What is it about?

Physicists are fascinated by universal behaviors that appear in completely different physical systems near the critical point associated with a phase transition. In two-dimensions, critical models are linked to stochastic evolution curves (SLE), a wonderful mathematical result with deep physical implications. For example, SLE enable the prediction of universal properties such as the fractal dimension of connected regions in Ising or percolation models. Here we observe the formation of connected regions of vorticity in a turbulent quantum fluid of light. We found that the statistical distribution and the fractal dimension of the vorticity field follows the same universality class of critical percolation. This is the first experimental evidence suggesting that 2D quantum turbulence is conformal invariant.

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Why is it important?

This is the first evidence that 2D quantum turbulence is conformal invariant, with regions of clustered vorticity following the same statistical properties of 2D percolation near the critical point. That is, 2D turbulence is upgraded from scale invariant to conformal invariant, belonging to the same universality class of percolation. This idea was already suggested for classical 2D turbulence based on numerical simulations, but never experimentally confirmed. Finally, these results show that, when quantum vortices are strongly interacting, that is, in certain regimes of healing length and intervortex distance, 2D classical turbulence can be seen as the coarse-grained picture of 2D quantum turbulence.

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This page is a summary of: Conformal invariance of 2D quantum turbulence in an exciton–polariton fluid of light, Applied Physics Reviews, December 2023, American Institute of Physics,
DOI: 10.1063/5.0167655.
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