Driving-induced stability with long-range effects

TL;DR

This paper establishes a condition where rotation applied to medium particles stabilizes a probe at the center, with the effect influenced by the medium's potential and temperature, demonstrating robustness and temperature dependence.

Contribution

It provides a sufficient condition for stabilization of a probe via rotation-induced effects in a medium with long-range interactions, extending understanding of non-equilibrium stabilization mechanisms.

Findings

Rotation stabilizes the probe at the origin above a threshold.

Stabilization is robust near the quasi-static limit and weakly temperature-dependent.

Lower temperatures enhance the stabilization effect.

Abstract

We give a sufficient condition under which an applied rotation on medium particles stabilizes a slow probe in the rotation center. The symmetric part of the stiffness matrix thus gets a positive Lamb shift with respect to equilibrium. For illustration we take diffusive medium particles with a self-potential in the shape of a Mexican hat, high around the origin. There is a short-range attraction between the medium particles and the heavier probe, all immersed in an equilibrium thermal bath. 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 self-potential at large distances from the origin is irrelevant for the statistical force there. Above a certain rotation threshold, while the medium particles are still repelled from the origin, the probe stabilizes there and more details of the medium-density at large distance start to matter. The effect is robust around the quasi-static limit with rotation threshold only weakly depending on the temperature but the stabilization gets stronger at lower temperatures.