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arXiv · 1709.04980

Equivalence of position-position auto-correlations in the Slicer Map and the L\'evy-Lorentz gas

Claudio Giberti·Lamberto Rondoni·Muhammad Tayyab·Juergen Vollmer
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Abstract

The Slicer Map is a one-dimensional non-chaotic dynamical system that shows sub-, super-, and normal diffusion as a function of its control parameter. In a recent paper [Salari et al., CHAOS 25, 073113 (2015)] it was found that the moments of the position distributions as the Slicer Map have the same asymptotic behaviour as the L\'evy-Lorentz gas, a random walk on the line in which the scatterers are randomly distributed according to a L\'evy-stable probability distribution. Here we derive analytic expressions for the position-position correlations of the Slicer Map and, on the ground of this result, we formulate some conjectures about the asymptotic behaviour of position-position correlations of the L\'evy-Lorentz gas, for which the information in the literature is minimal. The numerically estimated position-position correlations of the L\'evy-Lorentz show a remarkable agreement with the conjectured asymptotic scaling.

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Claudio Giberti, Lamberto Rondoni, Muhammad Tayyab, Juergen Vollmer. 2017-09-14. Equivalence of position-position auto-correlations in the Slicer Map and the L\'evy-Lorentz gas. https://doi.org/10.1088/1361-6544%2Fab08f6

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