### Abstract

Despite the prominence of Onsager's point-vortex model as a statistical description of 2D classical turbulence, a first-principles development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system of quantum vortices described by the homogeneous 2D Gross-Pitaevskii equation (GPE) to the point-vortex model, enabling Monte Carlo sampling of the vortex microcanonical ensemble. We use this approach to survey the full range of vortex states in a 2D superfluid, from the vortex-dipole gas at positive temperature to negative-temperature states exhibiting both macroscopic vortex clustering and kinetic energy condensation, which we term an Onsager-Kraichnan condensate (OKC). Damped GPE simulations reveal that such OKC states can emerge dynamically, via aggregation of small-scale clusters into giant OKC clusters, as the end states of decaying 2D quantum turbulence in a compressible, finite-temperature superfluid. These statistical equilibrium states should be accessible in atomic Bose-Einstein condensate experiments.

Original language | English (US) |
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Article number | 145301 |

Journal | Physical review letters |

Volume | 112 |

Issue number | 14 |

DOIs | |

State | Published - Apr 11 2014 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Physical review letters*,

*112*(14), [145301]. https://doi.org/10.1103/PhysRevLett.112.145301