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arXiv:2511.05981

Quantum vortices in entanglement: a novel idea for large vortex filaments

S. V. Talalov

math-phquant-phSubmitted Nov 8, 2025• Announced Nov 11, 2025• Revised Dec 1, 2025 (v2)
v1 · Nov 8, 2025v2 · Dec 1, 2025
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Abstract

In this study, we propose a new approach to describing certain macroscopic objects that can arise in a quantum fluid. These objects are formed by means of quantum entanglement from the circular-shaped mesoscale and microscale vortices, and can be interpreted as a vortex filaments with any shape and size. The method is based on a quantization scheme for classical closed vortex filaments that was proposed by the author early \cite{Tal18,Tal22_1,Tal_Chaos25J}. The model we consider examines the instantaneous picture of the locations in space $\mathbb R_3$ of such filaments with a small, but non-zero, core diameter. Both energy and circulation of the studied filaments are calculated using the proposed approach. We demonstrate that the adopted concept leads to the emergence of secondary vortices around these investigated filament-like objects. We also study the specific mechanisms by which large vortex loops can disconnect and create the filament fragments . From our point of view, the proposed approach to describing vortex filaments within a vortex tangle can be seen as an important step toward understanding the appearance of quantum turbulence.

Journal reference
Chaos, Solitons and Fractals 202 (2026) 117582
DOI
10.1016/j.chaos.2025.117582

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In this study, we propose a new approach to describing certain macroscopic objects
that can arise in a quantum fluid. These objects are formed by means of quantum entanglement from the circular-shaped mesoscale and microscale vortices, and can be interpreted as a vortex filaments with any shape and size. The method is based on a quantization scheme for classical closed vortex filaments that was proposed by the author early \cite{Tal18,Tal22_1,Tal_Chaos25J}. The model we consider examines the instantaneous picture of the locations in space R3\mathbb R_3R3​ of such filaments with a small, but non-zero, core diameter.
Both energy and circulation of the studied filaments are calculated using the proposed approach. We demonstrate that the adopted concept leads to the emergence of secondary vortices around these investigated filament-like objects.
We also study the specific mechanisms by which large vortex loops can disconnect and create the filament fragments . From our point of view, the proposed approach to describing vortex filaments within a vortex tangle can be seen as an important step toward understanding the appearance of quantum turbulence.
Here, we investigate the motion of a thin circular quantum vortex filament near the infinite planar surface. The fluid surrounding this surface moves with a non-zero velocity v\bf{v}v, which is parallel to the surface. We study the specific features of this quantum system and show that they are quite suitable for the boundary layer theory. The developed model allows us to calculate the vortex energy spectrum, E=E(p)E = E({\bf p})E=E(p), where p{\bf p}p is the total momentum of a vortex ring. We have demonstrated that this function has complex non-trivial dependence on the velocity v\bf{v}v. It is stated that the inverse effective mass of a vortex under consideration is of a tensorial nature. In certain quantum states, the system shows the possibility of both negative and positive effective mass existing. This study employs a novel quantization method for classical closed vortex filaments, developed by the author earlier.
We explore the movement of a thin, circular quantum vortex filament within an infinite cylindrical pipe. The fluid surrounding the vortex ring moves through the pipe at a non-zero velocity denoted by vvv. Our study examines the energy spectrum E=E(p)E = E(p)E=E(p), where ppp represents the total momentum of a vortex ring. We have demonstrated that the function E(p)E(p)E(p) significantly depends on the velocity vvv. The discovered spectrum E(p)E(p)E(p) reveals the existence of states with both negative and extremely large effective masses. We also explored the hypothesis regarding the existence of coupled vortex pairs possessing finite summary effective masses. Every pair consists of vortices that possess both positive and negative masses, with the magnitude of these masses being unrestricted. In our model, the criterion for the appearance of these states is based on comparing two numbers. The first is seen as a quantum counterpart to the Reynolds number, while the second represents its critical value for a flow with a single vortex. We also explore how this studied effect might contribute to the emergence of quantum turbulence. This study discusses a method for determining the critical Reynolds number in quantum turbulence, using the proposed model as a framework. Here, we use a new quantization technique for classical closed vortex filaments developed by the author earlier.
Quantum turbulence is characterised by the collective motion of mutually interplaying thin and discrete vortex filaments of fixed circulation which move in two mutually interacting fluid components. Despite this very peculiar nature determined by quantum-mechanical effects, turbulence in quantum fluids may exhibit very similar features to classical turbulence in terms of the vortex dynamics, energy spectrum and decay and intermittency. The recent work by Blaha et al. (2025 J. Fluid. Mech. 1015, A57) reveals an additional classical behaviour of quantum turbulence, by showing that the trajectories of starting vortices shed by accelerating airfoils in a quantum fluid are almost indistinguishable from their counterpart in classical viscous flows. These results strongly support the suggestive idea that turbulent flows, both classical and quantum, may be described by the collective dynamics of interacting, thin and discrete filaments of fixed circulation.
The idea that chaotic set of quantum vortices can mimic classical turbulence, or at least reproduce many main features, is currently actively being developed. Appreciating significance of the challenging problem of the classical turbulence it can be expressed that the idea to study it in terms of quantized line is indeed very important and may be regarded as a breakthrough. For this reason, this theory should be carefully scrutinized. One of the basic arguments supporting this point of view is the fact that vortex tangle decays at zero temperature, when the apparent mechanism of dissipation (mutual friction) is absent. Since the all possible mechanisms of dissipation of the vortex energy, discussed in the literature, are related to the small scales, it is natural to suggest that the Kolmogorov cascade takes the place with the flow of the energy, just as in the classical turbulence. In a series of recent experiment attenuation of vortex line density was observed and authors attribute this decay to the properties of the Kolmogorov turbulence. In the present work we discuss alternative possibility of decay of the vortex tangle, which is not related to dissipation at small scales. This mechanism is just the diffusive like spreading of the vortex tangle. We discuss a number of the key experiments, considering them both from the point of view of alternative explanation and of the theory of Kolmogorov turbulence in quantum fluids.
Interactions and reconnections of vortices are fundamental in many areas of physics, including classical and quantum fluids where they are central to understanding phenomena such as turbulence. In three-dimensional (3D) superfluids, quantum vortices are one-dimensional filaments that can intersect, reconnect, and recoil with irreversible dynamics described by near-universal scaling laws. We explore quantum-vortex reconnections in a four-dimensional superfluid, where a vortex is a two-dimensional surface. Using real-time numerical simulations, we find much richer behavior than in 3D, including stable intersecting vortex surfaces which do not reconnect, and unusual vortex reconnections which occur without significant energy dissipation, which may indicate quasireversible dynamics. Our work raises many interesting questions about vortex physics in extradimensional systems and may be further extended to look at vortex dynamics and turbulence in higher-dimensional spaces.
Entangled vortex filaments are essential to turbulence, serving as coherent structures that govern nonlinear fluid dynamics and support the reconstruction of fluid fields to reveal statistical properties. This study introduces a quantum implicit representation of vortex filaments in turbulence, employing a levelset method that models the filaments as the intersection of the real and imaginary zero iso-surfaces of a complex scalar field. Describing the fluid field via the scalar field offers distinct advantages in capturing complex structures, topological properties and fluid dynamics, while opening new avenues for innovative solutions through quantum computing platforms. The representation is reformulated into an eigenvalue problem for Hermitian matrices, enabling the conversion of velocity fields into complex scalar fields that embed the vortex filaments. The resulting optimisation is addressed using a variational quantum eigensolver, with Pauli operator truncation and deep learning techniques applied to improve efficiency and reduce noise. The proposed quantum framework achieves a near-linear time complexity and a exponential storage reduction while maintaining a balance of accuracy, robustness and versatility, presenting a promising tool for turbulence analysis, vortex dynamics research, and machine learning dataset generation.