{"title":"On Bose–Einstein condensates in the Thomas–Fermi regime","authors":"Daniele Dimonte, Emanuela L. Giacomelli","doi":"10.1007/s11040-022-09439-0","DOIUrl":null,"url":null,"abstract":"<div><p>We study a system of <i>N</i> trapped bosons in the Thomas–Fermi regime with an interacting pair potential of the form <span>\\( g_N N^{3\\beta -1} V(N^\\beta x) \\)</span>, for some <span>\\( \\beta \\in (0,1/3) \\)</span> and <span>\\( g_N \\)</span> diverging as <span>\\( N \\rightarrow \\infty \\)</span>. We prove that there is complete Bose–Einstein condensation at the level of the ground state and, furthermore, that, if <span>\\( \\beta \\in (0,1/6) \\)</span>, condensation is preserved by the time evolution.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"25 4","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-022-09439-0.pdf","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-022-09439-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 4
Abstract
We study a system of N trapped bosons in the Thomas–Fermi regime with an interacting pair potential of the form \( g_N N^{3\beta -1} V(N^\beta x) \), for some \( \beta \in (0,1/3) \) and \( g_N \) diverging as \( N \rightarrow \infty \). We prove that there is complete Bose–Einstein condensation at the level of the ground state and, furthermore, that, if \( \beta \in (0,1/6) \), condensation is preserved by the time evolution.
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