Steady inverse energy cascade in forced two-dimensional quantum fluids
In plain words
Flat superfluids made of ultracold atoms have been seen to gather same-direction vortices into giant clusters, as predicted by Lars Onsager, a theoretical chemist and physicist. Simulations show energy flowing steadily to large scales under stirring, but no experiment has yet shown such a lasting flow of energy.
Precise statement
In a 2D compressible Bose-Einstein condensate described by the Gross-Pitaevskii equation, forced at scales of a few healing lengths or larger, does a stationary inverse energy cascade with $E(k) \sim k^{-5/3}$ and constant upscale flux over a decade form in experiment, and how do compressibility, sound emission, vortex-antivortex annihilation and damping set the conditions for it? Answer: yes or no for given conditions, with the measured flux.
What would settle it
A forced $2\mathrm{D}$ condensate experiment showing a stationary $k^{-5/3}$ range with measured constant upscale flux over a decade, or a demonstration that none forms under stated conditions.
Status in the literature
Gross-Pitaevskii simulations with stirred obstacles report an inverse cascade with a $k^{-5/3}$ range (Reeves, Billam, Anderson, Bradley, PRL 2013); Onsager clusters were observed in decaying experiments (2019); no experiment has shown a stationary forced cascade with measured constant upscale flux.