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}t1/3. This second regime of coarsening is associated with spin wave energy transport from low to high wavevectors, bringing about the the eventual equilibrium state. 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.
Highlights
A spin-1 condensate can be described by three interacting classical fields ψm for condensates in the three spin components with spin projections m = −1, 0, 1
Spatial correlations of the order parameter at different times t collapse onto a single curve when rescaled by L, and the domains grow as L ∼ t1/η with the scaling exponent η determined by the dynamic universality class [1]
We have shown that vortex driven coarsening of an isolated easy-plane ferromagnetic spin-1 condensate does not take the system to equilibrium
Summary
Quenching a system across a continuous phase transition from a high to low symmetry phase causes the system to spontaneously break symmetry. Spatial correlations of the order parameter at different times t collapse onto a single curve when rescaled by L, and the domains grow as L ∼ t1/η with the scaling exponent η determined by the dynamic universality class [1] Such universal dynamics has been explored in a vast variety of systems, ranging from the early universe [2] to superfluid formation [3] to opinion spreading in sociology [4]. Simulations of a homogeneous quasi-2D spin-1 condensate quenched from the polar phase to the easyplane ferromagnetic phase, see Fig. 1(a), identified coarsening dynamics driven by the mutual annihilation of transverse spin vortices with domain size growing as L ∼ t/ log t [19, 20]. Our results give new insights into the phase ordering dynamics of isolated systems and provide a potential profitable connection between phase ordering and wave turbulence
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