Quantum Fields in a Dielectric: Langevin and Exact Diagonalization Approaches

TL;DR

This paper compares Langevin and Fano diagonalization methods for quantizing electromagnetic fields in dispersive, dissipative dielectrics, demonstrating their equivalence in form and correlation functions in thermal equilibrium.

Contribution

It establishes the equivalence of Langevin and Fano diagonalization approaches for quantum fields in dielectrics, providing a unified understanding of their results.

Findings

Both methods yield identical quantized electric and magnetic fields.

Correlation functions in thermal equilibrium are the same in both approaches.

The paper clarifies the relationship between dissipative quantum field models.

Abstract

We derive expressions for the quantum electromagnetic field in a dispersive and dissipative dielectric medium, treating the medium as a continuum. We compare the Langevin approach with the Fano diagonalization procedure for the coupled system composed of the electromagnetic field, the dielectric medium, and the reservoir. In particular, we show that the quantized electric and magnetic fields obtained in both methods have exactly the same form. More generally, in thermal equilibrium, correlation functions computed in both methods are identical.