Abstract
We have studied statistical mechanics of a gas of vortices in two dimensions. We introduce a new observable—a condensate fraction of Onsager vortices—to quantify the emergence of the vortex condensate. The condensation of Onsager vortices is most transparently observed in a single vortex species system and occurs due to a competition between solid body rotation (see vortex lattice) and potential flow (see multiple quantum vortex state). We propose an experiment to observe the condensation transition of the vortices in such a single vortex species system.
Highlights
Perhaps the most astonishing aspect of turbulence is not the complexity of its dynamics but rather that it feeds the emergence of ordered structures out of chaos
Notwithstanding the negative absolute Boltzmann temperature states were observed in nuclear spin systems [3,4,5] soon after Onsager’s theoretical prediction, and more recently in the motional degrees of freedom of cold atoms confined in optical lattices [6], the negative temperature Onsager vortex states in their original context of 2Dfluid turbulence have remained elusive, until recently
In a neutral system with Ntot vortices in total, the condensation of Onsager vortices occurs at a critical negative temperature TEBC = −αNtot/4 [11,12,13], where a = rs k2 4pkB = THH is the critical positive temperature for the Hauge–Hemmer pair-collapse transition [14, 15], which in the case of non-zero vortex core size becomes renormalised to the Berezinskii–Kosterlitz– Thouless (BKT) critical temperature TBKT = THH/2 [16,17,18]
Summary
Original content from this Abstract work may be used under We have studied statistical mechanics of a gas of vortices in two dimensions. The condensation of Onsager vortices is most transparently observed in a single vortex. We propose an experiment to observe the the work, journal citation condensation transition of the vortices in such a single vortex species system
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