Long-wavelength instabilities in a system of interacting active particles

Based on a microscopic model, we develop a continuum description for a suspension of microscopic self-propelled particles. With this continuum description we study the role of long-range interactions in destabilizing macroscopic ordered phases that are developed by short-range interactions. Long-wavelength fluctuations can destabilize both isotropic and symmetry-broken polar phases in a suspension of dipolar particles. The instabilities in a suspension of pullers (pushers) arise from splay (bend) fluctuations. Such instabilities are not seen in a suspension of quadrupolar particles. (paper: classical statistical mechanics, equilibrium and non-equilibrium)