Non-equilibrium Casimir forces: Spheres and sphere-plate

TL;DR

This paper develops a formalism for non-equilibrium Casimir forces between objects at different temperatures, focusing on spheres and sphere-plate configurations, revealing stronger forces, oscillations, and stable equilibrium points.

Contribution

It introduces a general theoretical framework for non-equilibrium Casimir forces and provides analytical results for small spheres near plates and other spheres, including novel stable and self-propelling states.

Findings

Non-equilibrium forces are stronger than equilibrium forces.

Forces can oscillate with separation due to material resonances.

Stable equilibrium points and self-propelling states are identified.

Abstract

We discuss non-equilibrium extensions of the Casimir force (due to electromagnetic fluctuations), where the objects as well as the environment are held at different temperatures. While the formalism we develop is quite general, we focus on a sphere in front of a plate, as well as two spheres, when the radius is small compared to separation and thermal wavelengths. In this limit the forces can be expressed analytically in terms of the lowest order multipoles, and corroborated with results obtained by diluting parallel plates of vanishing thickness. Non-equilibrium forces are generally stronger than their equilibrium counterpart, and may oscillate with separation (at a scale set by material resonances). For both geometries we obtain stable points of zero net force, while two spheres may have equal forces in magnitude and direction resulting in a self-propelling state.