Electrodynamic Casimir effect in a medium-filled wedge. II

Abstract

We consider the Casimir energy in a geometry of an infinite magnetodielectric wedge closed by a circularly cylindrical, perfectly reflecting arc embedded in another magnetodielectric medium, under the condition that the speed of light be the same in both media. An expression for the Casimir energy corresponding to the arc is obtained and it is found that in the limit where the reflectivity of the wedge boundaries tends to unity the finite part of the Casimir energy of a perfectly conducting wedge-shaped sheet closed by a circular cylinder is regained. The energy of the latter geometry possesses divergences due to the presence of sharp corners. We argue how this is a pathology of the assumption of ideal conductor boundaries and that no analogous term enters in the present geometry.

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

“…More details were published in Ref. 29. The sum over orders of the Bessel function partial waves is now not simply equidistant values ν = mp as before but the zeros of the dispersion function for ν = iη:…”

“…29 and the details of the procedure will not be iterated here. The energy is plotted as a function of the opening angle α for different values of the reflection coefficient |ξ| in Fig.…”

“…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.…”

Error bounds for uniform asymptotic expansions—modified bessel function of purely imaginary order

“…It is also the kernel of the Lebedev transform (see [16,Chapter 6]). This transform has recently been used in problems concerning electrowetting with two immiscible electrolytic solutions (see [8]) and electrodynamic Casimir effect in medium-field wedge (see [13]). An interesting feature of the function K iν (νa) is that there are infinitely many saddle points on the steepest descent path of the phase function in its integral representation…”