Casimir-Lifshitz pressure on cavity walls

TL;DR

This paper investigates the electromagnetic Casimir-Lifshitz pressure on spherical cavity walls, revealing that its sign depends on material properties and is geometry-independent under general conditions, extending previous theoretical work.

Contribution

The authors extend previous models to analyze the Casimir-Lifshitz pressure on cavity walls, demonstrating the sign's independence from geometry and connecting it to established theoretical results.

Findings

Pressure sign depends on response functions, not geometry.

Main result aligns with Dzyaloshinskii-Lifshitz-Pitaevskii theory.

Adaptation of invariant imbedding for inside scattering analysis.

Abstract

We extend our previous work on the electromagnetic Casimir-Lifshitz interaction between two bodies when one is contained within the other. We focus on the fluctuation-induced pressure acting on the cavity wall, which is assumed to be spherical. This pressure can be positive or negative depending on the response functions describing the bodies and the medium filling the cavity. However, we find that, under general hypotheses, the sign is independent of the geometry of the configuration. This result is based on the representation of the Casimir-Lifshitz energy in terms of transition operators. In particular, we study the components of these operators related to inside scattering amplitudes, adapting the invariant imbedding procedure to this unfamiliar scattering setup. We find that our main result is in agreement with the Dzyaloshinskii-Lifshitz-Pitaevskii result, which is obtained as a limiting case.