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arXiv · 1803.05413

Ground state energy of mixture of Bose gases

Alessandro Michelangeli·Phan Thành Nam·Alessandro Olgiati
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Abstract

We 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 details.

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Alessandro Michelangeli, Phan Thành Nam, Alessandro Olgiati. 2018-03-14. Ground state energy of mixture of Bose gases. https://doi.org/10.1142/s0129055x19500053

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