Hydrodynamic Theory of Two-dimensional Chiral Malthusian Flocks

TL;DR

This paper develops a hydrodynamic theory for two-dimensional chiral Malthusian flocks, revealing a time cholesteric state and universality class of KPZ, with testable predictions for correlations.

Contribution

It introduces a hydrodynamic framework for chiral dry Malthusian flocks, identifying a time cholesteric state and connecting fluctuations to the KPZ universality class.

Findings

Formation of a time cholesteric state with uniform rotation

Fluctuations belong to the (2+1)-KPZ universality class

Predictions for correlations are testable in simulations and experiments

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)-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 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.