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The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime

We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in N (Gross–Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubo...

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Detalles Bibliográficos
Autores principales: Caraci, Cristina, Cenatiempo, Serena, Schlein, Benjamin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10328896/
https://www.ncbi.nlm.nih.gov/pubmed/37424535
http://dx.doi.org/10.1007/s00023-023-01278-1
Descripción
Sumario:We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in N (Gross–Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit [Formula: see text] .