  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.
