Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach

Abstract We show that Bogoliubov theory correctly predicts the low-energy spectral properties of Bose gases in the Gross-Pitaevskii regime. We recover recent results from 6, 7. While our main strategy is similar to the one developed in 6, 7, we combine it with new ideas, taken in part from 15, 25; this makes our proof substantially simpler and shorter. As an important step towards the proof of Bogoliubov theory, we show that low-energy states exhibit complete Bose-Einstein condensation with optimal control over the number of orthogonal excitations.