{"title":"BCS Critical Temperature on Half-Spaces","authors":"Barbara Roos, Robert Seiringer","doi":"10.1007/s00205-025-02088-x","DOIUrl":null,"url":null,"abstract":"<div><p>We study the BCS critical temperature on half-spaces in dimensions <span>\\(d=1,2,3\\)</span> with Dirichlet or Neumann boundary conditions. We prove that the critical temperature on a half-space is strictly higher than on <span>\\(\\mathbb {R}^d\\)</span>, at least at weak coupling in <span>\\(d=1,2\\)</span> and weak coupling and small chemical potential in <span>\\(d=3\\)</span>. Furthermore, we show that the relative shift in critical temperature vanishes in the weak coupling limit.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 2","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2025-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-025-02088-x.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Rational Mechanics and Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-025-02088-x","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We study the BCS critical temperature on half-spaces in dimensions \(d=1,2,3\) with Dirichlet or Neumann boundary conditions. We prove that the critical temperature on a half-space is strictly higher than on \(\mathbb {R}^d\), at least at weak coupling in \(d=1,2\) and weak coupling and small chemical potential in \(d=3\). Furthermore, we show that the relative shift in critical temperature vanishes in the weak coupling limit.
期刊介绍:
The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.