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arXiv · 2512.09479

Mathematical and numerical studies on ground states of trapped unitary Fermi gases

Yongyong Cai·Xinran Ruan·Yanzhi Zhang
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Abstract

We mathematically and numerically study the ground states of unitary Fermi gases. Starting from the three-dimensional nonlinear Schr\"{o}dinger 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.

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Yongyong Cai, Xinran Ruan, Yanzhi Zhang. 2025-12-10. Mathematical and numerical studies on ground states of trapped unitary Fermi gases. https://arxiv.org/abs/2512.09479

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