Work

Mathematical and Numerical Studies on Ground States of Trapped Unitary Fermi Gases

Year: 2026

Type: article

Abstract: . We mathematically and numerically study the ground states of unitary Fermi gases. Starting from the three-dimensional nonlinear Schrödinger equation that contains a quantum pressure term and an angular momentum rotation term, we first nondimensionalize the equation and then obtain its one-dimensional and two-dimensional counterparts in some limit regimes of the external potentials. Existence and uniqueness of the ground states of the unitary Fermi gases are studied with/without the angular momentum rotation term. We present a regularized normalized gradient flow method to compute the ground states of trapped unitary Fermi gases. Our numerical results show that the quantum pressure term has a significant effect on the ground state properties. Specifically, with the presence of the quantum pressure term, the vortex lattices are very different from those obtained in conventional Bose–Einstein condensation.

Source: SIAM Journal on Applied Mathematics

DOI: 10.1137/25m1830067

Authors: Yongyong Cai, Xinran Ruan, Yanzhi Zhang

Institutions: Beijing Normal University, Capital Normal University, Missouri University of Science and Technology

Language: English

Topic: Cold Atom Physics and Bose-Einstein Condensates

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China

Awards: G1831493023, Mathematical and Computational Studies on Bose-Einstein Superfluid, G7708759533