Mean-field quantum dynamics with magnetic fields

We consider a system of $N$ bosons in three dimensions interacting through a mean-field Coulomb potential in an external magnetic field. For initially factorized states we show that the one-particle density matrix associated with the solution of the $N$-body Schrödinger equation converges to the projection onto the solution of the magnetic Hartree equation in trace norm and in energy as $N \rightarrow \infty$. Estimates on the rate of convergence are provided.

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