  Nonequilibrium dynamics of noninteracting bosons in a one-dimensional
ring-shaped lattice is studied by means of the Kinetic Monte Carlo method. The
system is approximated by the classical XY model (the kinetic term is
neglected) and then the simulations are performed for the planar classical
spins. We study the dynamics that follows a finite-time quench to zero
temperature. If the quench is slow enough the system can equilibrate and
finally reaches the ground state with uniform spin alignment. However, we show
that if the quench is faster than the relaxation rate, the system can get
locked in a current-carrying metastable state characterized by a nonzero
winding number. We analyze how the zero-temperature state depends on the quench
rate.
