Renormalized Bogoliubov Theory for the Nelson Model - Université de Technologie de Belfort-Montbeliard Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Renormalized Bogoliubov Theory for the Nelson Model

Résumé

We consider the time evolution of the renormalized Nelson model, which describes $N$ bosons linearly coupled to a quantized scalar field, in the mean-field limit of many particles $N\gg 1$ with coupling constant proportional to $N^{-1/2}$. First, we show that initial states exhibiting Bose-Einstein condensation for the particles and approximating a coherent state for the quantum field retain their structure under the many-body time evolution. Concretely, the dynamics of the reduced densities are approximated by solutions of two coupled PDEs, the Schr\"odinger-Klein-Gordon equations. Second, we construct a renormalized Bogoliubov evolution that describes the quantum fluctuations around the Schr\"odinger-Klein-Gordon equations. This evolution is used to extend the approximation of the evolved many-body state to the full norm topology. In summary, we provide a comprehensive analysis of the Nelson model that reveals the role of renormalization in the mean-field Bogoliubov theory.
Fichier principal
Vignette du fichier
2305.06722.pdf (889.3 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04098830 , version 1 (16-05-2023)

Identifiants

Citer

Marco Falconi, Jonas Lampart, Nikolai Leopold, David Mitrouskas. Renormalized Bogoliubov Theory for the Nelson Model. 2023. ⟨hal-04098830⟩
4 Consultations
7 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More