Header

UZH-Logo

Maintenance Infos

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


Hainzl, Christian; Schlein, Benjamin; Triay, Arnaud (2022). Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach. Forum of mathematics. Sigma, 10:e90.

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.

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.

Statistics

Citations

Dimensions.ai Metrics
8 citations in Web of Science®
9 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

8 downloads since deposited on 17 Nov 2022
2 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Theoretical Computer Science
Physical Sciences > Algebra and Number Theory
Physical Sciences > Statistics and Probability
Physical Sciences > Mathematical Physics
Physical Sciences > Geometry and Topology
Physical Sciences > Discrete Mathematics and Combinatorics
Physical Sciences > Computational Mathematics
Uncontrolled Keywords:Computational Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Theoretical Computer Science, Analysis
Language:English
Date:1 January 2022
Deposited On:17 Nov 2022 17:51
Last Modified:27 Apr 2024 01:41
Publisher:Cambridge University Press
ISSN:2050-5094
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1017/fms.2022.78
Other Identification Number:MR4498777
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)