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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2022
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