Active Brownian particles in power-law viscoelastic media

TL;DR

This paper models active Brownian particles in power-law viscoelastic media using a fractional Langevin equation, revealing new diffusion behaviors and the impact of viscoelasticity on active matter dynamics.

Contribution

It introduces a generalized fractional Langevin framework for active particles in scale-free viscoelastic environments, providing analytical solutions and numerical validation.

Findings

Discovery of diverse diffusion regimes influenced by viscoelastic properties

Identification of superdiffusive persistence exceeding ballistic motion

Alteration of the relation between persistence and propulsion in active matter

Abstract

Many active particles are embedded in environments that exhibit viscoelastic properties. An important class of such media lacks a single characteristic relaxation timescale when subjected to a time-dependent stress. Rather, the stress response spans a broad continuum of timescales, a behavior naturally described by a scale-free, fractal-like power-law relaxation modulus. Using a generalization of the fractional Langevin equation, we investigate an active Brownian particle embedded in a power-law viscoelastic environment with translational and rotational dynamics governed by independent fractional orders. We solve the model analytically, develop a numerical scheme to validate the theoretical predictions, and provide tools that can be used in further studies. A rich variety of diffusion regimes emerges, which modify the intermediate-time behavior of the mean squared displacement. Notably, we find that the competition between translational and rotational contributions favors a superdiffusive persistence over the standard ballistic motion, and over-stretches its characteristic timescale, fundamentally altering the standard relation between persistence and propulsion in active matter.