Breakdown of Ergodicity and Self-Averaging in Polar Flocks with Quenched Disorder

TL;DR

This paper investigates how spatial quenched disorder impacts the behavior of polar active matter, revealing complex effects such as loss of ergodicity and non-self-averaging in the ordered phase of the 2D Vicsek model.

Contribution

It demonstrates that different types of quenched disorder lead to qualitatively different effects on polar order and ergodicity, challenging previous assumptions.

Findings

Ergodicity is lost in the ordered phase due to quenched disorder.

Random couplings maintain long-range order, but differ from pure systems.

Random scatterers cause strong non-self-averaging and sample-to-sample fluctuations.

Abstract

We show that spatial quenched disorder affects polar active matter in ways more complex and far-reaching than believed heretofore. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we find in particular that ergodicity is lost in the ordered phase, the nature of which we show to depend qualitatively on the type of quenched disorder: for random couplings, it remains long-range ordered, but qualitatively different from the pure (disorderless) case. For random scatterers, polar order varies with system size but we find strong non-self-averaging, with sample-to-sample fluctuations dominating asymptotically, which prevents us from elucidating the asymptotic status of order.