Swarming in the dirt: Flocking in the presence of quenched disorder

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 < <b>v</b> >) persists in the presence of quenched disorder even in spatial dimension d = 3, while it is destroyed even by arbitrarily weak disorder in d &#8804 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) occur 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 of both two and three dimensional systems.