  The kinetic separation of repulsive active Brownian particles into a dense
and a dilute phase is analyzed using a systematic coarse-graining strategy. We
derive an effective Cahn-Hilliard equation on large length and time scales,
which implies that the separation process can be mapped onto that of passive
particles. A lower density threshold for clustering is found, and using our
approach we demonstrate that clustering first proceeds via a hysteretic
nucleation scenario and above a higher threshold changes into a spinodal-like
instability. Our results are in agreement with particle-resolved computer
simulations and can be verified in experiments of artificial or biological
microswimmers.
