Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime.

We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order N - 1 + κ , for κ > 0 . Assuming that κ ∈ ( 0 ; 1 / 43 ) , we show that low-energy states exhibit Bose-Einstein condensation and we provide bounds on the expectation and on higher moments of the number of excitations.