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≪H 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.
Emig, Thorsten; Hanke, Andreas; Golestanian, Ramin; and Kardar, Mehran, "Probing the Strong Boundary Shape Dependence of the Casimir Force" (2001). Physics and Astronomy Faculty Publications and Presentations. 371.
Physical Review Letters