Third Order Corrections to the Ground State Energy of a Bose Gas in the Gross–Pitaevskii Regime

Abstract For a translation invariant system of N bosons in the Gross–Pitaevskii regime, we establish a precise bound for the ground state energy EN E N. While the leading, order N, contribution to EN E N has been known since (Lieb et al. in Phys Rev A 61: 043602, 2000; Lieb and Yngvason in Phys Rev Lett 80: 2504–2507, 1998) and the second order corrections (of order one) have been first determined in Boccato et al. (Acta Math 222 (2): 219–335, 2019), our estimate also resolves the next term in the asymptotic expansion of EN E N, which is of the order (N) / N (log N) / N.