Bose–Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross–Pitaevskii Regime

We consider a Bose gas consisting of N particles in {R}³, trapped by an external field and interacting through a two-body potential with scattering length of order N^-1. We prove that low energy states exhibit complete Bose–Einstein condensation with optimal rate, generalizing previous work in Boccato et al. (Commun Math Phys 359 (3): 975–1026, 2018; 376: 1311–1395, 2020), restricted to translation invariant systems. This extends recent results in Nam et al. (Preprint, 2001. arXiv: 2001. 04364), removing the smallness assumption on the size of the scattering length.