Universal Casimir interactions in the sphere-sphere geometry

TL;DR

This paper investigates universal Casimir interactions in sphere-sphere configurations, highlighting their independence from material details and their dependence on geometry, especially in the high-temperature and long-distance regimes.

Contribution

It introduces a dual analysis of Casimir interactions for spheres modeled by Drude metals and dielectric spheres in salted solutions, emphasizing their universal features.

Findings

Casimir interactions are dominated by low-frequency thermal fluctuations.

These interactions are independent of specific dielectric properties.

They exhibit universal dependence on geometric dimensions.

Abstract

We study universal Casimir interactions in two configurations which appear as dual to each other. The first involves spheres described by the Drude model and separated by vacuum while the second involves dielectric spheres immersed in a salted solution at distances larger than the Debye screening length. In both cases, the long-distance limit, equivalently the high-temperature limit, is dominated by the effect of low-frequency transverse magnetic thermal fluctuations. They are independent of the details of dielectric functions of materials, due to the finite conductivity of metals in the former case and of salted water in the latter one. They also show universality properties in their dependence on geometric dimensions, in relation to an approximate conformal invariance of the reduced free energy.