The cutoff-dependence of the Casimir force within an inhomogeneous medium

TL;DR

This paper investigates how the Casimir force in a piston geometry depends on the medium's inhomogeneity and the regularisation scheme, revealing cutoff dependence that challenges recent regularisation proposals.

Contribution

It demonstrates that in inhomogeneous media, the Casimir energy and pressure depend on high-frequency details, contrasting with the idealized case where they are cutoff-independent.

Findings

Casimir energy becomes cutoff-dependent in inhomogeneous media

Casimir pressure depends on large wave-vector behaviour

Challenges recent regularisation approaches for inhomogeneous media

Abstract

We consider the ground state energy of the electromagnetic field in a piston geometry. In the idealised case, where the piston and the walls of the chamber are taken as perfect mirrors, the Casimir pressure on the piston is finite and independent of the small scale physics of the media that compose the mirrors; the Casimir-energy of the system can be regularised and is cutoff-independent. Yet we find that, when the body of the piston is filled with an inhomogeneous dielectric medium, the Casimir energy is cutoff-dependent, and the value of the pressure is thus inextricably dependent on the detailed behaviour of the mirror and the medium at large wave-vectors. This result is inconsistent with recent proposals for regularising Casimir forces in inhomogeneous media.