Electrodynamic Casimir effect in a medium-filled wedge

Abstract

We re-examine the electrodynamic Casimir effect in a wedge defined by two perfect conductors making dihedral angle α = π/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 ε1, µ1 for distance from the axis r < a, and ε2, µ2 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, |ε1 − ε2| ≪ 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.

Electromagnetic Casimir Effect in Wedge Geometry and the Energy-Momentum Tensor in Media

“…Detailed expansions of the electric and magnetic fields are given in Ref. 28. In region 1 there are two independent polarizations, one TM polarization where the mode eigenvalues are determined by J mp (k ⊥ a) = 0 with m = 1, 2, 3, ..., and one TE polarization where the eigenvalues are determined by J mp (k ⊥ a) = 0.…”

“…The material of these two sections is based on two recent papers. 28,29 New developments are a closer examination of the behavior at finite temperature. As an introductory step, we delineate in the next section the essentials of classic Casimir theory for the perfectly conducting wedge.…”

Casimir theory of the relativistic composite string revisited, and a formally related problem in scalar QFT

“…If this assumption were removed, the regularization would be difficult to handle; there would remain an ambiguity how to construct the counter term. Another point worth noticing is the close connection between the relativistic invariance property and the theory of an electromagnetic field propagating in an isorefractive medium meaning that the refractive index is equal to one, or at least a constant everywhere in the material system [16,17]. Again, if the isorefractive (or relativistic) condition were removed in the electromagnetic case, the regularization procedure would be rather difficult to deal with, as the contact term to be subtracted off would then depend on which of the media one chooses for this purpose.…”

Multiple Scattering: Dispersion, Temperature Dependence, and Annular Pistons

“…(If that is not done for the wedge, the differential equations are no longer separable.) See Refs [10,11,12] for more detail. Consider now case (d).…”