Towards a robust criterion of anomalous diffusion

TL;DR

This paper introduces a robust power-spectral analysis criterion to distinguish between normal and anomalous diffusion in single-particle trajectories, addressing ambiguities caused by measurement errors.

Contribution

The authors develop and validate a new spectral criterion for identifying anomalous diffusion, demonstrating its robustness against measurement noise and its effectiveness in practical experiments.

Findings

The criterion reliably detects anomalous diffusion in fractional Brownian motion.

It remains effective despite the presence of measurement errors.

Experimental tests confirm its applicability to real-world data.

Abstract

Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian -- or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.