Hydrodynamic Theory of Flocking in the Presence of Quenched Disorder

TL;DR

This paper develops a hydrodynamic theory showing that active polar systems maintain long-range order despite quenched disorder, unlike equilibrium systems, with simulations confirming these theoretical predictions.

Contribution

It introduces a hydrodynamic framework demonstrating the robustness of active flocking against quenched disorder, contrasting with equilibrium behavior.

Findings

Long-range order persists in 3D active systems with quenched disorder.

Quasi-long-range order occurs in 2D active systems under quenched disorder.

Simulations confirm theoretical predictions in 2D and 3D.

Abstract

The effect of quenched (frozen) orientational disorder on the collective motion of active particles is analyzed. We find that, as with annealed disorder (Langevin noise), active polar systems are far more robust against quenched disorder than their equilibrium counterparts. In particular, long ranged order (i.e., the existence of a non-zero average velocity $\langle {\bf v} \rangle$) persists in the presence of quenched disorder even in spatial dimensions $d=3$, while it is destroyed even by arbitrarily weak disorder in $d \le 4$ in equilibrium systems. Furthermore, in $d=2$, quasi-long-ranged order (i.e., spatial velocity correlations that decay as a power law with distance) occurs when quenched disorder is present, in contrast to the short-ranged order that is all that can survive in equilibrium. These predictions are borne out by simulations in both two and three dimensions.