# Anomalous phase ordering of a quenched ferromagnetic superfluid

## TL;DR

This paper reveals an anomalous phase ordering process in a quenched ferromagnetic superfluid, where coarsening proceeds via a slow spin wave energy cascade rather than vortex annihilation alone, challenging traditional theories.

## Contribution

It uncovers a second slow coarsening regime driven by spin wave energy transport, distinct from the standard defect annihilation mechanism in phase ordering.

## Key findings

- Vortex annihilation does not lead directly to equilibrium.
- A nonequilibrium spin wave background persists at BKT temperature.
- Coarsening exhibits a $t^{1/3}$ growth law in the second regime.

## Abstract

Coarsening dynamics, the canonical theory of phase ordering following a quench across a symmetry breaking phase transition, is thought to be driven by the annihilation of topological defects. Here we show that this understanding is incomplete. We simulate the dynamics of an isolated spin-1 condensate quenched into the easy-plane ferromagnetic phase and find that the mutual annihilation of spin vortices does not take the system to the equilibrium state. A nonequilibrium background of long wavelength spin waves remain at the Berezinskii-Kosterlitz-Thouless temperature, an order of magnitude hotter than the equilibrium temperature. The coarsening continues through a second much slower scale invariant process with a length scale that grows with time as $t^{1/3}$. This second regime of coarsening is associated with spin wave energy transport from low to high wavevectors, bringing about the the eventual equilibrium state. Because the relevant spin waves are noninteracting, the transport occurs through a dynamic coupling to other degrees of freedom of the system. The transport displays features of a spin wave energy cascade, providing a potential profitable connection with the emerging field of spin wave turbulence. Strongly coupling the system to a reservoir destroys the second regime of coarsening, allowing the system to thermalise following the annihilation of vortices.