Electrodynamic Casimir Effect in a Medium-Filled Wedge

TL;DR

This paper analyzes the electrodynamic Casimir effect in a medium-filled wedge with perfect conductors, exploring finite energy results, divergences, and radiation effects related to cosmic strings and dielectric media.

Contribution

It provides a detailed analysis of the Casimir effect in a wedge geometry with dielectric materials, including finite energy calculations and radiation phenomena associated with cosmic strings.

Findings

Finite Casimir energy results for specific conditions

Zero-mode divergence addressed by boundary conditions

Radiation emitted by cosmic string formation

Abstract

We re-examine the electrodynamic Casimir effect in a wedge defined by two perfect conductors making dihedral angle \alpha=\pi/p. This system is analogous to the system defined by a cosmic string. We consider the wedge region as filled with an azimuthally symmetric material, with permittivity/permeability \epsilon_1,\mu_1 for distance from the axis r<a, and \epsilon_2,\mu_2 for r>a. The results are closely related to those for a circular-cylindrical geometry, but with non-integer azimuthal quantum number mp. Apart from a zero-mode divergence, which may be removed by choosing periodic boundary conditions on the wedge, and may be made finite if dispersion is included, we obtain finite results for the free energy corresponding to changes in 'a' for the case when the speed of light is the same inside and outside the radius 'a', and for weak coupling, |\epsilon_1- \epsilon_2| \ll 1, for purely dielectric media. We also consider the radiation produced by the sudden appearance of an infinite cosmic string, situated along the cusp line of the pre-existing wedge.