Bogoliubov Theory in the Gross-Pitaevskii Limit

Abstract

We consider Bose gases consisting of $N$ particles trapped in a box with volume one and interacting through a repulsive potential with 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 vanishing as $N\to \infty$. Our results confirm Bogoliubov's predictions.

arXiv commentnew version, with no assumption on the size of the interaction