Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach
Forum of Mathematics, Sigma, Tome 10 (2022)
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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.
@article{10_1017_fms_2022_78,
author = {Christian Hainzl and Benjamin Schlein and Arnaud Triay},
title = {Bogoliubov theory in the {Gross-Pitaevskii} limit: a simplified approach},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.78},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.78/}
}
TY - JOUR AU - Christian Hainzl AU - Benjamin Schlein AU - Arnaud Triay TI - Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach JO - Forum of Mathematics, Sigma PY - 2022 VL - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.78/ DO - 10.1017/fms.2022.78 LA - en ID - 10_1017_fms_2022_78 ER -
%0 Journal Article %A Christian Hainzl %A Benjamin Schlein %A Arnaud Triay %T Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach %J Forum of Mathematics, Sigma %D 2022 %V 10 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.78/ %R 10.1017/fms.2022.78 %G en %F 10_1017_fms_2022_78
Christian Hainzl; Benjamin Schlein; Arnaud Triay. Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.78
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