| Summary: | 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<<h a="" approximately="" behavior="" by="" commonly="" compared="" decay="" der="" find="" for="" forces,="" h(-4),="" h(-5)="" is="" lambda="" of="" only="" pairwise="" predicted="" slower="" summation="" the="" to="" used="" valid="" van="" waals="" we="" which="">>H.</h>
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