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

Hainzl, Christian ; Schlein, Benjamin und Triay, Arnaud (2022): Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach. In: Forum of Mathematics, Sigma, Bd. 10, Nr. e90: S. 1-39

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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 2050-5094
• Sprache: Englisch
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892