  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.
