Complete Bose–Einstein condensation in the Gross–Pitaevskii regime

This is the authors' abstract. We don't add key points for this paper.

We consider a gas of N bosons in a box with volume one interacting through a two-body potential with scattering length of order (Formula presented.) (Gross–Pitaevskii limit). Assuming the (unscaled) potential to be sufficiently weak, we prove complete Bose–Einstein condensation for the ground state and for many-body states with finite excitation energy in the limit of large N with a uniform (N-independent) bound on the number of excitations.