Here we present supplementary online video material concerning the following publication:

Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas

Markus Karl1, 2, 3, ∗ and Thomas Gasenzer1, 3

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 3ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291 Darmstadt, Germany

Universal scaling behavior in the relaxation dynamics of an isolated two-dimensional Bose gas is studied by means of semi-classical stochastic simulations of the Gross-Pitaevskii model. The system is quenched far out of equilibrium by imprinting vortex defects into an otherwise phase-coherent condensate. A strongly anomalous non-thermal fixed point is identified, associated with a slowed decay of the defects in the case that the dissipative coupling to the thermal background noise is suppressed. At this fixed point, a large anomalous exponent η ≈ −3 and, related to this, a large dynamical exponent z ≈5 are identified. The corresponding power-law decay is found to be consistent with three-vortex-collision induced loss. The article discusses these aspects of non-thermal fixed points in the context of phase-ordering kinetics and coarsening dynamics, thus relating phenomenological and analytical approaches to classifying far-from-equilibrium scaling dynamics with each other. In particular, a close connection between the anomalous scaling exponent η, introduced in a quantum-field theoretic approach, and conservation-law induced scaling in classical phase-ordering kinetics is revealed. Moreover, the relation to superfluid turbulence as well as to driven stationary systems is discussed.

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All videos by Markus Karl.

Video 1: Anomalous non-thermal fixed point

The video shows the approach of the system towards the anomalous non-thermal fixed point, corresponding qualitatively to the snapshots and spectra shown in Figs. 1-4 in the article. Top left panel: density. Top right: phase. Bottom left: Flow field and circulation of vortices (anti-vortices) marked in orange (green) color. Bottom right: occupation number spectrum.

The video shows the approach of the system towards the Gaussian non-thermal fixed point, corresponding qualitatively to the spectra shown in Figs. 5, 6, and the snapshot in Fig. C.1b in the article. Top left panel: density. Top right: phase. Bottom left: Flow field and circulation of vortices (anti-vortices) marked in orange (green) color. Bottom right: occupation number spectrum.

Video 3: Anomalous non-thermal fixed point in a driven-dissipative system

The videos show the approach of the system towards the anomalous non-thermal fixed point during the early stage of evolution of a driven-dissipative system, starting from an 8 x 8 lattice of non-elementary vortices with winding number |w|=6. At later times, the evolution corresponds to dynamics near the Gaussian fixed point. The run belongs to the data set depicted by the red squares in Fig. 8 in the article. The first video shows the time interval from 0 to 10^{4} ξ_{h}^{2}, the second video the interval from 10^{4}to 1.6·10^{5}ξ_{h}^{2}.

Video 4: Gaussian non-thermal fixed point in a driven-dissipative system

The video shows the approach of the driven-dissipative system towards the (near-) Gaussian non-thermal fixed point, starting from an 8 x 8 lattice of non-elementary vortices with winding number |w|=6. The run belongs to the data set depicted by the blue triangles in Fig. 8 in the article.