Semi-classical limit of an attractive Fermi gas in one or two dimensions

TL;DR

This paper investigates the ground-state properties of an attractive Fermi gas in one or two dimensions, demonstrating convergence to a Thomas-Fermi energy and ground state in the large particle number limit.

Contribution

It establishes the semi-classical limit of an attractive Fermi gas, proving energy and state convergence in the large N regime for 1D and 2D systems.

Findings

Ground state energy converges to Thomas-Fermi energy as N increases.

Ground states converge in the sense of Husimi functions.

Results apply to short-range attractive interactions in low dimensions.

Abstract

We study the ground-state of a Fermi gas with short range attrative interactions in one or two dimensions. N fermions are placed in a confining potential, and interact with each other through a negative potential, whose range is larger than the typical distance between particles. We show the convergence of the ground state energy of the Hamiltonian to a Thomas-Fermi energy in the large N limit. Furthermore, we prove convergence of the ground states, in the sense of their Husimi functions.