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arXiv · 2301.05621

Universality in low-dimensional BCS theory

Joscha Henheik·Asbjørn Bækgaard Lauritsen·Barbara Roos
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Abstract

It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature $\Xi$ 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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Joscha Henheik, Asbjørn Bækgaard Lauritsen, Barbara Roos. 2023-01-13. Universality in low-dimensional BCS theory. https://doi.org/10.1142/s0129055x2360005x

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