Long-range velocity correlations from active dopants

Active matter systems display collective behaviors that are impossible in thermodynamic equilibrium. One such feature, observed in in dense active matter systems is the appearance of long-range velocity correlations without explicit aligning interaction. However, the conditions for the appearance of these correlations remain largely unexplored. Here we show that such long-range velocity correlations can also be generated in a dense athermal passive system by the inclusion of a very small fraction of active Brownian particles. We develop a continuum theory to explain the emergence of velocity correlations generated via such active dopants. We validate the predictions for the effects of magnitude and persistence time of the active force and the area fractions of active and passive particles using extensive Brownian dynamics simulation of a canonical active-passive mixture. Our work decouples the roles that density and activity play in generating long-range velocity correlations in such exotic non-equilibrium steady states.