  Mott insulator - superfluid transition in a periodic lattice of Josephson
junctions can be driven by tunneling rate increase. Resulting winding numbers
$W$ of the condensate wavefunction decrease with increasing quench time in
accord with the Kibble-Zurek mechanism (KZM). However, in very slow quenches
Bose-Hubbard dynamics rearranges wavefunction phase so that its random walk
cools, $\bar{W^2}$ decreases and eventually the wavefunction becomes too cold
to overcome potential barriers separating different $W$. Thus, in contrast with
KZM, in very slow quenches $\bar{W^2}$ is set by random walk with "critical"
step size, independently of $\tau_Q$.
