Equilibrium forces on non-reciprocal materials

TL;DR

This paper analyzes Casimir forces between non-reciprocal objects at thermal equilibrium, revealing conditions for attraction, repulsion, and stable configurations, and clarifying the role of three-body interactions.

Contribution

It provides a theoretical framework for understanding Casimir forces in non-reciprocal systems, including the decomposition of free energy and stability analysis.

Findings

Force can be decomposed into reciprocal and anti-reciprocal contributions

Non-reciprocal objects can exhibit repulsive Casimir forces

Stable configurations are possible for non-reciprocal objects

Abstract

We discuss and analyze the properties of Casimir forces acting between nonreciprocal objects in thermal equilibrium. By starting from the fluctuation-dissipation theorem and splitting the force into those arising from individual sources, we show that if all temperatures are equal, the resulting force is reciprocal and is derivable as the gradient of a Casimir (free) energy. While the expression for the free energy is identical to the one for reciprocal objects, there are several distinct features: To leading order in reflections, the free energy can be decomposed as the sum of two terms, the first corresponding to two reciprocal objects, and the second corresponding to two anti-reciprocal objects. The first term is negative and typically yields attraction, while the second can have either sign. For the case of two objects that are each other's mirror images, the second term is positive and yields repulsion. The sum of terms can lead to overall repulsive forces, in agreement with previous observations. Stable configurations, ruled out for reciprocal cases, appear possible for nonreciprocal objects. We show that for three objects, a three-body free energy exists, indicating that previously found persistent heat currents in situations of three objects cannot be used to produce persistent torques.