On non-equilibrium photon distributions in the Casimir effect

TL;DR

This paper derives the photon distribution function in non-equilibrium stationary states of the electromagnetic field in Casimir geometries, confirming results with fluctuation electrodynamics and illustrating energy spectra.

Contribution

It provides a detailed derivation of photon distributions in Casimir setups using the Schwinger-Keldysh formalism, extending understanding of non-equilibrium quantum fields.

Findings

Photon distribution functions match Rytov fluctuation electrodynamics results.

Energy density spectra between plates are computed and visualized.

The formalism applies to stationary non-equilibrium states in Casimir geometries.

Abstract

The electromagnetic field in a typical geometry of the Casimir effect is described in the Schwinger-Keldysh formalism. The main result is the photon distribution function (Keldysh Green function) in any stationary state of the field. A two-plate geometry with a sliding interface in local equilibrium is studied in detail, and full agreement with the results of Rytov fluctuation electrodynamics is found. As an illustration, plots are shown for a spectrum of the energy density between the plates.