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arXiv · 0910.4649

Casimir Force at a Knife's Edge

Noah Graham·Alexander Shpunt·Thorsten Emig·Sahand Jamal Rahi·Robert L. Jaffe·Mehran Kardar
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Abstract

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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Noah Graham, Alexander Shpunt, Thorsten Emig, Sahand Jamal Rahi, Robert L. Jaffe, Mehran Kardar. 2009-10-24. Casimir Force at a Knife's Edge. https://doi.org/10.1103/physrevd.81.061701

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