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NUMBER M21008
AUTHOR Lee, Jinyeop
TITLE Rate of convergence towards Hartree type equations for mixture condensates with factorized initial data
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JOURNAL Journal of Mathematical Physics (SCI Journal, Accepted),
ABSTRACT We consider a system of $p$ {species} of bosons, each of which consists of $N_{1},N_{2},\dots,N_{p}$ particles. The bosons are in three dimensions with interactions via an interaction potential {$V$ such that $V \leq D(1-\Delta)$} which includes the Coulomb interaction. We set the initial condition to describe a mixture condensate, i.e., a tensor product of factorized states. We show that the difference between the many-body Schr\"odinger evolution in the mean-field regime and the corresponding $p$-particle dynamics due to a {system of coupled Hartree equations} is $O(N^{-1})$ where $N=\sum_{q=1}^{p}N_{q}$.
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