Casimir effect for Dirac lattices

Abstract

We consider polarizable sheets, which recently received some attention, especially in context of the dispersion interaction of thin sheets like graphene. These sheets are modeled by a collection of delta function potentials and resemble "zero range potentials", known in quantum mechanics. We develop a theoretical description and apply the so-called "TGTG"-formula to calculate the interaction of two such lattices. Thereby we make use of the formulation of the scattering of waves off such sheets provided earlier. We consider all limiting cases, providing link to earlier results. Also, we discuss the relation to the pairwise summation method.

12 pages, 4 figures

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Cited by in corpus (7)

• Casimir Energy for concentric $\delta$-${\delta }^{\prime }$ spheres
• Band spectra of periodic hybrid $\delta$-${\delta }^{\prime }$ structures
• The role of scalar current coupling along surfaces
• Vacuum polarization with zero-range potentials on a hyperplane
• The Casimir energy anomaly for a point interaction
• On finite temperature Casimir effect for Dirac lattices
• Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric Two Point Interactions