Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries

Noah Graham 1, Alexander Shpunt 2, Thorsten Emig 3, Sahand Jamal Rahi 2, 4, Robert L. Jaffe 2, Mehran Kardar 2

Physical Review D 83 (2011) 125007

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.

  • 1. Middlebury College,
    Middlebury Colleg
  • 2. Department of Physics,
    Massachusetts Institute of Technology
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 4. Center for Studies in Physics and Biology,
    The Rockefeller University