FLUID
In the literature: contested
Energy transfer across the classical-quantum crossover scale
In plain words
In superfluid turbulence, energy moves first through swirls made of many vortex lines and then along single lines. At the handover scale energy may pile up, and theories disagree on how.
Precise statement
At scales near the mean intervortex spacing $\ell = L^{-1/2}$, energy passes from the Kolmogorov cascade carried by polarized vortex bundles to the Kelvin-wave cascade on individual lines. Determine the energy spectrum across this crossover at $T \to 0$ (a bottleneck pile-up predicted by L'vov, Nazarenko and Rudenko, versus a reconnection-driven crossover proposed by Kozik and Svistunov) and its consequence for $\nu'$.
What would settle it
Vortex-filament or Gross-Pitaevskii simulations resolving at least a decade on each side of l, compared with the predicted crossover spectra.