Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

TL;DR

This paper develops a mean-field theoretical framework for active Brownian particles' phase separation, deriving an effective free energy and analyzing the dynamics through weakly non-linear analysis, supported by numerical simulations.

Contribution

It explicitly connects microscopic dynamics of active particles to a large-scale Ginzburg-Landau free energy description, advancing understanding of active phase separation.

Findings

Derivation of an effective Cahn-Hilliard equation for active particles.

Identification of a Ginzburg-Landau free energy form for active phase separation.

Numerical simulations confirming analytical predictions.

Abstract

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Phys. Rev. Lett. 112, 218304 (2014)]. Here we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (mobility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the dynamics. We finally discuss results from numerical simulations corroborating the analytical results.