Here we present supplementary online video material concerning the following publication:
Niklas Rasch1, ∗ and Thomas Gasenzer1, 2
1Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
2Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
Anomalously slow coarsening in a dilute two-dimensional (2d) superfluid, associated with a non-thermal fixed point in the closed system’s universal dynamics, and characterized by 3-vortex collisions which initiate vortex-pair annihilations, is found to exhibit spatial scaling characteristics of Kraichnan-Kolmogorov turbulence. During an inertial interval, when the characteristic length scale related to the inter-defect distance grows as lv ∼ tβ, with β ≈ 1/5, moments of the superfluid velocity circulation around an area of extent r scale as predicted by classical turbulence theory, Γp(r) ∼ r4p/3. Intermittency corrections seen for higher values of p are found to be consistent with values measured for fully developed, classical turbulence. Hence, we link the decaying quantum turbulence cascade in a closed superfluid to universal dynamics close to a non-thermal fixed point. The decay exponent β clearly deviates from values known for classical systems.
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All videos by Niklas Rasch.
The video shows the evolution of a 2D Bose condensate with contact interactions in the vicinity of an anomalous non-thermal fixed point. The panels show: (top left) the 2D condensate density variation relative to the mean density, ρ2/⟨ρ2⟩, (top center) the normalized fluid current |j|/⟨|j|⟩, (top right) the mean 2nd moment Γ2(r) of the circulation Γ(r, x), i.e., of the velocity field line integrated along closed circular paths of radius r, centered at x. See paper for details. (bottom left) The single-particle occupation number distribution of bosons over radial momenta (angle averaged). (bottom center) The anomalous fixed point implies subdiffusive coarsening with a temporal power-law growth of the characteristic length scale as lv ~ t1/5 which is a measure for the mean interdefect distance. At the same time, the mean vortex number decreases, accordingly, as Nv ~ t –2/5. (bottom right) Comparison of the time-varying fitted β exponent extracted from the vortex number in (bottom center) and the maximal local slope λ2,max from the circulation moment (top right). The system approaches universal dynamics, indicated by β ≈ 1/5, at the highlighted intermediate times which is accompanied by the buildup of a transient 2d turbulent Kolmogorov-Kraichnan scaling corresponding to a decaying inverse energy cascade. Snapshots of the run are shown in Fig. 1 in the article where more details can be found.
