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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Autores principales: Caraci, Cristina, Cenatiempo, Serena, Schlein, Benjamin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Article
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
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author Caraci, Cristina
Cenatiempo, Serena
Schlein, Benjamin
author_facet Caraci, Cristina
Cenatiempo, Serena
Schlein, Benjamin
author_sort Caraci, Cristina
collection PubMed
description 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] .
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spelling pubmed-103288962023-07-09 The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime Caraci, Cristina Cenatiempo, Serena Schlein, Benjamin Ann Henri Poincare Article 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] . Springer International Publishing 2023-03-23 2023 /pmc/articles/PMC10328896/ /pubmed/37424535 http://dx.doi.org/10.1007/s00023-023-01278-1 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Caraci, Cristina
Cenatiempo, Serena
Schlein, Benjamin
The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime
title The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime
title_full The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime
title_fullStr The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime
title_full_unstemmed The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime
title_short The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime
title_sort excitation spectrum of two-dimensional bose gases in the gross–pitaevskii regime
topic Article
url 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
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