# Pressure and Flow of Exponentially Self-Correlated Active Particles

## TL;DR

This paper derives exact and approximate descriptions of the steady-state behavior of exponentially self-correlated active particles, revealing phenomena like particle trapping and effective pressures in confined geometries.

## Contribution

It provides an exact steady-state phase-space density for an Ornstein-Uhlenbeck particle and explores complex geometries, uncovering novel trapping and pressure effects.

## Key findings

- Exact steady-state density for OUP in quadratic potential
- Particle trapping leads to wall repulsion in narrow gaps
- Net stresses in annular geometry resemble Laplace pressure

## Abstract

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.