Ground State Energy of Dilute Bose Gas in Small Negative Potential Case

TL;DR

This paper proves that the ground state energy formula for a dilute Bose gas remains valid even when the interaction potential has a small negative component, extending previous results that required non-negativity.

Contribution

The authors extend the known ground state energy formula to potentials with small negative parts, relaxing the non-negativity condition.

Findings

Ground state energy formula holds with small negative potentials.

The negative part of the potential can be small without affecting the energy result.

The proof generalizes previous results to a broader class of potentials.

Abstract

It is well known that the ground state energy of a three dimensional dilute Bose gas in the thermodynamic limit is $E=4\pi a \rho N$ when the particles interact via a non-negative, finite range, symmetric, two-body potential. Here, $N$ is the number of particles, $\rho$ is the density of the gas, and $a$ is the scattering length of the potential. In this paper, we prove the same result without the non-negativity condition on the potential, provided the negative part is small.