Dissipation and Decay of Three-Dimensional Holographic Quantum Turbulence

Abstract

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∼t−1.5 to L∼t−1, similar to the experimental observation of He3 in Bradley [], and of He4 in Stalp [] and in Walmsley and Golov []. 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 . Published by the American Physical Society 2025