A microscopic approach to Casimir and Casimir-Polder forces between metallic bodies

TL;DR

This paper investigates the microscopic origins of Casimir and Casimir-Polder forces between metallic bodies by analyzing many-body dispersion interactions, revealing the limitations of pairwise approximations and the significance of three-body effects.

Contribution

It derives explicit expressions for microscopic two- and three-body dispersion interactions in metals and applies them to evaluate macroscopic Casimir forces, highlighting the non-applicability of pairwise approximations.

Findings

Three-body interactions are repulsive and comparable in magnitude to two-body interactions.

Pairwise approximation is not valid for the studied geometries.

Microscopic analysis aligns with macroscopic results for nanoparticle/half-space geometry.

Abstract

We consider the Casimir-Polder interaction energy between a metallic nanoparticle and a metallic plate, as well as the Casimir interaction energy between two macroscopic metal plates, in terms of the many-body dispersion interactions between their constituents. Expressions for two- and three-body dispersion interactions between the microscopic parts of a real metal are first obtained, both in the retarded and non-retarded limits. These expressions are then used to evaluate, a compare each other, the overall two- and three-body contributions to the macroscopic Casimir-Polder and Casimir force, by summing up the contributions from the microscopic constituents of the bodies (metal nanoparticles), for two geometries: metal nanoparticle/half-space and half-space/half-space, where all the materials are assumed perfect conductors. In the case of nanoparticle/half-space, our results fully agree with those that can be extracted from the corresponding macroscopic results, and explicitly show the non-applicability of the pairwise approximation for the geometry considered. In both cases, we find that, while the overall two-body contribution yields an attractive force, the overall three-body contribution is repulsive. Also, they turn out to be of the same order, consistently with the known nonapplicability of the pairwise approximation. The issue of the rapidity of convergence of the many-body expansion is also briefly discussed.