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arXiv:2606.15803

Quantum vortex in a fluid flow: negative effective mass and a novel mechanism for turbulence formation

S. V. Talalov

physics.flu-dynmath-phquant-phSubmitted Jun 14, 2026• Announced Jun 16, 2026
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Abstract

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 $v$. Our study examines the energy spectrum $E = E(p)$, where $p$ represents the total momentum of a vortex ring. We have demonstrated that the function $E(p)$ significantly depends on the velocity $v$. The discovered spectrum $E(p)$ 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.

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Guillaume Gauthier, Matthew T. Reeves, Xiaoquan Yu +6 more

Turbulence in classical fluids is a ubiquitous non-equilibrium phenomenon, yet a complete theoretical description for turbulent flow remains a challenging problem. A useful simplification for ideal two-dimensional (2D) fluids is to describe the turbulent flow with long-range-interacting point vortices, each possessing quantised circulation. In 1949, Onsager applied statistical mechanics to determine the equilibria of this model. He showed that at sufficiently high energies, like-circulation vortices preferentially aggregate into large-scale clusters, and are characterised by a negative absolute temperature. Onsager's theory has been highly influential, providing understanding of diverse quasi-2D systems such as turbulent soap films, guiding-centre plasmas, and self-gravitating systems. It also predicts the striking tendency of 2D turbulence to spontaneously form large-scale, long-lived vortices -- Jupiter's Great Red Spot is a well-known example. However, Onsager's theory doesn't quantitatively apply to classical fluids where vorticity is continuous, and experimental systems demonstrating Onsager's point-vortex statistical mechanics have remained elusive. Here we realise high energy, negative-temperature vortex clusters in a uniform superfluid Bose-Einstein condensate. Our results confirm Onsager's prediction of negative temperature clustered phases of quantum vortices, and demonstrate the utility of point-vortex statistical mechanics in 2D quantum fluids. This work opens future directions for the study of turbulent dynamics and we anticipate exploring the entire phase diagram of 2D quantum vortices, including the formation of clusters from 2D quantum turbulence.

•Jan 22, 2018•3 citations
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.
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.
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.
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.
Abstract Chapter 5 delves into quantum turbulence in superfluid helium and atomic Bose-Einstein condensates (BECs). The foundation of quantum turbulence research lies in classical fluid dynamics and turbulence, which is why we begin by covering essential concepts like the Reynolds number and Kolmogorov’s -5/3 power law in the energy spectrum. These principles are crucial for understanding quantum turbulence. We then explore the shared aspects of quantum turbulence in superfluid helium and atomic BECs, such as the differences in vortex configurations compared to classical turbulence, energy spectra, cascades, and the distinction between quasiclassical (Kolmogorov) and ultraquantum (Vinen) turbulence, focusing on their decay behaviors. In superfluid helium, we emphasize experimental studies in thermal counterflow and numerical simulations using the Vortex Filament Model (VFM). The advent of visualization experiments in the mid-2000s was transformative, allowing the observation of normal fluid velocity profiles and accelerations via tracer particles, which led to more accurate simulations coupling the VFM with normal fluid dynamics. Another significant topic is the energy spectrum of quantum turbulence, and whether it mirrors classical turbulence remains a key question. In addition to thermal counterflow, localized quantum turbulence generated by oscillating objects has been a major area of study. We present research showing how quantized vortices grow and evolve into turbulence. Superfluid 3He-B also provides a platform for quantum turbulence, with advancements in microfabrication bringing MEMS and NEMS into focus for studying quantum hydrodynamics at micro- and nanoscale, influenced by boundary conditions. In atomic BECs, confined by potentials, turbulence is induced through techniques like shaking or moving potentials. A unique aspect of BECs is two-dimensional quantum turbulence, featuring inverse energy cascades, Onsager vortices, and negative temperature states. Finally, atomic BECs, being compressible, serve as a platform for both vortex and wave turbulence. Multicomponent BECs, such as spinor BECs, introduce spin turbulence, further diversifying the field.
The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluid model is the most successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state as well as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposed method. We apply this method to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure. We show that at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures.
Turbulence in classical fluids is a ubiquitous non-equilibrium phenomenon, yet a complete theoretical description for turbulent flow remains a challenging problem. A useful simplification for ideal two-dimensional (2D) fluids is to describe the turbulent flow with long-range-interacting point vortices, each possessing quantised circulation. In 1949, Onsager applied statistical mechanics to determine the equilibria of this model. He showed that at sufficiently high energies, like-circulation vortices preferentially aggregate into large-scale clusters, and are characterised by a negative absolute temperature. Onsager's theory has been highly influential, providing understanding of diverse quasi-2D systems such as turbulent soap films, guiding-centre plasmas, and self-gravitating systems. It also predicts the striking tendency of 2D turbulence to spontaneously form large-scale, long-lived vortices -- Jupiter's Great Red Spot is a well-known example. However, Onsager's theory doesn't quantitatively apply to classical fluids where vorticity is continuous, and experimental systems demonstrating Onsager's point-vortex statistical mechanics have remained elusive. Here we realise high energy, negative-temperature vortex clusters in a uniform superfluid Bose-Einstein condensate. Our results confirm Onsager's prediction of negative temperature clustered phases of quantum vortices, and demonstrate the utility of point-vortex statistical mechanics in 2D quantum fluids. This work opens future directions for the study of turbulent dynamics and we anticipate exploring the entire phase diagram of 2D quantum vortices, including the formation of clusters from 2D quantum turbulence.