# Anomalous phase ordering of a quenched ferromagnetic superfluid

### Submission summary

 As Contributors: Lewis Williamson Arxiv Link: https://arxiv.org/abs/1902.10792v4 Date accepted: 2019-08-19 Date submitted: 2019-08-06 Submitted by: Williamson, Lewis Submitted to: SciPost Physics Discipline: Physics Subject area: Atomic, Molecular and Optical Physics - Theory Approaches: Theoretical, Computational

### 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.

### Ontology / Topics

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Published as SciPost Phys. 7, 029 (2019)

We thank the referee for their constructive comments. We address the referee's points 1) and 2) below.

1) For clarity, we have renamed $E_\text{tot}$ to $E_\text{sw}$, and slightly reworded how this term is described, to make it clear that this quantity is only the spin wave contribution to the total energy, which is not a conserved quantity. The paper contains a description of where the lost energy goes,
"There is also a net decrease in the total spin wave energy $E_\text{sw}$, showing that energy is also lost from the spin wave excitations, either to other quadratic excitations [36,46–48] or to excitations beyond quadratic order."

2) We have clarified in the Conclusion that ascribing our universal dynamics to the scalar model B dynamic universality class is only speculation. This is based on the scaling observed and the symmetry and dimension of the $nF_z$ field, which follows closely the dynamics of the order parameter. We have also left open the possibility for the dynamics to belong to a different dynamic universality class.

### List of changes

1) For clarity, we have renamed $E_\text{tot}$ to $E_\text{sw}$, and slightly reworded how this term is described, to make it clear that this quantity is only the spin wave contribution to the total energy, which is not a conserved quantity. The paper contains a description of where the lost energy goes,
"There is also a net decrease in the total spin wave energy $E_\text{sw}$, showing that energy is also lost from the spin wave excitations, either to other quadratic excitations [36,46–48] or to excitations beyond quadratic order."

2) We have clarified in the Conclusion that ascribing our universal dynamics to the scalar model B dynamic universality class is only speculation. This is based on the scaling observed and the symmetry and dimension of the $nF_z$ field, which follows closely the dynamics of the order parameter. We have also left open the possibility for the dynamics to belong to a different dynamic universality class.

### Submission & Refereeing History

Resubmission 1902.10792v4 on 6 August 2019
Submission 1902.10792v3 on 5 June 2019