Using boundary methods to compute the Casimir energy

TL;DR

This paper introduces boundary methods combined with complex analysis to numerically compute Casimir energies for waveguides of arbitrary shapes, including media with different permittivities, demonstrated through various geometries.

Contribution

It presents a novel numerical approach using boundary methods and Cauchy's theorem for calculating Casimir energies in complex geometries and media.

Findings

Numerical evaluations for concentric corrugated cylinders

Vacuum energy computation for media with different permittivities

Effective boundary method for arbitrary waveguide sections

Abstract

We discuss new approaches to compute numerically the Casimir interaction energy for waveguides of arbitrary section, based on the boundary methods traditionally used to compute eigenvalues of the 2D Helmholtz equation. These methods are combined with the Cauchy's theorem in order to perform the sum over modes. As an illustration, we describe a point-matching technique to compute the vacuum energy for waveguides containing media with different permittivities. We present explicit numerical evaluations for perfect conducting surfaces in the case of concentric corrugated cylinders and a circular cylinder inside an elliptic one.