Classification of nonthermal fixed points and their scaling exponents

In an isolated Bose gas after a quench, the momentum occupation obeys $f(k,t)=t^{\alpha} f_s(t^{\beta} k)$ in a scaling window. Determine the set of fixed points ($\alpha, \beta$ and the scaling function $f_s$) and the properties that select them: dimension d, number of field components and symmetry (scalar or spinor), conservation laws, and topological defects. Experimental inputs: 1D (Erne et al., Nature 563, 225, 2018), spinor (Prufer et al., Nature 563, 217, 2018), 3D homogeneous (Glidden et al., Nature Physics 17, 457, 2021). Answer: a classification with computed exponents matching the measured ones.

A renormalization-group or kinetic theory predicting $\alpha$ and $\beta$ for each experimental system, confirmed by measurements in which $d$ or the symmetry is varied.