Casimir forces in inhomogeneous media: renormalization and the principle of virtual work

Abstract

We calculate the Casimir forces in two configurations, namely, three parallel dielectric slabs and a dielectric slab between two perfectly conducting plates, where the dielectric materials are dispersive and inhomogeneous in the direction perpendicular to the interfaces. A renormalization scheme is proposed consisting of subtracting the effect of one interface with a single inhomogeneous medium. Some examples are worked out to illustrate this scheme. Our method always gives finite results and is consistent with the principle of virtual work; it extends the Dzyaloshinskii-Lifshitz-Pitaeveskii force to inhomogeneous media.

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• Vacuum energy density and pressure inside a soft wall
• Casimir energy due to inhomogeneous thin plates
• Casimir self-energy of a δ-δ' sphere
• Van der Waals chain: a simple model for Casimir forces in dielectrics
• Scarf for Lifshitz
• Casimir energy for spinor fields with $\delta$-shell potentials
• Casimir-Lifshitz pressure on cavity walls