Probing the Strong Boundary Shape Dependence of the Casimir Force

Abstract

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 δ\cal E in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for δ\cal E as a function of the ratio of the mean plate distance H, to the corrugation length λ: For λ\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 λ\gg H.

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

References in corpus (2)

• Temperature dependence of the Casimir force between real metals: problems and approach to their resolution
• Modified critical correlations close to modulated and rough surfaces

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