Onsager-Kraichnan Condensation in Decaying Two-Dimensional Quantum Turbulence

TL;DR

This paper develops a first-principles approach to connect quantum vortex dynamics in superfluids with classical 2D turbulence models, revealing the emergence of Onsager-Kraichnan condensates through vortex clustering and energy condensation.

Contribution

It introduces a mapping from the Gross-Pitaevskii equation to the point-vortex model, enabling Monte Carlo sampling of vortex states and uncovering new negative-temperature vortex phases.

Findings

Identification of negative-temperature vortex states with macroscopic clustering

Observation of energy condensation into large vortex clusters

Demonstration of dynamical formation of Onsager-Kraichnan condensates

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.