D005740:Gases; D016014:Linear Models; D008962:Models, Theoretical
chemical_list: D005740:Gases