Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence

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

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.

Citation

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. https://doi.org/10.1103/physrevlett.112.145301

• 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
• DOI: https://doi.org/10.1103/physrevlett.112.145301
• Public URL: https://durham-repository.worktribe.com/output/1456240