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

We show that spatial quenched disorder affects polar active matter in ways more complex and far reaching than heretofore believed. 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.

Automated summary

The study reveals that spatial quenched disorder has a more complex and profound impact on polar active matter than previously believed. Simulations of the 2D Vicsek model show that in the ordered phase, ergodicity is lost, and the nature of the system depends qualitatively on the type of quenched disorder: random couplings lead to long-range ordered system, while random scatterers result in non-self-averaging with dominating sample-to-sample fluctuations.