Decaying superfluid turbulence near an anomalous non-thermal fixed point

Abstract

We investigate anomalously slow coarsening in a dilute two-dimensional (2d) superfluid closed with respect to particle and energy exchange with the environment. The dynamics is demonstrated to be closely connected to both, a non-thermal fixed point (NTFP) in a far-from-equilibrium quantum system, and to Kraichnan-Kolmogorov turbulence. During a universal dynamical regime associated with an anomalous NTFP, vortex dynamics are understood to be governed by three-vortex collisions that trigger vortex-antivortex annihilation events, leading to a subdiffusive decay of the vortex density and thus growth of the characteristic inter-defect length scale, $\ell_\text{v}\sim t^{\,β}$ with $β\approx1/5$. It is found that, during the same time when this power law in time is seen, the moments of the superfluid velocity circulation $Γ$ around an area of spatial extent $r$ exhibit power-law scaling $Γ^{2}(r)\sim r^{8/3}$, in agreement with Kraichnan-Kolmogorov predictions for an inverse energy cascade in the inertial range, in a driven-open setting. Moreover, in high-order moments, intermittent deviations from linear scaling $Γ^{2p}(r)\sim [Γ^{2}(r)]^{p}$ are observed that are consistent with bifractal intermittency corrections previously measured in fully developed classical turbulence. These results establish a quantitative link between decaying quantum turbulence in a closed superfluid and universal dynamics near a non-thermal fixed point. Notably, the subdiffusive decay exponent $β\approx1/5$ deviates significantly from values reported for classical systems.