Excitation spectrum of Bose gases beyond the Gross–Pitaevskii regime

We consider Bose gases of N particles in a box of volume one, interacting through a repulsive potential with scattering length of order N−1+κ, for κ>0. Such regimes interpolate between the Gross–Pitaevskii and thermodynamic limits. Assuming that κ is sufficiently small, we determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing in the limit N→∞