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

TL;DR

This paper investigates the mathematical properties and numerical computation of ground states in trapped unitary Fermi gases, highlighting the impact of quantum pressure on vortex lattice structures.

Contribution

It introduces a regularized normalized gradient flow method for computing ground states and analyzes the effects of quantum pressure and angular momentum rotation.

Findings

Quantum pressure significantly alters ground state properties.

Vortex lattices differ markedly from those in Bose-Einstein condensates.

Existence and uniqueness of ground states are established under various conditions.

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.