Casimir Effect for a Semitransparent Wedge and an Annular Piston

TL;DR

This paper calculates the Casimir energy and torque for a scalar field in a wedge and annular region with semitransparent boundaries, introducing new methods for complex geometries and providing numerical results.

Contribution

It presents a finite expression for Casimir energy in semitransparent wedge geometries and develops alternative methods for annular regions, advancing the calculation techniques for such configurations.

Findings

Numerical results for Casimir torque on wedge sidewalls.

Generalized formulas for Casimir energies in separable geometries.

Methodology applicable to complex semitransparent boundary configurations.

Abstract

We consider the Casimir energy due to a massless scalar field in a geometry of an infinite wedge closed by a Dirichlet circular cylinder, where the wedge is formed by $\delta$-function potentials, so-called semitransparent boundaries. A finite expression for the Casimir energy corresponding to the arc and the presence of both semitransparent potentials is obtained, from which the torque on the sidewalls can be derived. The most interesting part of the calculation is the nontrivial nature of the angular mode functions. Numerical results are obtained which are closely analogous to those recently found for a magnetodielectric wedge, with the same speed of light on both sides of the wedge boundaries. Alternative methods are developed for annular regions with radial semitransparent potentials, based on reduced Green's functions for the angular dependence, which allows calculations using the multiple-scattering formalism. Numerical results corresponding to the torque on the radial plates are likewise computed, which generalize those for the wedge geometry. Generally useful formulas for calculating Casimir energies in separable geometries are derived.