Probing the Strong Boundary Shape Dependence of the Casimir Force

Details Probing the Strong Boundary Shape Dependence of the Casimir Force Probing the Strong Boundary Shape Dependence of the Casimir Force

2001-06-03

arxiv.org/abs/cond-mat/0106028v2

Phys.Rev.Lett. 87 (2001) 260402

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures, accepted for publication in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.87.260402

We study the geometry dependence of the Casimir energy for deformed metal plates by a path integral quantization of the electromagnetic field. For the first time, we give a complete analytical result for the deformation induced change in Casimir energy \delta\cal E in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for \delta\cal E as a function of the ratio of the mean plate distance H, to the corrugation length \lambda: For \lambda \ll H we find a {\em slower} decay \sim H^{-4}, compared to the H^{-5} behavior predicted by the commonly used pairwise summation of van der Waals forces, which is valid only for \lambda \gg H.

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