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A large scale dynamical simulation of the superfluid to Mott insulatortransition in the gas of ultra cold atoms placed in an optical lattice isperformed using the time dependent Gutzwiller mean field approach. Thisapproximate treatment allows us to take into account most of the details of therecent experiment [Nature 415, 39 (2002)] where by changing the depth of thelattice potential an adiabatic transition from a superfluid to a Mott insulatorstate has been reported. Our simulations reveal a significant excitation of thesystem with a transition to insulator in restricted regions of the trap.Comment: final version, correct Fig.7 (the published version contains wrong  fig.7 by mistake

Mean-field dynamics of the superfluid-insulator phase transition in a gas of ultracold atoms