Thermal Casimir effect for Drude metals in the plane-sphere geometry

TL;DR

This paper presents a comprehensive calculation of the thermal Casimir effect between a plane and a sphere, accounting for curvature, temperature, and material properties, relevant for precise experimental setups.

Contribution

It develops a scattering formula applicable to arbitrary sphere sizes, distances, temperatures, and dielectric functions, advancing the theoretical understanding of Casimir interactions.

Findings

Curvature, temperature, and conductivity significantly influence the Casimir force.

The scattering formula is valid for a wide range of parameters and materials.

Results highlight complex interplay between physical effects in metallic surfaces.

Abstract

We compute the Casimir interaction between a plane and a sphere, the configuration employed in the most precise experiments. The scattering formula is developed by taking a suitably chosen plane-wave and multipole basis and is valid for arbitrary values of the sphere radius, inter-plate distance, temperature and arbitrary dielectric functions for both sphere and plate. Our analytical and numerical results for metallic surfaces show a non-trivial interplay between the effects of curvature, temperature, finite conductivity and dissipation.