Rate of convergence toward Hartree type equations for mixture condensates with factorized initial data

We consider a system of p species bosons, each which consists N1, N2, …, Np particles. The bosons are in three dimensions with interactions via an interaction potential V such that ≤ D(1 − Δ), includes the Coulomb interaction. set initial condition to describe mixture condensate, i.e., tensor product factorized states. show difference between many-body Schrödinger evolution mean-field regime and corresponding particle dynamics due coupled Hartree equations is O(N−1), where N=∑q=1pNq.