Casimir Force at a Knife's Edge

Details Casimir Force at a Knife's Edge Casimir Force at a Knife's Edge

2009-10-24

arxiv.org/abs/0910.4649v4

Phys.Rev.D81:061701,2010

Physics

Quantum Physics

5 pages, 3 figures, uses RevTeX; v2: expanded conclusions; v3: fixed missing factor in Eq. (3) and incorrect diagram label (no

Scientific paper

10.1103/PhysRevD.81.061701

The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, $H$ and $\theta$, and the cylinder's parabolic radius $R$. As $H/R\to 0$, the proximity force approximation becomes exact. The opposite limit of $R/H\to 0$ corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.

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