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

Abstract

Active Brownian particles (ABPs, such as self-phoretic colloids) swim at\nfixed speed $v$ along a body-axis ${\\bf u}$ that rotates by slow angular\ndiffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with\nconstant $\\u$ until a random tumble event suddenly decorrelates the\norientation. We show that when the motility parameters depend on density $\\rho$\nbut not on ${\\bf u}$, the coarse-grained fluctuating hydrodynamics of\ninteracting ABPs and RTPs can be mapped onto each other and are thus strictly\nequivalent. In both cases, a steeply enough decreasing $v(\\rho)$ causes phase\nseparation in dimensions $d=2,3$, even when no attractive forces act between\nthe particles. This points to a generic role for motility-induced phase\nseparation in active matter. However, we show that the ABP/RTP equivalence does\nnot automatically extend to the more general case of $\\u$-dependent motilities.\n