https://doi.org/10.1140/epja/s10050-023-01077-6
Regular Article - Theoretical Physics
Corrections to local-density approximation for superfluid trapped fermionic atoms from the Wigner-Kirkwood
expansion
1
Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405, Orsay, France
2
Université Grenoble Alpes, CNRS, LPMMC, 38000, Grenoble, France
3
Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos, Facultat de Física, Universitat de Barcelona, Diagonal 645, 08028, Barcelona, Spain
4
Institut Menorquí d’Estudis, Camí des Castell 28, 07702, Maó, Spain
b
michael.urban@ijclab.in2p3.fr
c
xavier@fqa.ub.edu
Received:
4
June
2023
Accepted:
3
July
2023
Published online:
19
July
2023
A semiclassical second-order differential equation for the inhomogeneous local gap is derived from a strict second-order
expansion of the anomalous pairing tensor and compared with a similar equation given in Simonucci and Strinati (in Phys Rev B 89:054511, 2014). The second-order normal density matrix is given as well. Several extra gradient terms are revealed. Second-order expressions at finite temperature are given for the first time. The corresponding Ginzburg–Landau equation is presented and it is shown that, compared to the equation of Baranov and Petrov (in Phys Rev A 58:R801, 1998), an extra second-order gradient term is present. Applications to the pairing gap in cold atoms in a harmonic trap are discussed.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.