Electromagnetic Casimir forces of parabolic cylinder and knife-edge geometries

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.

Electromagnetic Casimir energy of a disk opposite a plane

“…By relating the scattering matrix for a collection of spheres [14] or disks [15] to the objects' individual scattering matrices, Bulgac, Magierski, and Wirzba were also able to use this result to investigate the scalar and fermionic Casimir effect for disks and spheres [16][17][18]. A more general formalism, developed in [19][20][21], has made it possible to extend these results to other coordinate systems, an approach that is particularly useful for geometries, such as the ones we consider here, with edges and tips [22][23][24][25][26][27][28][29][30]. It can also be applied to dilute objects in perturbation theory [31] and extended to efficient, general-purpose numerical calculations [32]; a review and further references can be found in Ref.…”

Unifying Theory for Casimir Forces: Bulk and Surface Formulations

“…These approaches are limited to scalar fields with Dirichlet or Neumann boundary conditions [24], or the electromagnetic field with perfectly conducting boundary conditions [25], with the exception of a similar approach for dielectric boundaries [26]. However, such analytical (and semi-analytical) methods have been restricted to symmetric and simple shapes, like spheres, cylinders or ellipsoids [27][28][29][30][31]. Geometries where parts of the bodies interpenetrate, such as those shown in Figure 1a, cannot be studied with scattering approaches.…”

Casimir effect for a Bose–Einstein condensate inside a cylindrical tube

“…Systems with different geometry of the confining plates, eg. sinusoidally corrugated geometry, eccentric-cylindrical geometry, grating geometry, parabolic geometry, concentric-cylindrical geometry, etc, have also been studied both experimentally and theoretically, in the context of the quantum Casimir force [8][9][10][11][12][13]. Casimir effects for classical and quantum fluids (specially for superfluid 4 He) in slab geometry have been the subject of a number of experimental and theoretical works [2,6,[14][15][16][17].…”