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Annales Henri Poincaré

Bogoliubov Theory for Trapped Bosons in the Gross–Pitaevskii Regime

Christian Brennecke, Benjamin Schlein, Severin Schraven

Published Feb 25, 2022• 39 citations
Publisher
DOI
10.1007/s00023-021-01151-z

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Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime

Christian Brennecke, Benjamin Schlein, Severin Schraven

We consider systems of $N$ bosons in $\mathbb{R}^3$, trapped by an external potential. The interaction is repulsive and has a scattering length of the order $N^{-1}$ (Gross-Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum up to errors that vanish in the limit $N\to \infty$.

arXiv:2108.11129•Aug 25, 2021•0 citations
We consider systems of NNN bosons in R3\mathbb{R}^3R3, trapped by an external potential. The interaction is repulsive and has a scattering length of the order N−1N^{-1}N−1 (Gross-Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum up to errors that vanish in the limit N→∞N\to \inftyN→∞.