Universality in low-dimensional BCS theory

It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ and the critical temperature T c is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite...

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Bibliographic Details
Published inReviews in mathematical physics Vol. 36; no. 9
Main Authors Henheik, Joscha, Lauritsen, Asbjørn Bækgaard, Roos, Barbara
Format Journal Article
LanguageEnglish
Published Singapore World Scientific Publishing Company 01.10.2024
World Scientific Publishing Co. Pte., Ltd
Subjects
BCS theory
Coupling
Critical temperature
Density
Energy gap
critical temperature
energy gap
BCS universality
BCS theory
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ISSN0129-055X
1793-6659
DOI10.1142/S0129055X2360005X

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Summary:It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ and the critical temperature T c is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d = 1 , 2 and give an exemplary proof in the weak coupling limit.
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ISSN:0129-055X
1793-6659
DOI:10.1142/S0129055X2360005X