Long-range velocity correlations in a passive system with active dopants

Active matter systems exhibit fascinating collective behaviour across a wide range of lengths and time scales. Active Brownian particles are a canonical example of such active matter systems. Such systems show surprisingly long-ranged correlations in the velocity field in the dense phase during motility-induced phase separation.



To test whether such long-range velocity correlations require these high densities of active particles, we combined theory and simulation to study an athermal passive dense medium that is agitated by a small fraction of active particles (active dopants). Long-range velocity correlations can indeed be generated in the passive medium by a very small fraction of active dopants if the passive medium is sufficiently dense.

We investigated the dependence of the velocity correlations on the densities of active and passive particles and on the activity parameters: for fixed rotational diffusion, the correlation length remains almost unchanged when one changes the active force. For a fixed self-propulsion force, the correlation length scales with the square root of the persistence time, which is consistent with results for purely active systems. Our work decouples the roles of density and activity in generating such long-range velocity correlations in a non-equilibrium steady state.