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Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence

Billam, T.P.; Reeves, M.T.; Anderson, B.P.; Bradley, A.S.

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T.P. Billam

M.T. Reeves

B.P. Anderson

A.S. Bradley


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.


Billam, T., Reeves, M., Anderson, B., & Bradley, A. (2014). Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence. Physical Review Letters, 112(14), Article 145301.

Journal Article Type Article
Publication Date Apr 1, 2014
Deposit Date Jul 23, 2014
Publicly Available Date Sep 9, 2014
Journal Physical Review Letters
Print ISSN 0031-9007
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 112
Issue 14
Article Number 145301


Published Journal Article (1.7 Mb)

Copyright Statement
Reprinted with permission from the American Physical Society: Phys. Rev. Lett. 112, 145301 © (2014) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.

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