Casimir effect for Dirac lattices

TL;DR

This paper develops a theoretical framework to calculate the Casimir interaction between polarizable Dirac lattices, modeled as delta function potentials, using the TGTG-formula and scattering theory, with links to previous results and pairwise summation.

Contribution

It introduces a novel application of the TGTG-formula to Dirac lattices modeled by delta potentials, extending Casimir effect calculations to these systems.

Findings

Derived explicit formulas for Casimir interaction between Dirac lattices.

Analyzed limiting cases and connected results to previous models.

Discussed the relation to pairwise summation methods.

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.