Mode-Coupling Theory for Tagged-Particle Motion of Active Brownian Particles

TL;DR

This paper develops a mode-coupling theory to describe the dynamics of tracer particles in dense active Brownian particle systems, accurately predicting behavior near the glass transition and validated by simulations.

Contribution

The paper introduces a novel mode-coupling theory for active Brownian particles, extending understanding of tracer dynamics in dense active matter systems.

Findings

Theory accurately predicts tracer dynamics near the glass transition.

Quantitative agreement between theory and Brownian dynamics simulations.

Active systems exhibit non-equilibrium features like time-reversal asymmetry.

Abstract

We derive a mode-coupling theory (MCT) to describe the dynamics of tracer particles in dense systems of active Brownian particles (ABPs) 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 close to the glass transition: 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. Simulation and theory are found in quantitative agreement, provided one adjusts the overall density (as known from the passive description of glassy dynamics), and allows for a rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency for 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.