Active matter in infinite dimensions: Fokker-Planck equation and dynamical mean-field theory at low density

TL;DR

This paper compares Fokker-Planck and dynamical mean-field theory approaches to analyze active matter in infinite dimensions, deriving analytical expressions and exploring transient dynamics at low densities.

Contribution

It demonstrates the consistency of two major theoretical approaches and extends previous results to non-monotonous potentials in active matter systems.

Findings

Analytic pair distribution function obtained

Effective self-propulsion derived to first order in density

Transient behavior of active hard spheres analyzed

Abstract

We investigate the behavior of self-propelled particles in infinite space dimensions by comparing two powerful approaches in many-body dynamics: the Fokker-Planck equation and dynamical mean-field theory. The dynamics of the particles at low densities and infinite persistence time is solved in the steady-state with both methods, thereby proving the consistency of the two approaches in a paradigmatic out-of-equilibrium system. We obtain the analytic expression for the pair distribution function and the effective self-propulsion to first order in the density, confirming the results obtained in a previous paper and extending them to the case of a non-monotonous interaction potential. Furthermore, we obtain the transient behavior of active hard spheres when relaxing from equilibrium to the nonequilibrium steady-state. Our results show how collective dynamics is affected by interactions to first order in the density, and point out future directions for further analytical and numerical solutions of this problem.