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 deltaE 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 << H we find a slower decay similar toH(-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 >> H.