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

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.

Comments added, some sections rewritten

References in corpus (8)

• The cooperative Lamb shift in an atomic nanolayer
• Casimir-Polder forces: A non-perturbative approach
• Casimir Forces between Compact Objects: I. The Scalar Case
• Local-field correction to the spontaneous decay rate of atoms embedded in bodies of finite size
• Local-field correction to one- and two-atom van der Waals interactions
• Quantum Multiple Scattering
• Casimir-Polder interaction of atoms with magnetodielectric bodies
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Cited by in corpus (7)

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• Casimir Momentum of a Chiral Molecule in a Magnetic Field
• Casimir-Polder induced Rabi oscillations
• Quantum corrections to the classical electrostatic interaction between induced dipoles
• On the coherent effect of vacuum fluctuations on driven atoms
• Superradiant cascade emissions in an atomic ensemble via four-wave mixing
• Resonant scattering of a single atom with gain: a wavefunction-diagrammatic approach