Probing the Strong Boundary Shape Dependence of the Casimir Force

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 $\delta E$ in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for $\delta E$ as a function of the ratio of the mean plate distance $H$, to the corrugation length $\lambda$: For $\lambda \ll H$ we find a slower decay $\sim H^{-4\mathrm{}}$, compared to the $H^{-5\mathrm{}}$ behavior predicted by the commonly used pairwise summation of van der Waals forces, which is valid only for $\lambda \gg H$.