Chiara Boccato, C. Brennecke, S. Cenatiempo, B. Schlein
{"title":"Bogoliubov theory in the Gross–Pitaevskii limit","authors":"Chiara Boccato, C. Brennecke, S. Cenatiempo, B. Schlein","doi":"10.4310/ACTA.2019.V222.N2.A1","DOIUrl":null,"url":null,"abstract":"We consider Bose gases consisting of $N$ particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of the order $N^{-1}$(Gross-Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as $N \\to \\infty$. Our results confirm Bogoliubov's predictions.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":" ","pages":""},"PeriodicalIF":4.9000,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"89","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/ACTA.2019.V222.N2.A1","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 89
Abstract
We consider Bose gases consisting of $N$ particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of the order $N^{-1}$(Gross-Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as $N \to \infty$. Our results confirm Bogoliubov's predictions.
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