On the Ground State Energy of the Delta-Function Fermi Gas II: Further Asymptotics

TL;DR

This paper derives higher-order asymptotic expressions for the ground state energy of the delta-function Fermi gas at weak coupling, extending previous results with a versatile method applicable to convolution operators.

Contribution

It provides the second-order weak coupling asymptotics of the ground state energy, advancing the analytical understanding of the delta-function Fermi gas.

Findings

Derived ground state energy asymptotics to order γ^2

Extended previous weak coupling results

Introduced a general method for convolution operators

Abstract

Building on previous work of the authors, we here derive the weak coupling asymptotics to order $\gamma^2$ of the ground state energy of the delta-function Fermi gas. We use a method that can be applied to a large class of finite convolution operators.