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arXiv · 2006.11932

Origin of universality in the onset of superdiffusion in L\'evy walks

Asaf Miron
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Abstract

Superdiffusion arises when complicated, correlated and noisy motion at the microscopic scale conspires to yield peculiar dynamics at the macroscopic scale. It ubiquitously appears in a variety of scenarios, spanning a broad range of scientific disciplines. The approach of superdiffusive systems towards their long-time, asymptotic behavior was recently studied using the L\'evy walk of order $1<\beta<2$, revealing a universal transition at the critical $\beta_{c}=3/2$. Here, we investigate the origin of this transition and identify two crucial ingredients: a finite velocity which couples the walker's position to time and a corresponding transition in the fluctuations of the number of walks $n$ completed by the walker at time $t$.

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BibTeXRIS

Asaf Miron. 2020-06-21. Origin of universality in the onset of superdiffusion in L\'evy walks. https://doi.org/10.1103/physrevresearch.2.032042

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