Stabilization in the eye of a cyclone

TL;DR

This paper demonstrates that applying a rotational force to an overdamped diffusive medium can stabilize a fixed point, turning an unstable equilibrium into a stable one through nonequilibrium effects.

Contribution

It provides a rigorous analysis showing how rotational forces enhance stability in a nonequilibrium medium, including a universal expression for the induced stiffness.

Findings

Rotational force can stabilize an unstable fixed point.

Stability enhancement occurs at second-order in the nonequilibrium amplitude.

Induced stiffness converges to a universal form proportional to average mechanical stiffness.

Abstract

We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around that center, where the induced force vanishes. We prove that the introduction of the rotational force in general enhances the stability of that point (and may turn it from unstable to stable!), starting at second-order in the nonequilibrium amplitude. When the driving is further enhanced the stabilization occurs for a wide range of rotation profiles and the induced stiffness converges to a universal expression proportional to the average mechanical stiffness. The model thus provides a rigorous example of stabilization of a fixed point due to contact with a nonequilibrium medium and beyond linear order around equilibrium.