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

Abstract

We consider a system of p species of bosons, each of which consists of N1, N2, …, Np particles. The bosons are in three dimensions with interactions via an interaction potential V such that V ≤ D(1 − Δ), 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 Schrödinger 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=∑q=1pNq.