Directed percolation universality class in transition of quantum turbulence
Quantum turbulence in quantum fluid features a spatially and dynamically complicated structure of quantized vortices with quantized circulation. I talk about non-equilibrium phase transition from quantum turbulence with vortices to vortex-free state of quantum fluid obtained by our numerical simulations of the dissipative Gross-Piteavskii equation. In the case of quantum fluid, we can easily distinguish turbulent and vortex-free states as a system with or without vortices. Defining the vortex density as the “order parameter of turbulence”, we find that the transition of quantum turbulence can be regarded as the non-equilibrium phase transition belonging to the temporally-directed percolation universality class by obtaining three independent critical exponents for vortex density in steady state, vortex density in quench dynamics, and fractal dimension of vortices in steady state. The key concept is that vortices has a finite energy barrier to be nucleated and cannot be re-nucleated after their extinction.