### 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) |
---|---|

Journal | Physical Review Letters |

Volume | 112 |

Issue number | 14 |

DOIs | |

State | Published - Apr 11 2014 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*112*(14). https://doi.org/10.1103/PhysRevLett.112.145301

**Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence.** / Billam, T. P.; Reeves, M. T.; Anderson, Brian P; Bradley, A. S.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 112, no. 14. https://doi.org/10.1103/PhysRevLett.112.145301

}

TY - JOUR

T1 - Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence

AU - Billam, T. P.

AU - Reeves, M. T.

AU - Anderson, Brian P

AU - Bradley, A. S.

PY - 2014/4/11

Y1 - 2014/4/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84898909581&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898909581&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.112.145301

DO - 10.1103/PhysRevLett.112.145301

M3 - Article

AN - SCOPUS:84898909581

VL - 112

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 14

ER -