On Bose–Einstein condensates in the Thomas–Fermi regime

We study a system of N trapped bosons in the Thomas–Fermi regime with an interacting pair potential of the form g_N N^3β -1 V(N^β x) , for some β∈ (0,1/3) and g_N diverging as N →∞ . We prove that there is complete Bose–Einstein condensation at the level of the ground state and, furthermore, that, if β∈ (0,1/6) , condensation is preserved by the time evolution.