Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries

TL;DR

This paper provides exact calculations of electromagnetic Casimir forces involving parabolic cylinders and related geometries, highlighting boundary effects and geometric configurations, including the knife-edge limit and temperature dependence.

Contribution

It introduces a precise method for computing Casimir forces in complex parabolic and cylindrical geometries, extending to nonzero temperatures and various orientations.

Findings

Casimir forces computed for parabolic cylinder-plane and cylinder-cylinder configurations.

Boundary effects analyzed through the knife-edge limit and geometric rotations.

Results applicable to nonzero temperature scenarios.

Abstract

An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the "knife-edge" limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.