Electromagnetic vacuum of complex media II: the Lamb shift and the total vacuum energy

TL;DR

This paper investigates the electromagnetic vacuum energy in complex media, focusing on the Lamb shift, the total vacuum energy, and their relation to dielectric properties, revealing limitations of effective medium theories.

Contribution

It clarifies the relationship between vacuum energy, Lamb shift, and dielectric properties, highlighting the limitations of effective medium models in accounting for total vacuum energy.

Findings

The Lamb shift depends only on electrical susceptibility.

Effective medium bulk energy does not represent total vacuum energy.

Local field factors act as natural cutoffs for vacuum energy spectrum.

Abstract

We study the physical content of the electromagnetic vacuum energy of a random medium made of atomic electric dipoles. First, we evaluate the contribution of statistical fluctuations to the average total vacuum energy, which is made out of the integration of the variations of the Lamb shift with respect to the coupling constant. While the Lamb shift is a function of the electrical susceptibility only, the vacuum energy is generally not. Second, we make clear why the effective medium bulk energy does not account for the total vacuum energy of a molecular dielectric. Consequently, the Lamb shift does not derive from the effective medium bulk energy except at leading order in the molecular density. The local field factors provide natural cutoffs for the spectrum of the total vacuum energy at a wavelength of the order of the correlation length. Third, we investigate to what extent shifts in the spectrum of the dielectric constant may be attributed to the binding energy of a dielectric. In particular, in the continuum approximation we have found a relation between the electrostatic binding energy and the Lorentz-Lorenz shift. Nonetheless, we conclude that the knowledge of the spectrum of the refractive index is insufficient either to quantify the energy of radiative modes or to estimate the electrostatic binding energy of molecular clusters.