Casimir Forces in Multi-Sphere Configurations

TL;DR

This paper calculates Casimir forces in multi-sphere dielectric configurations, analyzing interactions among many spheres at various temperatures and in different dielectric backgrounds, including large-N limits.

Contribution

It introduces a method to compute Casimir forces in complex multi-sphere systems, including large-N scaling behavior and finite temperature effects.

Findings

Casimir force computed for two and three spheres at zero and finite temperature.

Large-N scaling limit of Casimir force analyzed.

Interactions depend on dielectric properties and temperature.

Abstract

We calculate the Casimir force on an isolated dielectric sphere in an ensemble of $N$ spheres due to multiple mutual interactions of the collection of spheres. In particular we consider dielectric spheres immersed in some other background dielectric. As an example, the Casimir force between two and three spheres at zero and finite temperature is evaluated. For a very large number of spheres, we consider a large-$N$ scaling limit of the Casimir force.