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 δE in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for δE as a function of the ratio of the mean plate distance H, to the corrugation length λ: For λ≪A we find a slower decay ∼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≫H. © 2001 The American Physical Society.