Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime

Abstract

We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order $N^{-1+\kappa }$ , for $\kappa >0$ . Assuming that $\kappa \in (0;1/43)$ , 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.