Universal singularities of anomalous diffusion in the Richardson class
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.
Cite
@article{arxiv.2211.14878,
title = {Universal singularities of anomalous diffusion in the Richardson class},
author = {Attilio L. Stella and Aleksei Chechkin and Gianluca Teza},
journal= {arXiv preprint arXiv:2211.14878},
year = {2023}
}