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

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 $\eta$, of a flat mirror. The perturbative expansion is carried out up to the fourth order in the deformation $\eta$, 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.

10 pages, 3 figures. Version to appear in Phys. Rev. D

References in corpus (8)

• The Casimir effect within scattering theory
• Lateral Casimir force beyond the Proximity Force Approximation
• Casimir forces beyond the proximity approximation
• The proximity force approximation for the Casimir energy as a derivative expansion
• Non-contact gears: I. Next-to-leading order contribution to lateral Casimir force between corrugated parallel plates
• Derivative expansion of the electromagnetic Casimir energy for two thin mirrors
• Derivative expansion for the Casimir effect at zero and finite temperature in $d+1$ dimensions
• A Field Theoretic Approach to Roughness Corrections

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• Electrostatic Interaction due to Patch Potentials on Smooth Conducting Surfaces
• Perturbative Roughness Corrections to Electromagnetic Casimir Energies
• On the Casimir repulsion in sphere-plate geometry
• The effect of concurrent geometry and roughness in interacting surfaces