Classification of nonthermal fixed points and their scaling exponents
In plain words
Experiments in one-, two- and three-dimensional atomic gases find self-similar stretching of correlations, with exponents that differ between systems. Which distinct universal classes exist, and what selects the class, is not known.
Precise statement
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.
What would settle it
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.
Status in the literature
Wave-kinetic and defect-dominated fixed points are identified in theory; not every measured exponent set is matched to a predicted class (moderate confidence).
Related problems
- More general than Dynamical exponent of the vortex-dominated fixed point in two dimensions
- More general than Do quantum fluctuations change nonthermal fixed-point exponents