Weizsacker energy of unitary Fermi gas in a harmonic trap

TL;DR

This paper develops a universal method to establish rigorous lower bounds for the Weizsacker energy in a unitary Fermi gas confined in a harmonic trap, providing insights into density functional theory accuracy at unitarity.

Contribution

It introduces a universal approach for constructing rigorous lower bounds to the Weizsacker energy and applies it to a few-fermion system at unitarity, enhancing understanding of DFT in such regimes.

Findings

Derived rigorous lower bounds for Weizsacker energy.

Established bounds for DFT ground state energy within LDA.

Provided estimates for the accuracy of the method.

Abstract

The universal method of construction of the rigorous lower bounds to the Weizsacker energy is presented. We study a few-fermion systemat the unitarity. Upper and lower bounds to the density functional theory(DFT) ground state energy within the local density approximation (LDA) aregiven. Therigorous lower bounds to the accuracy of the method are derived.