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 BBCS,BBCS4. While our main strategy is similar to the one developed in BBCS,BBCS4, we combine it with new ideas, taken in part from Hainzl,NT; 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 on the number of orthogonal excitations.
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