Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential

TL;DR

This paper extends the understanding of the correlation energy in a weakly interacting Fermi gas to larger interaction potentials, using advanced bosonization techniques to improve bounds and control in the analysis.

Contribution

It generalizes previous results to larger interaction potentials by relaxing the small norm assumption, employing approximate bosonization in three dimensions.

Findings

Derived the correlation energy for larger potentials.

Improved bounds on non-bosonizable terms.

Enhanced control of bosonization of kinetic energy.

Abstract

Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only $|\cdot| \hat{V} \in \ell^1 (\mathbb{Z}^3)$. Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy.