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 \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.