Casimir force between metallic mirrors

TL;DR

This paper analyzes how finite metallic conductivity affects the Casimir force and energy between metallic mirrors, providing explicit theoretical evaluations for experimental comparison, considering realistic dielectric responses of metals like Al, Au, and Cu.

Contribution

It offers detailed theoretical calculations of the Casimir force and energy reduction due to finite conductivity, using realistic dielectric functions, and compares different models with recent experimental data.

Findings

Finite conductivity reduces the Casimir force and energy.

Results differ significantly from recent publications when using optical data.

Theoretical evaluations aid in comparing experimental results with models.

Abstract

We study the influence of finite conductivity of metals on the Casimir effect. We put the emphasis on explicit theoretical evaluations which can help comparing experimental results with theory. The reduction of the Casimir force is evaluated for plane metallic plates. The reduction of the Casimir energy in the same configuration is also calculated. It can be used to infer the reduction of the force in the plane-sphere geometry through the `proximity theorem'. Frequency dependent dielectric response functions of the metals are represented either by the simple plasma model or, more accurately, by using the optical data known for the metals used in recent experiments, that is Al, Au and Cu. In the two latter cases, the results obtained here differ significantly from those published recently.