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arXiv · 2203.03440

Bogoliubov Theory in the Gross-Pitaevskii Limit: a Simplified Approach

Christian Hainzl·Benjamin Schlein·Arnaud Triay
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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 \cite{BBCS,BBCS4}. While our main strategy is similar to the one developed in \cite{BBCS,BBCS4}, we combine it with new ideas, taken in part from \cite{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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Christian Hainzl, Benjamin Schlein, Arnaud Triay. 2022-03-07. Bogoliubov Theory in the Gross-Pitaevskii Limit: a Simplified Approach. https://arxiv.org/abs/2203.03440

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