Dynamics of Quantum Phase Transition in an Array of Josephson Junctions

We study the dynamics of the Mott insulator-superfluid quantum phase transition in a periodic 1D array of Josephson junctions. We show that crossing the critical point diabatically i.e. at a finite rate with a quench time $\tau_Q$ induces finite quantum fluctuations of the current around the loop proportional to $\tau_Q^{-1/6}$. This scaling could be experimentally verified with in array of weakly coupled Bose-Einstein condensates or superconducting grains.