2013/10/01 by Lucia Salari, Lamberto Rondoni, Salari, Lucia +3
Mathematics · Physics and Astronomy · #37E05 #82C20 #82C23 #82C41 #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #msc:37E05 #msc:82C20 #msc:82C23 #msc:82C41
paper · pdf · doi:10.48550/arxiv.1310.0472
19 pages, 6 figures
arxiv created 2013/10/01 · openalex publication_date 2013/10/01 · arxiv updated 2013/10/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In search for mathematically tractable models of anomalous diffusion, we introduce a simple dynamical system consisting of a chain of coupled maps of the interval whose Lyapunov exponents vanish everywhere. The volume preserving property and the vanishing Lyapunov exponents are intended to mimic the dynamics of polygonal billiards, which are known to give rise to anomalous diffusion, but which are too complicated to be analyzed as thoroughly as desired. Depending on the value taken by a single parameter α, our map experiences sub-diffusion, super-diffusion or normal diffusion. Therefore its transport properties can be compared with those of given Lévy walks describing transport in quenched disordered media. Fixing α so that the mean square displacement generated by our map and that generated by the corresponding Lévy walk asymptotically coincide, we prove that all moments of the corresponding asymptotic distributions coincide as well, hence all observables which are expressed in terms of the moments coincide.