Ground state energy of the dilute spin-polarized Fermi gas: Lower bound

TL;DR

This paper establishes a lower bound on the ground state energy of a dilute spin-polarized Fermi gas, accounting for interaction effects via the p-wave scattering length, aligning with existing upper bounds.

Contribution

It provides a rigorous lower bound on the energy that captures the leading interaction correction, advancing understanding of dilute Fermi gases.

Findings

Lower bound matches the upper bound from previous work.

Correction depends on the p-wave scattering length.

Results improve theoretical understanding of dilute Fermi gases.

Abstract

We prove a lower bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. This correction depends on the $p$-wave scattering length of the interaction and matches the corresponding upper bound in [J. Funct. Anal. 286.7 (2024), p. 110320].