01241nas a2200121 4500008004100000245004900041210004900090520085800139100002900997700002101026700002401047856004801071 2018 en d00aGround state energy of mixture of Bose gases0 aGround state energy of mixture of Bose gases3 aWe consider the asymptotic behavior of a system of multi-component
trapped bosons, when the total particle number N becomes large. In the dilute regime,
when the interaction potentials have the length scale of order O(N-1), we show that the
leading order of the ground state energy is captured correctly by the Gross-Pitaevskii
energy functional and that the many-body ground state fully condensates on the Gross-
Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is
O(1), we are able to verify Bogoliubov's approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaption to the multi-component setting is non-trivial in various respects and the analysis will be presented in details1 aMichelangeli, Alessandro1 aNam, Phan, Thanh1 aOlgiati, Alessandro uhttp://preprints.sissa.it/handle/1963/35312