# Anomalous phase ordering of a quenched ferromagnetic superfluid

### Submission summary

 As Contributors: Lewis Williamson Arxiv Link: https://arxiv.org/abs/1902.10792v3 Date submitted: 2019-06-05 Submitted by: Williamson, Lewis Submitted to: SciPost Physics Domain(s): Theor. & Comp. Subject area: Atomic, Molecular and Optical Physics - Theory

### 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.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1902.10792v3 on 5 June 2019

## Reports on this Submission

### Strengths

1) The authors found a new regime of coarsening, which needs long-time simulations.
2) They also found features of a novel turbulent cascade.

### Report

The authors study the coarsening dynamics of a spin-1 condensate quenched into the easy-plane ferromagnetic phase. In the isolated case, after the coarsening driven by pair annihilation of spin vortices, slow coarsening associated with spin wave energy transport continues. They point out that the transport shows features of a spin wave energy cascade. They also study open system dynamics and show that the system thermalizes after the annihilation of vortices in that case.

I recommend to publish this manuscript in SciPost Physics. However, I have a few questions.

1) The total energy of spin waves decreases in the isolated system (Fig.2(c)), although the energy is conserved. Where did the rest of energy go?

2) It is sure that the $t^{1/3}$ behavior is a feature of the model B universality class. Isn't there any other universality classes that show $t^{1/3}$ behavior? Since the symmetry of the system is different from that of the model B, I am not sure if the model B should be mentioned in Conclusion.

### Requested changes

1) The total energy of spin waves decreases, which is shown in Fig. 2(c). Mention what the decrement transformed into.
2) Discussion on the comparison with the model B should be revised.

• validity: good
• significance: good
• originality: high
• clarity: good
• formatting: good
• grammar: excellent