Rigorous mean-field dynamics of lattice bosons: quenches from the Mott insulator

We provide a rigorous derivation of Gutzwiller mean-field dynamics for lattice bosons, showing that it is exact on fully connected lattices. We apply this formalism to quenches in the interaction parameter from the Mott insulator to the superfluid state. Although within mean-field the Mott insulator is a steady state, we show that a dynamical critical interaction Ud exists, such that for final interaction parameter Uf > Ud the Mott insulator is exponentially unstable towards emerging long-range superfluid order, whereas for Uf < Ud the Mott insulating state is stable. We discuss the implications of this prediction for finite-dimensional systems.