When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation

摘要

Active Brownian particles (ABPs, such as self-phoretic colloids) swim atfixed speed $v$ along a body-axis ${\bf u}$ that rotates by slow angulardiffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim withconstant $\u$ until a random tumble event suddenly decorrelates theorientation. We show that when the motility parameters depend on density $\rho$but not on ${\bf u}$, the coarse-grained fluctuating hydrodynamics ofinteracting ABPs and RTPs can be mapped onto each other and are thus strictlyequivalent. In both cases, a steeply enough decreasing $v(\rho)$ causes phaseseparation in dimensions $d=2,3$, even when no attractive forces act betweenthe particles. This points to a generic role for motility-induced phaseseparation in active matter. However, we show that the ABP/RTP equivalence doesnot automatically extend to the more general case of $\u$-dependent motilities.