The Casimir effect in the sphere-plane geometry

TL;DR

This paper investigates the Casimir force between a sphere and a plane, analyzing how geometry, temperature, and material imperfections influence the interaction, and assessing the accuracy of the Proximity Force Approximation.

Contribution

It provides detailed analytical and numerical calculations of the Casimir effect in the sphere-plane geometry, including effects of imperfect reflection and temperature, improving understanding beyond PFA.

Findings

PFA accuracy is affected by imperfect reflection.

Finite conductivity and temperature significantly influence the Casimir force.

Geometry and curvature interplay with material properties to modify the force.

Abstract

We present calculations of the Casimir interaction between a sphere and a plane, using a multipolar expansion of the scattering formula. This configuration enables us to study the nontrivial dependence of the Casimir force on the geometry, and its correlations with the effects of imperfect reflection and temperature. The accuracy of the Proximity Force Approximation (PFA) is assessed, and is shown to be affected by imperfect reflexion. Our analytical and numerical results at ambient temperature show a rich variety of interplays between the effects of curvature, temperature, finite conductivity, and dissipation.