Classical Casimir interaction in the plane-sphere geometry

TL;DR

This paper analyzes the classical high-temperature Casimir interaction in a plane-sphere setup, revealing a universal behavior independent of conductivity and distinct from perfect reflector models, with implications for experimental testing.

Contribution

It demonstrates that the classical Casimir interaction in the Drude model is universal and independent of conductivity, providing a new universal function for the plane-sphere geometry.

Findings

The classical Casimir interaction is conductivity-independent in the Drude model.

A universal function describes the interaction depending only on the aspect ratio.

The asymptotic behavior fits polynomial expansions in logarithm of the aspect ratio.

Abstract

We study the Casimir interaction in the plane-sphere geometry in the classical limit of high temperatures. In this limit, the finite conductivity of the metallic plates needs to be taken into account. For the Drude model, the classical Casimir interaction is nevertheless found to be independent of the conductivity so that it can be described by a single universal function depending only on the aspect ratio $x=L/R$ where $L$ is the interplate distance and $R$ the sphere radius. This universal function differs from the one found for perfect reflectors and is in principle amenable to experimental tests. The asymptotic approach of the exact result to the Proximity Force Approximation appears to be well fitted by polynomial expansions in $\ln x$.