Pressure and Flow of Exponentially Self-Correlated Active Particles

Microscopic swimming particles, which dissipate energy to execute persistent directed motion, are a classic example of a non-equilibrium system. We investigate the non-interacting Ornstein--Uhlenbeck Particle (OUP), which is propelled through a viscous medium by a force which is correlated over a finite time. We obtain an exact expression for the steady state phase-space density of a single OUP confined by a quadratic potential, and use the result to explore more complex geometries, both through analytical approximations and numerical simulations. In a "Casimir"-style setup involving two narrowly-spaced walls, we describe a particle-trapping phenomenon, which leads to a repulsive effective interaction between the walls; while in a two-dimensional annulus geometry, we observe net stresses which resemble the Laplace pressure.