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Despite the prominence of Onsager's point-vortex model as a statisticaldescription of 2D classical turbulence, a first-principles development of themodel for a realistic superfluid has remained an open problem. Here we developa mapping of a system of quantum vortices described by the homogeneous 2DGross-Pitaevskii equation (GPE) to the point-vortex model, enabling Monte-Carlosampling of the vortex microcanonical ensemble. We use this approach to surveythe full range of vortex states in a 2D superfluid, from the vortex-dipole gasat positive temperature to negative-temperature states exhibiting bothmacroscopic vortex clustering and kinetic energy condensation, which we term anOnsager-Kraichnan condensate (OKC). Damped GPE simulations reveal that such OKCstates can emerge dynamically, via aggregation of small-scale clusters intogiant OKC-clusters, as the end states of decaying 2D quantum turbulence in acompressible, finite-temperature superfluid. These statistical equilibriumstates should be accessible in atomic Bose-Einstein condensate experiments.

Onsager-Kraichnan Condensation in Decaying Two-Dimensional Quantum Turbulence