The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length

TL;DR

This paper extends the understanding of the ground state energy of dilute Bose gases, providing bounds for a wider class of interaction potentials with positive scattering length, including some with negative parts.

Contribution

It generalizes the known bounds on ground state energy to include interaction potentials with positive scattering length and certain shallow or narrow negative components.

Findings

Established upper bounds for a broad class of potentials.

Derived lower bounds for potentials with shallow or narrow negative parts.

Confirmed the leading term of the ground state energy in these generalized settings.

Abstract

The leading term of the ground state energy/particle of a dilute gas of bosons with mass $m$ in the thermodynamic limit is $2\pi \hbar^2 a \rho/m$ when the density of the gas is $\rho$, the interaction potential is non-negative and the scattering length $a$ is positive. In this paper, we generalize the upper bound part of this result to any interaction potential with positive scattering length, i.e, $a>0$ and the lower bound part to some interaction potentials with shallow and/or narrow negative parts.