Chiara Boccato, C. Brennecke, S. Cenatiempo, B. Schlein
{"title":"Gross-Pitaevskii极限下的Bogoliubov理论","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":"{\"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}","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}
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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