Quench from Mott Insulator to Superfluid
  We study a linear ramp of the nearest-neighbor tunneling rate in the Bose-Hubbard model driving the system from the Mott insulator state into the superfluid phase. We employ the truncated Wigner approximation to simulate linear quenches of a uniform system in 1,2, and 3 dimensions, and in a harmonic trap in 3 dimensions. In all these setups the excitation energy decays like one over third root of the quench time. The -1/3 scaling arises from an impulse-adiabatic approximation - a variant of the Kibble-Zurek mechanism - describing a crossover from non-adiabatic to adiabatic evolution when the system begins to keep pace with the increasing tunneling rate. 
Jacek Dziarmaga, Marek Tylutki, Wojciech H. Zurek
cond-mat.quant-gas cond-mat.mes-hall cond-mat.stat-mech quant-ph