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Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime
Published 25 Aug 2021 in math-ph, math.AP, and math.MP | (2108.11129v4)
Abstract: 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 $N\to \infty$.
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