{"title":"格罗斯-皮塔耶夫斯基制度及其他中的对角玻色气体","authors":"Morris Brooks","doi":"10.1007/s00220-024-05199-w","DOIUrl":null,"url":null,"abstract":"<div><p>We present a novel approach to the Bogoliubov theory of dilute Bose gases, allowing for an elementary derivation of the celebrated Lee–Huang–Yang formula in the Gross–Pitaevskii regime. Furthermore, we identify the low lying excitation spectrum beyond the Gross–Pitaevskii scaling, extending a recent result (Brennecke et al. in Rev Math Phys 34, 2022) to significantly more singular scaling regimes. Finally, we provide an upper bound on the ground state energy in the Gross–Pitaevskii regime that captures the correct expected order of magnitude beyond the Lee–Huang–Yang formula.\n</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05199-w.pdf","citationCount":"0","resultStr":"{\"title\":\"Diagonalizing Bose Gases in the Gross–Pitaevskii Regime and Beyond\",\"authors\":\"Morris Brooks\",\"doi\":\"10.1007/s00220-024-05199-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present a novel approach to the Bogoliubov theory of dilute Bose gases, allowing for an elementary derivation of the celebrated Lee–Huang–Yang formula in the Gross–Pitaevskii regime. Furthermore, we identify the low lying excitation spectrum beyond the Gross–Pitaevskii scaling, extending a recent result (Brennecke et al. in Rev Math Phys 34, 2022) to significantly more singular scaling regimes. Finally, we provide an upper bound on the ground state energy in the Gross–Pitaevskii regime that captures the correct expected order of magnitude beyond the Lee–Huang–Yang formula.\\n</p></div>\",\"PeriodicalId\":522,\"journal\":{\"name\":\"Communications in Mathematical Physics\",\"volume\":\"406 1\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-12-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00220-024-05199-w.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00220-024-05199-w\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-024-05199-w","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Diagonalizing Bose Gases in the Gross–Pitaevskii Regime and Beyond
We present a novel approach to the Bogoliubov theory of dilute Bose gases, allowing for an elementary derivation of the celebrated Lee–Huang–Yang formula in the Gross–Pitaevskii regime. Furthermore, we identify the low lying excitation spectrum beyond the Gross–Pitaevskii scaling, extending a recent result (Brennecke et al. in Rev Math Phys 34, 2022) to significantly more singular scaling regimes. Finally, we provide an upper bound on the ground state energy in the Gross–Pitaevskii regime that captures the correct expected order of magnitude beyond the Lee–Huang–Yang formula.
期刊介绍:
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.