Exact Solution for Vortex Dynamics in Temperature Quenches of Two-Dimensional Superfluids

An exact analytic solution for the dynamics of vortex pairs is obtained for rapid temperature quenches of a superfluid film starting from the line of critical points below the critical temperature ${T}_{\mathrm{KT}}$. An approximate solution for quenches at and above above ${T}_{\mathrm{KT}}$ provides insights into the origin of logarithmic transients in the vortex decay, and is in general agreement with recent simulations of the quenched $XY$ model. These results confirm that there is no ``creation'' of vortices whose density increases with the quench rate as predicted by the Kibble-Zurek theory but only monotonic decay of the thermal vortices already present at the initial temperature.