A new second order upper bound for the ground state energy of dilute Bose gases

TL;DR

This paper derives a new, simpler upper bound for the ground state energy of dilute Bose gases, accurately capturing the second order term as predicted by the Lee-Huang-Yang formula, improving previous results.

Contribution

It provides a novel, more straightforward proof for the second order upper bound of the ground state energy of dilute Bose gases, applicable to a broader class of potentials.

Findings

Established an upper bound matching the Lee-Huang-Yang prediction.

Improved the rate of convergence for the upper bound.

Simplified the proof technique compared to previous methods.

Abstract

We establish an upper bound for the ground state energy per unit volume of a dilute Bose gas in the thermodynamic limit, capturing the correct second order term, as predicted by the Lee-Huang-Yang formula. This result has been first established in J. Stat. Phys. 136(3) by H.-T. Yau and J. Yin. Our proof, which applies to repulsive and compactly supported $V \in L^3 (\mathbb{R}^3)$, gives better rates and, in our opinion, is substantially simpler.