Driving-induced stability with long-range effects

We give a sufficient condition under which a steady nonequilibrium driving in the form of a rotational force on medium particles stabilizes an immersed slow probe in the rotation center. We illustrate that scenario for a diffusive medium with an external potential in the shape of a Mexican hat, high around the origin, with a short-range attraction between those medium particles and a heavier probe. For no or small rotation force on the medium particles, the origin is an unstable fixed point for the probe and the precise shape of the Mexican hat at large distances from the origin is irrelevant for the statistical force there. Above a certain rotation threshold however the probe gets stabilized at the origin and more details of the medium-density at large distance start to matter. The focusing effect occurs for different types of differential rotation with rotation threshold only weakly depending on the ambient temperature and is also robust around the quasi-static limit. Copyright (C) EPLA, 2016