A theory for the dynamics of dense systems of athermal self-propelled particles

TL;DR

This paper develops a theoretical framework for understanding the time evolution of density fluctuations in dense, athermal self-propelled particle systems, highlighting how velocity correlations influence both short- and long-time dynamics.

Contribution

It derives an approximate evolution equation for particle positions by integrating out self-propulsions and introduces a memory function approach incorporating velocity correlations.

Findings

Velocity correlations affect short-time dynamics.

Velocity correlations modify long-time glassy behavior.

The theory provides a basis for predicting density fluctuation dynamics.

Abstract

We present a derivation of a recently proposed theory for the time dependence of density fluctuations in stationary states of strongly interacting, athermal, self-propelled particles. The derivation consists of two steps. First, we start from the equation of motion for the joint distribution of particles' positions and self-propulsions and we integrate out the self-propulsions. In this way we derive an approximate, many-particle evolution equation for the probability distribution of the particles' positions. Second, we use this evolution equation to describe the time dependence of steady-state density correlations. We derive a memory function representation of the density correlation function and then we use a factorization approximation to obtain an approximate expression for the memory function. In the final equation of motion for the density correlation function the non-equilibrium character of the active system manifests itself through the presence of a new steady-state correlation function that quantifies spatial correlations of the velocities of the particles. This correlation function enters into the frequency term, and thus it describes the dependence of the short-time dynamics on the properties of the self-propulsions. More importantly, the correlation function of particles' velocities enters into the vertex of the memory function and through the vertex it modifies the long-time glassy dynamics.