Casimir Force for Arbitrary Objects Using the Argument Principle and Boundary Element Methods

TL;DR

This paper introduces a flexible computational method for calculating Casimir forces between arbitrary three-dimensional objects using boundary element methods and the argument principle, simplifying the theoretical framework involved.

Contribution

It presents a novel approach combining the argument principle with the method of moments to compute Casimir forces for complex geometries and materials.

Findings

Enables calculation of Casimir forces for arbitrary geometries.

Utilizes boundary element methods for efficient computation.

Simplifies the theoretical derivation of Casimir forces.

Abstract

Recent progress in the simulation of Casimir forces between various objects has allowed traditional computational electromagnetic solvers to be used to find Casimir forces in arbitrary three-dimensional objects. The underlying theory to these approaches requires knowledge and manipulation of quantum field theory and statistical physics. We present a calculation of the Casimir force using the method of moments via the argument principle. This simplified derivation allows greater freedom in the moment matrix where the argument principle can be used to calculate Casimir forces for arbitrary geometries and materials with the use of various computational electromagnetic techniques.