Casimir stress in and force on a metal slab in a planar cavity

TL;DR

This paper analyzes the Casimir stress and force on a metal slab within a planar cavity, highlighting how these depend on slab thickness, boundary conditions, and cavity properties using generalized Fresnel coefficients.

Contribution

It extends previous work by demonstrating the dependence of Casimir stress on the medium properties and cavity parameters, especially in the Lifshitz configuration.

Findings

Casimir stress in thin slabs strongly depends on boundary medium properties.

Stress in thick slabs becomes insensitive to external boundary conditions.

Force and stress vary with cavity width and mirror reflectivity.

Abstract

Emphasizing first the utility of the generalized Fresnel coefficients in the theory of the Casimir effect in planar cavities, we complement our previous discussion of the ordinary Casimir force on and the Casimir stress in a metal (plasma) slab in a planar cavity. We demonstrate strong dependence of the Casimir stress in a thin slab on properties of the bounding medium in the symmetric Lifshitz configuration. Contrary to this, the stress in a thick slab gradually becomes insensitive on external boundary conditions. We also consider the position dependence of the Casimir force on and stress in a thin metal slab in a planar cavity. Whereas the force per unit area on the slab strongly increases when it approaches a mirror the stress in the slab decreases and eventually changes the sign. Generally, the stress decreases with the cavity width and decreasing reflectivity of the mirrors.