Mode-coupling theory for tagged-particle motion of active Brownian particles

Abstract

We derive a mode-coupling theory (MCT) to describe the dynamics of tracer particles in dense, glass-forming systems of active Brownian particles (ABP) in two spatial dimensions. The ABP undergo translational and rotational Brownian dynamics, and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density correlation functions describe the various cases of tracer dynamics at high densities: that of a passive colloidal particle in a suspension of ABP, that of a single active particle in a glass-forming passive host suspensions, and that of active tracers in a bath of active particles. Numerical results are presented for these cases assuming hard-sphere interactions among the particles. The qualitative and quantitative accuracy of the theory is tested against event-driven Brownian-dynamics (ED-BD) simulations of active and passive hard disks. The agreement between simulation and theory is found to be excellent, provided one allows for an adjustment of overall density known from the fully passive system, and for a simple rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency of kinetic arrest. We also confirm in the simulations a peculiar feature of the transient and stationary dynamical density correlation functions regarding their lack of symmetry under time reversal, demonstrating the non-equilibrium nature of the system and how it manifests itself in the theory.