Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence

• Published in: Physical review letters Vol. 112; no. 14; p. 145301
• Main Authors: Billam, T P, Reeves, M T, Anderson, B P, Bradley, A S
• Format: Journal Article
• Language: English
• Published: United States 11.04.2014
• ISSN: 1079-7114
• DOI: 10.1103/PhysRevLett.112.145301

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.