LMP Seminar: 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, we find that quenched disorder breaks ergodicity and rotational invariance in the flocking phase: several dynamical attractors coexist for a given realization of disorder. In the disordered phase, ergodicity is recovered, but the short correlation length dynamics are organized around an underlying sample-dependent skeleton best revealed in time-averaged fields. The type of disorder applied does not influence the aforementioned properties, but it can fundamentally change the structure of the phase diagram, self-averaging, and the nature of the ordered phase: a random coupling- (or noise-) strength landscape does not alter the phase diagram and yields a self-averaging long-range ordered phase, albeit different from the Toner-Tu liquid of the pure case. Random scatterers, on the other hand, deeply modify the layout of the phase diagram and leave nonergodic and non-self-averaging ordered regimes where three types of fluctuations compete: dynamical (thermal), sample to sample, but also between attractors existing for a given sample. Finally, exploring additional implementations of quench disorder we show that they lead to effects similar to either random couplings or scatterers, thus confirming the genericity of our results.