Casimir forces between spheres

TL;DR

This paper presents a method to calculate Casimir forces between multiple dielectric spheres using stress tensor evaluation, providing insights into multi-body interactions and large-N behavior.

Contribution

It introduces a direct stress tensor approach for Casimir force calculation between dielectric spheres, including multi-body and large-N approximations.

Findings

Computed two- and three-body Casimir forces for sphere systems.

Derived an approximate large-N limit for force dependence.

Demonstrated the method's applicability to multiple dielectric spheres.

Abstract

We discuss the calculation of Casimir forces between a collection of $N$-dielectric spheres. This is done by evaluating directly the force on a sphere constructed from a stress tensor, rather than an interaction energy. Two and three body forces between the spheres are evaluated for setups of two and three sphere systems respectively. An approximate large-$N$ limit is also obtained for the functional dependence on the number of spheres.