Ground state energy of a dilute Bose gas with three-body hard-core interactions

TL;DR

This paper derives the leading order ground state energy for a dilute Bose gas with three-body hard-core interactions, matching previous lower bounds and extending to combined two- and three-body interactions.

Contribution

It provides a rigorous upper bound on the ground state energy for a Bose gas with three-body hard-core interactions, confirming the leading order and generalizing previous results.

Findings

Upper bound on ground state energy derived

Result matches previous lower bounds

Method adaptable to combined two- and three-body interactions

Abstract

We consider a gas of bosons interacting through a three-body hard-core potential in the thermodynamic limit. We derive an upper bound on the ground state energy of the system at the leading order using a Jastrow factor. Our result matches the lower bound proven by Nam-Ricaud-Triay and therefore resolves the leading order. Moreover, a straightforward adaptation of our proof can be used for systems interacting via combined two-body and three-body interactions to generalise Theorem 1.2. from arXiv:2402.05646 to hard-core potentials.