Quenched or continuously driven quantum systems can show universal dynamics near non-thermal fixed points, generically in the form of scaling behaviour in space and time. Systems where such fixed points can be realized encompass post-inflationary evolution of the early universe, cold dark matter, dense neutron stars, heavy-ion collisions, to low-energy dynamics in cold gases. Key aspects of the theory of non-thermal fixed points will be briefly summarized [1,2], as well as recent experimental results for quenched systems [3,4]. Considering scaling transport of excitations to larger wave numbers similar to an inverse cascade, the underlying excitations can be either irregular phase excitations or (quasi) topological defects  exhibiting implications for quantum turbulence.
 C.-M. Schmied, A. N. Mikheev, T. Gasenzer, Non-thermal fixed points: Universal dynamics far from equilibrium, arXiv:1810.08143 [cond-mat.quant-gas]
 A. N. Mikheev, C.-M. Schmied, T. Gasenzer, Low-energy effective theory of non-thermal fixed points in a multicomponent Bose gas, Phys. Rev. A 99, 063622 (2019); arXiv:1807.10228 [cond-mat.quant-gas]
 M. Prüfer, P. Kunkel, H. Strobel, S. Lannig, D. Linnemann, C.-M. Schmied, J. Berges, T. Gasenzer, M.K. Oberthaler, Observation of universal dynamics in a spinor Bose gas far from equilibrium, Nature 563, 217 (2018).
 S. Erne, R. Bücker, T. Gasenzer, J. Berges and J. Schmiedmayer, Universal dynamics in an isolated one-dimensional Bose gas far from equilibrium, Nature 563, 225 (2018).
 M. Karl and T. Gasenzer, Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas, New J. Phys. 19, 093014 (2017).