Negative-Temperature Onsager Vortex Clusters in a Quantum Fluid.
Turbulence in classical fluids is a ubiquitous non-equilibrium phenomenon, yet a complete theoretical description for turbulent flow remains a challenging problem. A useful simplification for ideal two-dimensional (2D) fluids is to describe the turbulent flow with long-range-interacting point vortices, each possessing quantised circulation. In 1949, Onsager applied statistical mechanics to determine the equilibria of this model. He showed that at sufficiently high energies, like-circulation vortices preferentially aggregate into large-scale clusters, and are characterised by a negative absolute temperature. Onsager's theory has been highly influential, providing understanding of diverse quasi-2D systems such as turbulent soap films, guiding-centre plasmas, and self-gravitating systems. It also predicts the striking tendency of 2D turbulence to spontaneously form large-scale, long-lived vortices -- Jupiter's Great Red Spot is a well-known example. However, Onsager's theory doesn't quantitatively apply to classical fluids where vorticity is continuous, and experimental systems demonstrating Onsager's point-vortex statistical mechanics have remained elusive. Here we realise high energy, negative-temperature vortex clusters in a uniform superfluid Bose-Einstein condensate. Our results confirm Onsager's prediction of negative temperature clustered phases of quantum vortices, and demonstrate the utility of point-vortex statistical mechanics in 2D quantum fluids. This work opens future directions for the study of turbulent dynamics and we anticipate exploring the entire phase diagram of 2D quantum vortices, including the formation of clusters from 2D quantum turbulence.
Publisher URL: http://arxiv.org/abs/1801.06951
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