Perturbative zero-point energy for a cylinder of elliptical section

TL;DR

This paper investigates the Casimir effect for a perfectly conducting elliptical cylinder, using perturbation theory and Mathieu functions to evaluate how ellipticity influences the zero-point energy compared to the circular case.

Contribution

It introduces a perturbative approach to compute the Casimir energy for elliptical cylinders, extending known circular results with Mathieu function techniques.

Findings

Zero-point energy depends on ellipticity as a perturbation.

Mathematical framework using Mathieu functions is effective.

Results generalize circular cylinder Casimir energy calculations.

Abstract

We examine the Casimir effect for a perfectly conducting cylinder of elliptical section, taking as reference the known case of circular section. The zero-point energy of this system is evaluated by the mode summation method, using the ellipticity as a perturbation parameter. Mathieu function techniques are applied.