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The quantum phase transition from the Mott insulator state to the superfluidin the Bose-Hubbard model is investigated. We research one, two and threedimensional lattices in the truncated Wigner approximation. We compute bothkinetic and potential energy and they turn out to have a power law behaviour asa function of the transition rate, with the power equal to 1/3. The sameapplies to the total energy in a system with a harmonic trap, which is usuallypresent in the experimental set-up. These observations are in agreement withthe experiment of [8], where such scalings were also observed and the power ofthe decay was numerically close to 1/3. The results confirm the Kibble-Zurek(adiabatic-impulse-adiabatic approximation) scenario for this transition.

Dynamics of the Mott Insulator to Superfluid quantum phase transition in the truncated Wigner approximation