Bose-Einstein Condensation in Scalar Active Matter with Diffusivity Edge

Abstract: Due to their remarkable properties, systems that exhibit self-organization of their components resulting from intrinsic microscopic activity have been extensively studied in the last two decades. In a generic class of active matter, the interactions between the active components are represented via an effective density-dependent diffusivity in a mean-field single-particle description. Here, a new class of scalar active matter is proposed by incorporating a diffusivity edge into the dynamics: when the local density of the system surpasses a critical threshold, the diffusivity vanishes. The effect of the diffusivity edge is studied under the influence of an external potential, which introduces the ability to control the behaviour of the system by changing an effective temperature, which is defined in terms of the single-particle diffusivity and mobility. At a critical effective temperature, a system that is trapped by a harmonic potential is found to undergo a condensation transition, which manifests formal similarities to Bose-Einstein condensation.