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  • Letter
  • Open Access

Delayed active swimmer in a velocity landscape

Viktor Holubec1,2,*, Alexander Fischer2, Giovanni Volpe3, and Frank Cichos2,†

  • 1Department of Macromolecular Physics, Faculty of Mathematics and Physics, Charles University, 18000 Prague, Czech Republic
  • 2Molecular Nanophotonics Group, Peter Debye Institute for Soft Matter Physics, Universität Leipzig, 04103 Leipzig, Germany
  • 3Department of Physics, University of Gothenburg, 41296 Gothenburg, Sweden

  • *Contact author: viktor.holubec@matfyz.cuni.cz
  • †Contact author: cichos@physik.uni-leipzig.de
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Phys. Rev. Research 8, L022017 – Published 22 April, 2026

DOI: https://doi.org/10.1103/xn9x-ppjx

Abstract

Active systems in nature and synthetic environments commonly exhibit spatially heterogeneous activity patterns and time-delayed responses from internal feedback mechanisms, exemplified by bacterial chemotaxis. We study an idealized active gas where particles modulate their self-propulsion based on local environmental conditions with such delays. Through integrated theoretical, computational, and experimental approaches, we demonstrate that steady-state density distributions and collective polarization exhibit characteristic peaks and valleys as functions of response delay time. We find that delays can amplify polarization by nearly an order of magnitude and trigger complete polarization reversal when particle displacement during the delay period surpasses the persistence length. Multiparticle simulations incorporating interparticle interactions validate that these phenomena remain robust in sufficiently dilute collective systems. Since density and polarization determine the current in active matter, our findings show that temporally programming the delay time allows control over both static and dynamic states in active systems, with implications for biological microswimmers and engineered microrobots.

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Phys. Rev. Research 8, L022017– Published 22 April, 2026
  • Received 22 May 2025
  • Accepted 11 March 2026
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