Dynamical exponent of the vortex-dominated fixed point in two dimensions
In plain words
In a flat two-dimensional atomic gas stirred into a tangle of vortices (tiny whirlpools), simulations find correlations stretching much more slowly than standard coarsening theory predicts. The true slowing law, and whether it is universal, is not settled.
Precise statement
For the 2D Gross-Pitaevskii field after a quench to a dense vortex ensemble, classical-field simulations (Karl and Gasenzer, New J. Phys. 19, 093014, 2017) find a strongly anomalous fixed point with dynamical exponent $z \sim 5$ ($\beta = 1/z \sim 0.2$) and anomalous exponent $\eta \sim -3$, compared with $z$ of about 2 for ordinary vortex-annihilation coarsening. Determine $z$ at asymptotically long times and large sizes, and whether it depends on the initial vortex configuration (random versus clustered). Answer: z with uncertainty and its dependence on initial conditions.
What would settle it
Gross-Pitaevskii simulations over several decades in time with a theory of vortex-cluster dynamics predicting z, checked in a uniform 2D gas experiment.