The quantum phase transition from the Mott insulator state to the superfluid
in the Bose-Hubbard model is investigated. We research one, two and three
dimensional lattices in the truncated Wigner approximation. We compute both
kinetic and potential energy and they turn out to have a power law behaviour as
a function of the transition rate, with the power equal to 1/3. The same
applies to the total energy in a system with a harmonic trap, which is usually
present in the experimental set-up. These observations are in agreement with
the experiment of [8], where such scalings were also observed and the power of
the decay was numerically close to 1/3. The results confirm the Kibble-Zurek
(adiabatic-impulse-adiabatic approximation) scenario for this transition.Comment: 14 pages, 11 figures; Laser Physics Workshop (LPHYS'12) Proceedings,
Calgary 201
