Singularity of Lévy walks in the lifted Pomeau-Manneville map

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• Samuel Brevitt (Queen Mary University of London)
• Wednesday 04 September 2024, 12:05-12:25
• Seminar Room 1, Newton Institute.

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SSDW05 - Modelling and Applications of Anomalous Diffusions

It is well-known that simple deterministic dynamical systems can display intermittent dynamics leading to anomalous diffusion. An example is the Pomeau-Manneville (PM) map which, suitably lifted onto the whole real line, generates superdiffusion that can be reproduced by stochastic Lévy walks (LWs). Here we report that this matching only holds for parameter values of the PM map that are of Lebesgue measure zero in its two-dimensional parameter space. This is due to a bifurcation scenario that the map exhibits under variation of one parameter. Constraining this parameter to specific singular values at which the map generates superdiffusion, and varying the second parameter, we find quantitative deviations between deterministic PM diffusion and stochastic LW diffusion in a particular range of parameter values, which cannot be cured by simple LW modifcations. We also explore the effect of aging on superdiffusion in the PM map and show that this yields a profound change of the diffusive properties under variation of the aging time, which should be important for experiments. Authors: S. Brevitt, A. Schulz, D. Pegler, H. Kantz, R. Klages

This talk is part of the Isaac Newton Institute Seminar Series series.

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