A Universal Energy Functional for Trapped Fermi Gases with Large Scattering Length

TL;DR

This paper confirms and explicitly derives a universal energy functional for trapped Fermi gases with large scattering length, applicable to various smooth potentials, and calculates high-energy state occupations.

Contribution

It provides the first explicit form of the energy functional for such Fermi gases, extending its applicability beyond harmonic traps.

Findings

Confirmed Yoram Alhassid's conjecture.

Derived an explicit universal energy functional.

Calculated occupation probabilities of high energy states.

Abstract

Yoram Alhassid conjectured that the total energy of a harmonically trapped two-component Fermi gas with large scattering length is a linear functional of the occupation probabilities of single-particle energy eigenstates. We confirm his conjecture and derive the functional explicitly. We show that the functional applies to ALL smooth potentials having a minimum, not just harmonic traps. We also calculate the occupation probabilities of high energy states.