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Universal singularities of anomalous diffusion in the Richardson class
Attilio L Stella1, Aleksei Chechkin2, Gianluca Teza3
1Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy and INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy.
Physical Review. E
|June 17, 2023
Summary
Inhomogeneous environments cause anomalous diffusion. This study reveals a universal critical singularity in diffusion models, linked to non-Gaussian displacement scaling, independent of specific environmental details.
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- Diffusion processes often deviate from Gaussian behavior in natural inhomogeneous environments.
- Sub- and superdiffusion, observed across scales, arise from environmental features affecting particle motion.
Purpose of the Study:
- To investigate the behavior of diffusion models in inhomogeneous environments.
- To identify universal characteristics of anomalous diffusion.
Main Methods:
- Analysis of a model encompassing sub- and superdiffusion.
- Application of a method analyzing the normalized generator of cumulants.
- Focus on the asymptotics of the non-Gaussian scaling function of displacement.
Main Results:
- A critical singularity was identified in the normalized generator of cumulants.
- This singularity stems exclusively from the non-Gaussian displacement scaling function.
- The phenomenon exhibits a universal character, independent of specific environmental details.
Conclusions:
- The findings highlight a universal feature of anomalous diffusion in inhomogeneous media.
- The study connects scaling function asymptotics to diffusion exponents in the Richardson class.
- A nonstandard time extensivity of the cumulant generator was implied and numerically confirmed.
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