Universal anomalous turbulent diffusion in quantum fluids

TL;DR

This study reveals that vortices in turbulent quantum fluids exhibit universal anomalous diffusion at small times, transitioning to normal diffusion at larger times, driven by a generic scaling property of vortex velocity.

Contribution

It provides the first systematic numerical analysis of vortex diffusion in quantum turbulence, demonstrating universal superdiffusive behavior and its transition to normal diffusion.

Findings

Vortices exhibit superdiffusion at small times

Diffusion transitions to normal at large times

Vortex velocity scaling underpins the diffusion behavior

Abstract

In classical viscous fluids, turbulent eddies are known to be responsible for the rapid spreading of embedded particles. But in an inviscid quantum fluid where the turbulence is induced by a chaotic tangle of quantized vortices, dispersion of the particles is achieved via a non-classical mechanism, i.e., their binding to the evolving quantized vortices. However, there is limited existing knowledge on how the vortices diffuse and spread in turbulent quantum fluids. Here we report a systematic numerical study of the apparent diffusion of vortices in a random vortex tangle in superfluid helium-4 using full Biot-Savart simulation. We reveal that the vortices in pure superfluid exhibit a universal anomalous diffusion (superdiffusion) at small times, which transits to normal diffusion at large times. This behavior is found to be caused by a generic scaling property of the vortex velocity, which should exist in all quantum fluids where the Biot-Savart law governs the vortex motion. Our simulation at finite temperatures also nicely reproduces recent experimental observations. The knowledge obtained from this study may form the foundation for understanding turbulent transport and universal vortex dynamics in various condensed-matter and cosmic quantum fluids.