Casimir energy for surfaces with constant conductivity

Abstract

We consider the vacuum energy of the electromagnetic field in systems characterized by a constant conductivity using the zeta-regularization approach. The interaction in two cases is investigated: two infinitely thin parallel sheets and an infinitely thin spherical shell. We found that the Casimir energy for the planar system is always attractive and it has the same characteristic distance dependence as the interaction for two perfect semi-infinite metals. The Casimir energy for the spherical shell depends on the inverse radius of the sphere, but it maybe negative or positive depending on the value of the conductivity. If the conductivity is less than a certain critical value, the interaction is attractive, otherwise the Casimir force is repulsive regardless of the spherical shell radius.

arXiv comment10 pages, 4 figures, Accepted in PRD

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Cited by in corpus (8)

• A Materials Perspective on Casimir and van der Waals Interactions
• The Casimir-Polder effect for a stack of conductive planes
• The quest for Casimir repulsion between Chern-Simons surfaces
• Casimir interaction of strained graphene
• The Casimir effect for a stack of conductive planes
• The normal Casimir force for lateral moving planes with isotropic conductivities
• Casimir-Lifshitz force for moving graphene
• Impurities in graphene and their influence on the Casimir interaction