Negative frequencies and negative norms in analogue Hawking radiation systems

Raul Aguero-Santacruz; David Bermudez

doi:10.5802/crphys.177

Article de recherche

Negative frequencies and negative norms in analogue Hawking radiation systems
[Fréquences négatives et normes négatives dans les systèmes analogiques de rayonnement de Hawking]

Raul Aguero-Santacruz ¹ ; David Bermudez ¹

¹ Department of Physics, Cinvestav, A.P. 14-740, 07000 Ciudad de México, Mexico

Comptes Rendus. Physique, Online first (2024), pp. 1-17.

Résumé
Abstract

Dans ce travail, nous étudions les concepts fondamentaux du rayonnement de Hawking dans les systèmes astrophysiques et analogiques. Nous nous concentrons sur les fréquences négatives et les normes négatives : leur définition, leur relation et leur rôle dans le processus de création de particules de l’effet Hawking. Nous caractérisons la relation de dispersion par les signes de la fréquence et de la norme. Nous concluons que le cadre le plus naturel pour étudier l’effet Hawking est celui dans lequel l’horizon est statique, où le signe de la norme peut être rendu égal au signe de la fréquence décalée par effet Doppler dans ce cadre. Nous utilisons comme exemples les quatre systèmes analogues expérimentaux les plus réussis : les vagues d’eau, les condensats de Bose–Einstein, les fluides à polaritons et les fibres optiques.

In this work, we study the core concepts of Hawking radiation in the astrophysical and analogue systems. We focus on negative frequencies and negative norms: their definition, their relationship, and their role in the particle creation process of the Hawking effect. We characterize the dispersion relation by the signs of the frequency and the norm. We conclude that the most natural frame for studying the Hawking effect is that in which the horizon is static, where the sign of the norm can be made equal to the sign of the Doppler-shifted frequency in that frame. We use as examples the four most successful experimental analogue systems: water waves, Bose–Einstein condensates, polaritons fluids, and optical fibers.

Reçu le : 2023-10-07
Révisé le : 2023-12-08
Accepté le : 2023-12-21
Première publication : 2024-04-04

DOI : 10.5802/crphys.177

Keywords: analogue gravity, negative frequency, negative norm, Hawking radiation, optical pulse, Bose–Einstein condensate, polariton
Mot clés : gravité analogique, fréquence négative, norme négative, rayonnement de Hawking, impulsion optique, condensat de Bose–Einstein, polariton

Affiliations des auteurs :

Raul Aguero-Santacruz ¹ ; David Bermudez ¹

¹ Department of Physics, Cinvestav, A.P. 14-740, 07000 Ciudad de México, Mexico

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Negative frequencies and negative norms in analogue {Hawking} radiation systems},
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Raul Aguero-Santacruz; David Bermudez. Negative frequencies and negative norms in analogue Hawking radiation systems. Comptes Rendus. Physique, Online first (2024), pp. 1-17. doi : 10.5802/crphys.177.

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