Winding up by a quench: Insulator to superfluid phase transition in a   ring of BECs
  We study phase transition from the Mott insulator to superfluid in a periodic optical lattice. Kibble-Zurek mechanism predicts buildup of winding number through random walk of BEC phases, with the step size scaling as a the third root of transition rate. We confirm this and demonstrate that this scaling accounts for the net winding number after the transition. 
J. Dziarmaga, J. Meisner, and W.H. Zurek