On the ground state energy of the delta-function Bose gas

TL;DR

This paper derives the weak coupling asymptotics up to second order for the ground state energy of the delta-function Bose gas using an electrostatic interpretation of the Lieb-Liniger integral equation.

Contribution

It provides a detailed derivation of the ground state energy asymptotics to second order in the weak coupling regime for the delta-function Bose gas.

Findings

Derived the ground state energy asymptotics to order (c/ρ)^2

Used electrostatic interpretation of Lieb-Liniger integral equation

Enhanced understanding of weak coupling behavior in Bose gases

Abstract

The weak coupling asymptotics, to order $(c/\rho)^2$, of the ground state energy of the delta-function Bose gasmis derived. Here $2c\ge 0$ is the delta-function potential amplitude and $\rho$ the density of the gas in the thermodynamic limit. The analysis uses the electrostatic interpretation of the Lieb-Liniger integral equation.