Interfacial and density fluctuations in a lattice model of motility-induced phase separation

We analyze motility-induced phase separation and bubbly phase separation in a two-dimensional lattice model of self-propelled particles. We compare systems where the dense (liquid) phase has slab and droplet geometries. We find that interfacial fluctuations of the slab are well-described by capillary wave theory, despite the existence of bubbles in the dense phase. We attribute this to a separation of time scales between bubble expulsion and interfacial relaxation. We also characterize the dependence of liquid and vapor densities on the curvature of the liquid droplet, as well as the density fluctuations inside the phases. The vapor phase behaves similarly to an equilibrium system, displaying a Laplace pressure effect that shifts its density, and Gaussian density fluctuations. The liquid phase has large non-Gaussian fluctuations, but this is not accompanied by a large density shift, contrary to the equilibrium case. Nevertheless, the shift of the vapor density can be used to infer an effective surface tension that appears to also quantify capillary wave fluctuations.