title: Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles.
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 [Speck et al., 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 (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.
authors.affiliation: Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany.
authors.forename: Thomas
authors.initials: T
authors.lastname: Speck
authors.affiliation: Institut für Theoretische Physik II, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany.
authors.forename: Andreas M
authors.initials: AM
authors.lastname: Menzel
authors.affiliation: Institut für Theoretische Physik II, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany.
authors.forename: Julian
authors.initials: J
authors.lastname: Bialké
authors.affiliation: Institut für Theoretische Physik II, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany.
authors.forename: Hartmut
authors.initials: H
authors.lastname: Löwen