The Casimir effect for a stack of conductive planes

TL;DR

This paper investigates the Casimir effect in a stack of conductive planes, showing how different material response models significantly influence the distance dependence of the Casimir energy and force.

Contribution

It introduces a detailed analysis of the Casimir effect in layered conductive systems using both constant conductivity and Drude-Lorentz models, highlighting the impact on energy scaling and agreement with graphite cohesion.

Findings

Casimir energy scales as 1/d^3 with constant conductivity

Casimir energy scales as 1/d^{5/2} with Drude-Lorentz model

Calculated energies agree with experimental graphite cohesion data

Abstract

The Casimir interaction in a stack of equally spaced infinitely thin layers is investigated within the zero-frequency mode summation method. The response properties are considered to be described by a constant conductivity or by a Drude-Lorentz model with a finite set of oscillators consistent with the optical characteristics for graphite. It is found that the asymptotic distance dependence is affected significantly by the specific response. While the energy is $\sim 1/d^3$ for the constant conductivity model, the energy exhibits fractional dependence $\sim 1/d^{5/2}$ for the Drude-Lorentz description. The Casimir force on a plane is also strongly dependent upon the particular plane location in the stack. Furthermore, the calculated Casimir energy within the Drude-Lorentz model yields results in good agreement with measured cohesion energy in graphite.