Casimir force at a knife's edge

• Main Authors: Graham, Noah (Author), Shpunt, Alexander Anatoly (Contributor), Emig, Thorsten (Contributor), Rahi, Sahand Jamal (Contributor), Jaffe, Robert L. (Contributor), Kardar, Mehran (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2010-09-20T19:00:54Z.
• Subjects: Article
• Online Access: Get fulltext

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 θ, and the cylinder's parabolic radius R. As H/R→0, the proximity force approximation becomes exact. The opposite limit of R/H→0 corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.
National Science Foundation (Grants No. PHY05-5533, No. PHY08-55426, and No. DMR-08-03315)
United States. Defense Advanced Research Projects Agency (Contract No. S-000354)
Deutsche Forschungsgemeinschaft (Grant No. EM70/3)
United States. Dept. of Energy (Cooperative research agreement No. DFFC02-94ER40818)