{"title":"Norm convergence of confined fermionic systems at zero temperature","authors":"Esteban Cárdenas","doi":"10.1007/s11005-024-01785-0","DOIUrl":null,"url":null,"abstract":"<div><p>The semi-classical limit of ground states of large systems of fermions was studied by Fournais et al. (Calc Var Partial Differ Equ 57:105, 2018). In particular, the authors prove weak convergence toward classical states associated with the minimizers of the Thomas–Fermi functional. In this paper, we revisit this limit and show that under additional assumptions—and, using simple arguments—it is possible to prove that strong convergence holds in relevant normed spaces.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01785-0","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The semi-classical limit of ground states of large systems of fermions was studied by Fournais et al. (Calc Var Partial Differ Equ 57:105, 2018). In particular, the authors prove weak convergence toward classical states associated with the minimizers of the Thomas–Fermi functional. In this paper, we revisit this limit and show that under additional assumptions—and, using simple arguments—it is possible to prove that strong convergence holds in relevant normed spaces.
期刊介绍:
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.