Computing the Casimir energy using the point-matching method

TL;DR

This paper introduces a numerical point-matching method to compute Casimir energies for complex geometries, validated against known solutions and applied to novel configurations like corrugated cylinders.

Contribution

The paper presents a new numerical approach for calculating Casimir energies in arbitrary waveguide geometries, expanding computational capabilities beyond traditional methods.

Findings

Validated method with known geometries

Computed Casimir energies for new complex geometries

Demonstrated flexibility of the point-matching approach

Abstract

We use a point-matching approach to numerically compute the Casimir interaction energy for a two perfect-conductor waveguide of arbitrary section. We present the method and describe the procedure used to obtain the numerical results. At first, our technique is tested for geometries with known solutions, such as concentric and eccentric cylinders. Then, we apply the point-matching technique to compute the Casimir interaction energy for new geometries such as concentric corrugated cylinders and cylinders inside conductors with focal lines.