Motility-induced phase separation in active Brownian particles

Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed $v$ along a body-axis $ u$ that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant $\u$ until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density $ρ$ but not on $ u$, the coarse-grained dynamics of interacting ABPs and RTPs are equivalent. In both cases, a steeply enough decreasing $v(ρ)$ causes phase separation in dimensions $d=2,3$, even when no direct forces act between the particles. This points to a generic role for motility-induced phase separation in active colloids.