Origin of the inverse energy cascade in two-dimensional quantum turbulence

We establish a statistical relationship between the inverse energy cascade and the spatial correlations of clustered vortices in two-dimensional quantum turbulence. The Kolmogorov spectrum k^{-5 /3} on inertial scales r corresponds to a pair correlation function between the vortices with different signs that decays as a power law with the pair distance given as r^{-4 /3}. To test these scaling relations, we propose a forced and dissipative point vortex model that captures the turbulent dynamics of quantized vortices by the emergent clustering of same-sign vortices. The inverse energy cascade developing in a statistically neutral system originates from this vortex clustering that evolves with time.