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arXiv · 1209.1000

Fourth order perturbative expansion for the Casimir energy with a slightly deformed plate

C. D. Fosco·F. C. Lombardo·F. D. Mazzitelli
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Abstract

We apply a perturbative approach to evaluate the Casimir energy for a massless real scalar field in 3+1 dimensions, subject to Dirichlet boundary conditions on two surfaces. One of the surfaces is assumed to be flat, while the other corresponds to a small deformation, described by a single function $η$, of a flat mirror. The perturbative expansion is carried out up to the fourth order in the deformation $η$, and the results are applied to the calculation of the Casimir energy for corrugated mirrors in front of a plane. We also reconsider the proximity force approximation within the context of this expansion.

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C. D. Fosco, F. C. Lombardo, F. D. Mazzitelli. 2012-11-08. Fourth order perturbative expansion for the Casimir energy with a slightly deformed plate. https://doi.org/10.1103/physrevd.86.125018

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