On Bose–Einstein condensates in the Thomas–Fermi regime

Abstract

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