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Active Brownian particles in power-law viscoelastic media

D. S. Quevedo1,*, M. Conte2,*, M. Dijkstra2, and C. Morais Smith1

  • 1Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584CC Utrecht, The Netherlands
  • 2Soft Condensed Matter and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Utrecht, The Netherlands

  • *These authors contributed equally to this work.
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Phys. Rev. E 114, L013401 – Published 27 July, 2026

DOI: https://doi.org/10.1103/vz9f-c2lb

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 overstretches its characteristic timescale, fundamentally altering the standard relation between persistence and propulsion in active matter.

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Phys. Rev. E 114, L013401– Published 27 July, 2026
  • Received 23 December 2025
  • Accepted 30 June 2026
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