# Mode-coupling theory for the steady-state dynamics of active Brownian particles

## TL;DR

This paper develops a mode-coupling theory to describe the steady-state dynamics of active Brownian particles, linking microscopic activity to macroscopic glassy behavior through a novel correlation function.

## Contribution

It introduces a theoretical framework combining projection operators and mode-coupling approximations for active particles, incorporating nonequilibrium steady-state correlations.

## Key findings

- Steady-state correlation functions quantify activity effects.
- Activity influences short-time dynamics via spatial correlations.
- Long-time glassy dynamics are affected by microscopic currents.

## Abstract

We present a theory for the steady-state dynamics of a two-dimensional system of spherically symmetric active Brownian particles. The derivation of the theory consists of two steps. First, we integrate out the self-propulsions and obtain a many-particle evolution equation for the probability distribution of the particles' positions. Second, we use projection operator technique and a mode-coupling-like factorization approximation to derive an equation of motion for the density correlation function. The nonequilibrium character of the active system manifests itself through the presence of a steady-state correlation function that quantifies spatial correlations of microscopic steady-state currents of the particles. This function determines the dependence of the short-time dynamics on the activity. It also enters into the expression for the memory matrix and thus influences the long-time glassy dynamics.