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

References in corpus (7)

• The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem
• Fluctuation induced quantum interactions between compact objects and a plane mirror
• Multiple Scattering Methods in Casimir Calculations
• Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation
• Exact Casimir Interaction Between Semitransparent Spheres and Cylinders
• Monoatomically thin polarizable sheets
• Dirac lattices, zero-range potentials and self adjoint extension