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

TL;DR

This paper provides an exact analytic solution for vortex pair dynamics in superfluid films during rapid temperature quenches, clarifying vortex decay behavior and challenging the Kibble-Zurek vortex creation prediction.

Contribution

It introduces an exact solution for vortex dynamics in superfluid quenches and offers insights into vortex decay mechanisms, contrasting with previous theories.

Findings

Exact vortex dynamics solution for rapid quenches below $T_{KT}$

Logarithmic transients explain vortex decay above $T_{KT}$

Vortex density decreases monotonically, no creation predicted by Kibble-Zurek

Abstract

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 $T_{KT}$. An approximate solution for quenches at and above above $T_{KT}$ provides insights into the origin of logarithmic transients in the vortex decay, and are 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.