Casimir forces between cylinders at different temperatures

TL;DR

This paper derives a general formula for Casimir forces between cylinders at different temperatures, revealing enhanced forces and oscillations compared to equilibrium, especially for thin conducting nano-wires.

Contribution

It provides a new theoretical framework for non-equilibrium Casimir forces between cylinders of arbitrary sizes and properties, including a summation method for dilute objects.

Findings

Non-equilibrium forces are larger than equilibrium forces at large separations.

Forces can oscillate with separation, creating stable equilibrium points.

Thin conducting cylinders exhibit pronounced non-equilibrium effects due to high emissivity.

Abstract

We study Casimir interactions between cylinders in thermal non-equilibrium, where the objects as well as the environment are held at different temperatures. We provide the general formula for the force, in a one reflection approximation, for cylinders of arbitrary radii and optical properties. As is the case for equilibrium, we find that the force for optically diluted cylinders can be obtained by appropriate summation of the corresponding result for spheres. We find that the non-equilibrium forces are generally larger than their equilibrium counterpart at separations greater than the thermal wavelength. They may also exhibit oscillations as function of separation, leading to stable points of zero net force. These effects are particularly pronounced for thin conducting cylinders (e.g. 40nm diameter nano-wires of tungsten) due to their large emissivity.