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

Hainzl, Christian ; Schlein, Benjamin and Triay, Arnaud (2022): Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach. In: Forum of Mathematics, Sigma, Vol. 10, No. e90: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 2050-5094
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892