# Self-propelled particle in a nonconvex external potential: Persistent limit in one dimension

## TL;DR

This paper develops a method to predict the density profile of a one-dimensional active particle in arbitrary nonconvex potentials in the persistent limit, highlighting the influence of inflection points and nonlocal effects.

## Contribution

It introduces a novel approach to analyze active particles in nonconvex potentials under high persistence, extending beyond equilibrium mapping techniques.

## Key findings

- Predicts density profiles in nonconvex potentials in the persistent limit.
- Highlights the importance of inflection points in the potential.
- Shows nonlocal dependence of density on potential features.

## Abstract

Equilibrium mapping techniques for nonaligning self-propelled particles have made it possible to predict the density profile of an active ideal gas in a wide variety of external potentials, however they fail when the self-propulsion is very persistent and the potential is nonconvex, which is precisely when the most uniquely active phenomena occur. Here we show how to predict the density profile of a 1D active Ornstein-Uhlenbeck particle in an arbitrary external potential in the persistent limit and discuss the consequences of the potential's nonconvexity on the structure of the solution, including the central role of the potential's inflection points and the nonlocal dependence of the density profile on the potential.