Electromagnetic energy, absorption, and Casimir forces: Uniform dielectric media in thermal equilibrium

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.033812· OSTI ID:21413310

Rosa, F S. S.; Dalvit, D A. R.; Milonni, P W ^[1]

---

1. Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

The derivation of Casimir forces between dielectrics can be simplified by ignoring absorption, calculating energy changes due to displacements of the dielectrics, and only then admitting absorption by allowing permittivities to be complex. As a first step toward a better understanding of this situation we consider in this article the model of a dielectric as a collection of oscillators, each of which is coupled to a reservoir giving rise to damping and Langevin forces on the oscillators and a noise polarization acting as a source of a fluctuating electromagnetic field in the dielectric. The model leads naturally to expressions for the quantized electric and magnetic fields that are consistent with those obtained in approaches that diagonalize the coupled system of oscillators for the dielectric medium, the reservoir, and the electromagnetic field. It also results in a fluctuation-dissipation relation between the noise polarization and the imaginary part of the permittivity; comparison with the Rytov fluctuation-dissipation relation employed in the well-known Lifshitz theory for the van der Waals (or Casimir) force shows that the Lifshitz theory is actually a classical stochastic electrodynamical theory. The approximate classical expression for the energy density in a band of frequencies at which absorption in a dielectric is negligible is shown to be exact as a spectral thermal equilibrium expectation value in quantum electrodynamic theory. Our main result is the derivation of an expression for the QED energy density of a uniform dispersive, absorbing media in thermal equilibrium. The spectral density of the energy is found to have the same form with or without absorption. We also show how the fluctuation-dissipation theorem ensures a detailed balance of energy exchange between the (absorbing) medium, the reservoir, and the electromagnetic field in thermal equilibrium.

• OSTI ID: 21413310
• Journal Information: Physical Review. A, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.033812; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BERYLLIUM COMPLEXES
CASIMIR EFFECT
COMPARATIVE EVALUATIONS
DIELECTRIC MATERIALS
ELECTROMAGNETIC FIELDS
ENERGY ABSORPTION
ENERGY DENSITY
FLUCTUATIONS
NOISE
OSCILLATORS
PERMITTIVITY
POLARIZATION
QUANTUM ELECTRODYNAMICS
SPECTRAL DENSITY
STOCHASTIC PROCESSES
THERMAL EQUILIBRIUM
VAN DER WAALS FORCES
ABSORPTION
ALKALINE EARTH METAL COMPLEXES
CALCULATION METHODS
COMPLEXES
DIELECTRIC PROPERTIES
ELECTRICAL PROPERTIES
ELECTRODYNAMICS
ELECTRONIC EQUIPMENT
EQUILIBRIUM
EQUIPMENT
EVALUATION
FIELD THEORIES
FUNCTIONS
MATERIALS
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
SORPTION
SPECTRAL FUNCTIONS
VARIATIONS