title: A simple non-chaotic map generating subdiffusive, diffusive, and superdiffusive dynamics.
abstract: Analytically tractable dynamical systems exhibiting a whole range of normal and anomalous deterministic diffusion are rare. Here, we introduce a simple non-chaotic model in terms of an interval exchange transformation suitably lifted onto the whole real line which preserves distances except at a countable set of points. This property, which leads to vanishing Lyapunov exponents, is designed to mimic diffusion in non-chaotic polygonal billiards that give rise to normal and anomalous diffusion in a fully deterministic setting. As these billiards are typically too complicated to be analyzed from first principles, simplified models are needed to identify the minimal ingredients generating the different transport regimes. For our model, which we call the slicer map, we calculate all its moments in position analytically under variation of a single control parameter. We show that the slicer map exhibits a transition from subdiffusion over normal diffusion to superdiffusion under parameter variation. Our results may help to understand the delicate parameter dependence of the type of diffusion generated by polygonal billiards. We argue that in different parameter regions the transport properties of our simple model match to different classes of known stochastic processes. This may shed light on difficulties to match diffusion in polygonal billiards to a single anomalous stochastic process.
authors.affiliation: Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24 I-10129 Torino, Italy.
authors.forename: Lucia
authors.initials: L
authors.lastname: Salari
authors.affiliation: Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24 I-10129 Torino, Italy.
authors.forename: Lamberto
authors.initials: L
authors.lastname: Rondoni
authors.affiliation: Dipartimento di Scienze e Metodi dell'Ingegneria, Universita' di Modena e Reggio E., Via G. Amendola 2 - Pad. Morselli, I-42122 Reggio E., Italy.
authors.forename: Claudio
authors.initials: C
authors.lastname: Giberti
authors.affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom.
authors.forename: Rainer
authors.initials: R
authors.lastname: Klages