  We investigate the dynamics of second order phase transitions in two
dimensions, breaking a gauged U(1) symmetry. Using numerical simulations, we
show that the density of topological defects formed scales with the quench
timescale $\tau_Q$ as $n \sim \tau_Q^{-1/2}$ when the dynamics is overdamped at
the instant when the freezeout of thermal fluctuations takes place, and $n \sim
\tau_Q^{-2/3}$ in the underdamped case. This is predicted by the scenario
proposed by one of us [1].
