Universal dynamics of rogue waves in a quenched spinor Bose condensate

Abstract

Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time-evolution to a non-thermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent ${\delta }_{\mathrm{c}}\simeq 1/3$ for temporal scaling, which is different from the exponent ${\beta }_V\simeq 1/4$ characterizing the scaling of the correlation length ${\ell }_V\sim t^{{\beta }_V}$ in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as $t^{{\delta }_{\mathrm{I}}}$. This suggests that the universality class of a non-thermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early universe to geophysical dynamics and micro physics.

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• Stochastic Gross-Pitaevskii theory for a spin-1 Bose gas: Application to superfluidity in two dimensions
• Berezinskii-Kosterlitz-Thouless transitions in a ferromagnetic superfluid: effects of axial magnetization
• Collective excitations and universal coarsening dynamics of a spin-orbit-coupled spin-1 Bose-Einstein condensate
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