The Hawking effect in dielectric media and the Hopfield model

TL;DR

This paper analyzes the Hawking effect in dielectric media using the Hopfield model, deriving analytical results for spontaneous thermal emission and revealing a universal thermality mechanism in optical and acoustic black holes.

Contribution

It introduces a simplified Hopfield model with space-time dependent parameters to analytically compute spontaneous thermal emission in dielectric black holes.

Findings

Analytical calculation of spontaneous thermal emission in dielectric black holes.

Derivation of generalized Manley-Rowe identities in quantum scattering.

Identification of a universal thermality mechanism between optical and acoustic black holes.

Abstract

We consider the so-called Hopfield model for the electromagnetic field in a dielectric dispersive medium in a framework in which one allows a space-time dependence of microscopic parameters, aimed to a phenomenological description of a space-time varying dielectric perturbation induced by means of the Kerr effect. We discuss the analogue Hawking effect, by first analyzing the geometrical optics for the Hopfield model, and then by introducing a simplified model which has the bonus to avoid many difficulties which are involved in the full Hopfield model, still keeping the same dispersion relation. Amplitude calculations are indicated, and generalized Manley-Rowe identities are derived in a quantum scattering theory framework. Our main result is an analytical calculation of the spontaneous thermal emission in the single-branch case, which is provided non perturbatively for the first time in the framework of dielectric black holes. An universal mechanism for thermality between optical black holes and acoustic black holes is also pointed out.