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.
Braun, Oliver, et al. “Probing Molecular Free Energy Landscapes by Periodic Loading.” Physical Review Letters, vol. 93, no. 15, American Physical Society, Oct. 2004, p. 158105, doi:10.1103/PhysRevLett.93.158105.
Physical Review Letters