2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/23590We study the non-equilibrium dynamics of the zero temperature Mott insulator- superfluid quantum phase transition in a lattice of weakly coupled Bose-Einstein condensates. We show that crossing the critical point from the insulating to the superfluid phase at a finite rate results in a finite dispersion of current. Viceversa, crossing the critical point from the superfluid phase to the insulating one, results in a finite dispersion of the number of atoms per lattice site. We develop a microscopic dynamical model of the transition, and make quantitative predictions for realistic experiments.20 pages; proceedings of NATO ASI ``Patterns of Symmetry Breaking'', Krakow, Poland, September 2002Mesoscale and Nanoscale Physicstext