Bogoliubov theory {N. N. Bogoliubov, Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947) [J. Phys. (USSR) 11, 23 (1947) (in English)]} provides important predictions for the low energy properties of the weakly interacting Bose gas. Recently, Bogoliubov’s predictions were justified rigorously by Boccato et al. [Acta Math. 222(2), 219–335 (2019)] for translation invariant systems in the Gross–Pitaveskii regime, where N bosons in interact through a potential whose scattering length is of size N−1. In this article, we review recent results from the work of Brennecke et al. [Ann. Henri Poincaré 23, 1583–1658 (2022)], a joint work with Schlein and Schraven, which extends the analysis for translation invariant systems to systems of bosons in that are trapped by an external potential.
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Review Article|
May 19 2022
The low energy spectrum of trapped bosons in the Gross–Pitaevskii regime
Special Collection:
XX International Congress on Mathematical Physics
Christian Brennecke
Christian Brennecke
a)
Institute for Applied Mathematics, University of Bonn
, Endenicher Allee 60, 53115 Bonn, Germany
a)Author to whom correspondence should be addressed: brennecke@iam.uni-bonn.de
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a)Author to whom correspondence should be addressed: brennecke@iam.uni-bonn.de
Note: This paper is part of the Special Collection: XX International Congress on Mathematical Physics.
J. Math. Phys. 63, 051101 (2022)
Article history
Received:
February 27 2022
Accepted:
April 28 2022
Citation
Christian Brennecke; The low energy spectrum of trapped bosons in the Gross–Pitaevskii regime. J. Math. Phys. 1 May 2022; 63 (5): 051101. https://doi.org/10.1063/5.0089630
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