Bogoliubov theory in the Gross-Pitaevskii limit

We consider Bose gases consisting of N particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of order N−1 (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as N tends to infinity. Our results confirm Bogoliubov’s predictions.