Excitation spectrum of Bose gases beyond the Gross–Pitaevskii regime

We consider Bose gases of Formula: see text particles in a box of volume one, interacting through a repulsive potential with scattering length of order Formula: see text, for Formula: see text. Such regimes interpolate between the Gross–Pitaevskii and thermodynamic limits. Assuming that Formula: see text is sufficiently small, we determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing in the limit Formula: see text.