Electromagnetic Energy, Absorption, and Casimir Forces. Inhomogeneous Dielectric Media

TL;DR

This paper derives an exact formula for electromagnetic energy density and Casimir force in inhomogeneous, absorbing dielectric media, explicitly including dissipation through oscillator-reservoir coupling, advancing the understanding of Casimir effects in realistic materials.

Contribution

It provides a formal, exact expression for energy density and Casimir force in inhomogeneous, dissipative media, explicitly incorporating absorption effects.

Findings

Derived a general formula for energy density in absorbing media

Obtained Casimir force density considering dissipation explicitly

Connected energy and force densities to oscillator interactions and Poynting's theorem

Abstract

A general, exact formula is derived for the expectation value of the electromagnetic energy density of an inhomogeneous absorbing and dispersive dielectric medium in thermal equilibrium, assuming that the medium is well approximated as a continuum. From this formula we obtain the formal expression for the Casimir force density. Unlike most previous approaches to Casimir effects in which absorption is either ignored or admitted implicitly through the required analytic properties of the permittivity, we include dissipation explicitly via the coupling of each dipole oscillator of the medium to a reservoir of harmonic oscillators. We obtain the energy density and the Casimir force density as a consequence of the van der Waals interactions of the oscillators and also from Poynting's theorem.