Dissipation and Decay of Three Dimensional Holographic Quantum Turbulence

TL;DR

This paper uses holographic duality to simulate three-dimensional quantum turbulence decay, revealing different decay regimes and confirming the proportionality between energy dissipation rate and vortex line density, aligning with experimental observations.

Contribution

It introduces a holographic simulation framework for quantum turbulence decay and identifies decay behaviors consistent with experimental data.

Findings

Decay behaviors range from L~t^{-1.5} to L~t^{-1} depending on initial conditions.

Energy dissipation rate is proportional to the square of vortex line density.

Results align with experimental observations in superfluid helium.

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 $L\sim t^{-1.5}$ 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).