A computer simulation of two-dimensional quantum turbulence reports that the motion of the system’s normal-fluid component can become strongly directional and develop unusually heavy statistical tails. Across the reported parameter sets, those fluctuations weakened at higher temperatures even as the density of quantized vortices increased. The result comes from a specific holographic model and is reported in an arXiv preprint.
The study models the turbulence with a fully coupled description rather than prescribing how the fluid components interact. It uses real-time simulations of a two-dimensional holographic superfluid in a three-plus-one-dimensional spacetime. The calculation solves coupled gravity, electromagnetic and scalar-field equations, including momentum transfer, finite-temperature dissipation and mutual friction without empirical input.
How the turbulence was driven
The researchers continuously drove the simulated system by setting the global mean superfluid velocity above the Landau critical threshold, allowing vortices to be injected through the Landau instability. The setup used homogeneous vortex injection rather than an inhomogeneous external force. The calculation then tracked the resulting spectra, velocity distributions and vortex behavior.
The driven run settled into a statistically stationary regime. Its two energy spectra and several spatially averaged quantities reached plateaus with only small fluctuations, including mean superfluid velocity, vortex number, effective temperature and normal-fluid velocity. During the reported evolution, normal-fluid velocity and vortex number rose together, a pattern the paper reports as evidence of mutual-friction drag.
A turbulent signal with a preferred direction
The energy spectra separated the two fluid components. The superfluid spectrum showed different power-law regions across scales, including an inverse-wavenumber form at intermediate scales, a negative five-thirds exponent there and a negative-three form at small scales. The normal-fluid spectrum showed a negative five-thirds region at intermediate scales and a steeper negative-five region at small scales.
The normal-fluid velocity distributions were not shaped like simple bell curves. They had pronounced non-Gaussian tails, meaning unusually large deviations occurred more prominently than a Gaussian comparison would predict. The fluctuations were also anisotropic, with motion along the driving direction, labelled x, significantly larger than motion in the transverse y direction. The paper presents these features as signatures of dynamical backreaction from quantized vortices.
Temperature changed the pattern
The temperature trend ran against a simple vortex-count explanation. Across the reported parameter sets, normal-fluid velocity fluctuations decreased monotonically as temperature increased, while vortex density increased. The authors use this contrast to argue that vortex density is not the dominant control parameter in the driven simulations.
The comparison with freely decaying turbulence sharpened the distinction. In the decaying runs, temperature stayed approximately constant, vortex density fell and normal-fluid fluctuations fell with it. In the driven runs, normal-fluid fluctuations fell as temperature rose even though vortex density increased.
The decay data give a sense of the change in scale. The normal-fluid standard-deviation pair fell from (4.0, 2.8) × 10−3 at simulation time 3100 to (0.46, 0.49) × 10−3 at time 31000. The pair records the directional fluctuation values used in the study’s comparison of x and y motion.
Superfluid fluctuations did not follow the same simple pattern. Unlike the normal fluid, they varied non-monotonically with temperature, which the paper describes as reflecting competing effects from increasing vortex density and decreasing condensate stiffness.
What the simulation does not settle
The findings are outputs from a two-dimensional simulation, so they do not establish how the reported behavior would extend to three-dimensional turbulence. The study also does not directly validate whether its predicted velocity statistics transfer to laboratory systems. Those questions remain outside the evidence supplied here.
There is also a technical limit to the normal-fluid observable. The reported velocity is extracted at leading hydrodynamic order, and the paper cautions that hydrodynamic variables may not be fundamentally well-defined in vortex-rich, far-from-equilibrium regions, especially near vortex cores. The velocity results should therefore be read within that approximation.
The reported trends come without formal error bars, confidence intervals or inferential tests in the supplied analysis. They are therefore patterns in the simulated parameter sets rather than statistically quantified effects. The document is arXiv version 2, dated 30 September 2026.
Paper data and sources
Original title: Active normal-fluid feedback in quantum turbulence from holography
Authors: Yu-Ping An, Li Li, Makoto Tsubota et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-09-29
DOI: Not available
Original paper · Full text