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

For a translation invariant system of bosons in the Gross-Pitaevskii regime, we establish a precise bound for the ground state energy . While the leading, order , contribution to 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 , which is of the order .