Collective Behavior of the Closed-Shell Fermi Gas

TL;DR

This paper introduces a novel collective coordinate approach to describe the ground state and oscillations of a two-component Fermi gas, revealing limitations of the Hartree-Fock approximation for certain excitations.

Contribution

It develops an unconventional reduction of the many-body problem to a one-dimensional Schroedinger equation using the hyperradius, providing more accurate predictions for the Fermi gas properties.

Findings

Ground state properties agree with Hartree-Fock results across various scattering lengths.

Breathing mode frequency deviates from Hartree-Fock predictions, indicating its limitations.

The approach accurately captures collective behavior of the Fermi gas.

Abstract

We propose an unconventional description for the ground state and collective oscillations of the two-component normal Fermi gas with two-body zero-range interactions. The many-body problem can be accurately reduced to a linear, one-dimensional Schroedinger equation in a single collective coordinate, the hyperradius R of the N-atom system which is the root mean square radius. The calculated properties of the Fermi gas ground state are shown to agree accurately with results from the Hartree-Fock (HF) approximation over a wide range of interspecies scattering lengths. The breathing mode excitation frequency deviates qualitatively from HF predictions, but we show that this reflects a failure of the HF approach for this observable.