  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.
