Dissipation and Decay of Three Dimensional Holographic Quantum Turbulence

Quantum turbulence is a far-from-equilibrium process characterized by high nonlinearity. Holographic duality provides a systematic framework for simulating the decaying $(3+1)$-dimensional quantum turbulence by numerically solving the dual Abelian-Higgs theory in a $(4+1)$-dimensional black hole background. We reveal that different types of decay behavior of the total vortex line density $L$ emerge depending on the initial vortex line density, ranging from $L\sim t^{-1.5}$ to $L\sim t^{-1}$, similar to the experimental observation of $^3$He in Phys. Rev. Lett. 96, 035301 (2006), and of $^4$He in Phys. Rev. Lett. 82, 4831 (1999) and in Phys. Rev. Lett. 118, 134501 (2017). Furthermore, by measuring the energy flux at the black hole horizon, we determine that the energy dissipation rate $dE/dt$ is proportional to the square of the total vortex line density, consistent with the vortex line decay equation proposed by W. F. Vinen and also the experimental measurement in Nature Physics 7, 473 - 476 (2011).