Second order energy expansion of Bose gases with three-body interactions

TL;DR

This paper derives a second order energy expansion for Bose gases with three-body interactions, confirming a conjecture about the subleading term and demonstrating Bose-Einstein condensation with a specific rate.

Contribution

It provides the first rigorous derivation of the second order energy expansion for three-body interacting Bose gases in the Gross-Pitaevskii regime, confirming a prior conjecture.

Findings

Subleading energy term is of order √N.

Ground state exhibits Bose-Einstein condensation at rate 1/√N.

Validated the conjecture by Nam, Ricaud, and Triay.

Abstract

We provide a second order energy expansion for a gas of $N$ bosonic particles with three-body interactions in the Gross-Pitaevskii regime. We especially confirm a conjecture by Nam, Ricaud and Triay in [22], where they predict the subleading term in the asymptotic expansion of the ground state energy to be of the order $\sqrt{N}$. In addition, we show that the ground state satisfies Bose-Einstein condensation with a rate of the order $\frac{1}{\sqrt{N}}$.