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arXiv · 2211.14878

Universal singularities of anomalous diffusion in the Richardson class

Attilio L. Stella·Aleksei Chechkin·Gianluca Teza
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Abstract

Inhomogeneous environments are rather ubiquitous in nature, often implying anomalies resulting in deviation from Gaussianity of diffusion processes. While sub- and superdiffusion are usually due to conversing environmental features (hindering or favoring the motion, respectively), they are both observed in systems ranging from the micro- to the cosmological scale. Here we show how a model encompassing sub- and superdiffusion in an inhomogeneous environment exhibits a critical singularity in the normalized generator of the cumulants. The singularity originates directly from the asymptotics of the non-Gaussian scaling function of displacement, which we prove to be independent of other details and hence to retain a universal character. Our analysis, based on the method first applied in [A. L. Stella et al., arXiv:2209.02042 (2022)], further allows to establish a relation between the asympototics and diffusion exponents characteristic of processes in the Richardson class. Extensive numerical tests fully confirm the results.

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Attilio L. Stella, Aleksei Chechkin, Gianluca Teza. 2022-11-27. Universal singularities of anomalous diffusion in the Richardson class. https://doi.org/10.1103/physreve.107.054118

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