Repulsive fermions and shell effects on the surface of a sphere

Year: 2026

Authors: Frigato L., Bardin A., Salasnich L.

Autors Affiliation: Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Ist Nazl Fis Nucl INFN, Sez Padova, Via Marzolo 8, I-35131 Padua, Italy; Consiglio Nazl Ric CNR, Ist Nazl Ott INO, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.

Abstract: In recent years, ultracold atomic gases confined in curved geometries have attracted considerable theoretical interest. This is motivated by recent realizations of bubble traps in microgravity conditions, which open the possibility of investigating quantum many-body physics beyond the conventional flat-space paradigm. The theoretical interest up to now was mainly focused on Bose gases and their phenomenology, and the study of Fermi gases has been left behind. In this paper, we investigate a two-component repulsive Fermi gas constrained to the surface of a sphere at finite temperature. We first analyze the noninteracting case, showing how the intrinsic geometrical features of the spherical surface give rise to a shell structure and modify the low-temperature thermodynamics compared to the flat two-dimensional gas. Repulsive interactions are then considered through an effective path-integral approach within a Hartree-Fock mean-field approximation, enabling us to derive the grand canonical potential and to regularize the associated Matsubara summation. We then investigate the stability of the spin-balanced state and obtain the finite-temperature Stoner criterion for fermions on a sphere, highlighting the interplay between the repulsive interactions and shell effects.

Journal/Review: PHYSICAL REVIEW A

Volume: 113 (5)      Pages from: 53319-1  to: 53319-12

More Information: The authors are grateful to Cesare Vianello, Andrea Tononi, and Giacomo Gradenigo for helpful discussions and valuable suggestions. L.F. acknowledges the project Frontiere Quantistiche within the 2023 funding program Dipartimenti di Eccellenza of the Italian Ministry for Universities and Research. A.B. acknowledges the European Quantum Flagship Project PASQuanS 2. L.S. is partially supported by the European Union-NextGenerationEU within the National Center for HPC, Big Data, and Quantum Computing (Project No. CN00000013, CN1 Spoke 10: Quantum Computing). L.F., A.B., and L.S. are partially supported by Iniziativa Specifica Quantum of Istituto Nazionale di Fisica Nucleare (INFN) and the PRIN 2022 project Quantum Atomic Mixtures: Droplets, Topological Structures, and Vortices.
KeyWords: Bose-einstein Condensation; Gas; Superfluid
DOI: 10.1103/2jsk-6yf1