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

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 [25], 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 low-energy states satisfy Bose-Einstein condensation with a rate of the order $N^{-\frac {3}{4}}$ .