Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0502119

Slow Vortex Formation in Applied Flow: the Precursor to Superfluid Turbulence

Antti Finne, V. B. Eltsov, Georg Eska, Risto Hänninen, Juha Kopu, M. Krusius, E. V. Thuneberg, Makoto Tsubota

Published Feb 4, 2005• 0 citations
arXivHTMLPDF

Abstract

The dynamics of quantized vortices in rotating $^3$He-B is investigated in the low density (single-vortex) regime as a function of temperature. An abrupt transition is observed at $0.5 T_{\rm c}$. Above this temperature the number of vortex lines remains constant, as they evolve to their equilibrium positions. Below this temperature the number of vortices increases linearly in time until the vortex density has grown sufficiently for turbulence to switch on. On the basis of numerical calculations we suggest a mechanism responsible for vortex formation at low temperatures and identify the mutual friction parameter which governs its abrupt temperature dependence.

Related papers

Real-Time Dynamics of Quantized Vortices in a Unitary Fermi Superfluid

Aurel Bulgac, Yuan-Lung Luo, Piotr Magierski +2 more

We introduce a comprehensive theoretical framework for the fermionic superfluid dynamics, grounded on a local extension of the time-dependent density functional theory. With this approach, we describe the generation and the real-time evolution and interaction of quantized vortices, the large-amplitude collective modes, as well as the loss of superfluidity at high flow velocities. We demonstrate the formation of vortex rings and provide a microscopic description of the crossing and reconnection of quantized vortex lines in a fermion superfluid, which provide the mechanism for the emergence of quantum turbulence at very low temperatures. We observe that superfluidity often survives when these systems are stirred with velocities far exceeding the speed of sound.

arXiv:1011.5999•Science•Jun 10, 2011•80 citations

Modeling quantum fluid dynamics at nonzero temperatures

Natalia G. Berloff, Marc Brächet, Nick P. Proukakis

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.

Proceedings of the National Academy of Sciences•Mar 24, 2014•80 citations

Investigation of Quantum Turbulence in Superfluid (_^4)HeUsing Injected Ions and ?He?_2^* Molecules in the ZeroTemperature Limit

Fatemeh Pakpour

The decay of quantum turbulence in superfluid (_^4)He in the zero temperature limit wasinvestigated. Quantum turbulence was created by impulsive spin-down from a specific angular velocity to rest. A measurement of the vortex line density was performed using the scattering of charged vortex rings. The vortex line density decayed as L ? t^(-3/2) which is the characteristic of quasiclassical turbulence forced at large length scales. The interaction of metastable spin-triplet ?He?_2^* molecules with quantized vortex lines in superfluid (_^4)He at temperatures below 200 mK was studied too. The molecules were generated during an injection of electrons from a sharp metal tip at high voltage. They were detected as a current into a metal collector after ionization upon colliding with the collector surface. The detected current was suppressed by even a small rotation indicating the trapping of the molecules on quantized vortices. The presence of (_^3)He impurities at the level of 0.3 ppb strongly suppressed the detected signal. The temperature dependence of the detected signal showed a sharp peak, most probably associated with the condensation of (_^3)He atoms on vortex cores. The time of flight of the molecules as a function of temperature was measured. It was observed that there are three regimes for ?He?_2^* molecules transportation in superfluid (_^4)He : ballistic regime for T 200 mK, and an intermediate regime between them. The vortex lines were created by either rotation or ion injection. The trapping diameter of the molecules on quantized vortices was found to be 96 � 6 nm at pressure of 0.1 bar and 27 � 5 nm at 5.0 bar. It was also demonstrated that a tangle of vortices moving in superfluid (_^4)He are capable of conveying the ?He?_2^* molecules through the drift region.

•Sep 24, 2014•0 citations

Spontaneous vortices in the formation of fermionic superfluid

Xiangpei Liu, Xing-Can Yao, Youjin Deng +5 more

The generation of spontaneous vortices and the formation of superfluids are closely intertwined. Here, we report an experimental study of quench dynamics across the superfluid phase transition in a strongly interacting Fermi gas at unitarity, by ramping down the external trapping potential. The superfluid phase coherence is recorded, and several tens of vortices are found to be generated during the quench process. A universal growth dynamics is revealed that for different quenches, the experimental data of quasi-condensate collapse onto a single curve as a function of evolving time rescaled by characteristic coherence-formation time. Moreover, we find that for a wide range of quenches, the dependence of the vortex density on the quasi-condensate formation time, rather than the ramping time, is well described by the celebrated the Kibbble-Zurek mechanism. Our work paves the way to study the complex vortex dynamics in vortex turbulence systems.

•Feb 20, 2019•0 citations

Vortex waves in a rotating superfluid

Karen L. Henderson, Carlo F. Barenghi

In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in 3 He-B, that q = α/(1 − α') < 1.3, where α and α' are mutual friction parameters. The authors put forward a qualitative argument that q is the ratio of dissipative and inertial forces on the superfluid, so for q < 1 inertial forces should overcome the dissipative forces and cause turbulence. Thus 1/ q would play, for a quantum fluid, the same role played in classical fluid dynamics by the Reynolds number (the ratio of inertial forces and dissipative forces in the Navier-Stokes equation). The aim of this work is to supplement this qualitative condition q = 1 with a quantitative calculation. By analysing both axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid, we find that in the long axial wavelength limit the condition q = 1 is the crossover between damped and propagating Kelvin waves; thus, for q > 1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. Besides the relevance to the experiment of Finne et al. , the spectrum of oscillations which we find is relevant to the study of torsional oscillations of a rotating superfluid and generalises to three dimensions the spectrum of Kelvin waves on an isolated vortex line.

Europhysics Letters (EPL)•Jul 1, 2004•11 citations

Classical and quantum regimes of superfluid turbulence

Григорий Ефимович Воловик

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q −1 playing the same role as the Reynolds number Re= UR/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re≫1 in classical hydrodynamics, and q ≪1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Re s = UR/κ , which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. A phase diagram of the dynamical vortex states is suggested.

arXiv:cond-mat/0310021•Journal of Experimental and Theoretical Physics Letters•Nov 1, 2003•71 citations
The dynamics of quantized vortices in rotating 3^33He-B is investigated in the low density (single-vortex) regime as a function of temperature. An abrupt transition is observed at 0.5Tc0.5 T_{\rm c}0.5Tc​. Above this temperature the number of vortex lines remains constant, as they evolve to their equilibrium positions. Below this temperature the number of vortices increases linearly in time until the vortex density has grown sufficiently for turbulence to switch on. On the basis of numerical calculations we suggest a mechanism responsible for vortex formation at low temperatures and identify the mutual friction parameter which governs its abrupt temperature dependence.
We introduce a comprehensive theoretical framework for the fermionic superfluid dynamics, grounded on a local extension of the time-dependent density functional theory. With this approach, we describe the generation and the real-time evolution and interaction of quantized vortices, the large-amplitude collective modes, as well as the loss of superfluidity at high flow velocities. We demonstrate the formation of vortex rings and provide a microscopic description of the crossing and reconnection of quantized vortex lines in a fermion superfluid, which provide the mechanism for the emergence of quantum turbulence at very low temperatures. We observe that superfluidity often survives when these systems are stirred with velocities far exceeding the speed of sound.
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.
The decay of quantum turbulence in superfluid (_^4)He in the zero temperature limit wasinvestigated. Quantum turbulence was created by impulsive spin-down from a specific angular velocity to rest. A measurement of the vortex line density was performed using the scattering of charged vortex rings. The vortex line density decayed as L ? t^(-3/2) which is the characteristic of quasiclassical turbulence forced at large length scales. The interaction of metastable spin-triplet ?He?_2^* molecules with quantized vortex lines in superfluid (_^4)He at temperatures below 200 mK was studied too. The molecules were generated during an injection of electrons from a sharp metal tip at high voltage. They were detected as a current into a metal collector after ionization upon colliding with the collector surface. The detected current was suppressed by even a small rotation indicating the trapping of the molecules on quantized vortices. The presence of (_^3)He impurities at the level of 0.3 ppb strongly suppressed the detected signal. The temperature dependence of the detected signal showed a sharp peak, most probably associated with the condensation of (_^3)He atoms on vortex cores. The time of flight of the molecules as a function of temperature was measured. It was observed that there are three regimes for ?He?_2^* molecules transportation in superfluid (_^4)He : ballistic regime for T 200 mK, and an intermediate regime between them. The vortex lines were created by either rotation or ion injection. The trapping diameter of the molecules on quantized vortices was found to be 96 � 6 nm at pressure of 0.1 bar and 27 � 5 nm at 5.0 bar. It was also demonstrated that a tangle of vortices moving in superfluid (_^4)He are capable of conveying the ?He?_2^* molecules through the drift region.
The generation of spontaneous vortices and the formation of superfluids are closely intertwined. Here, we report an experimental study of quench dynamics across the superfluid phase transition in a strongly interacting Fermi gas at unitarity, by ramping down the external trapping potential. The superfluid phase coherence is recorded, and several tens of vortices are found to be generated during the quench process. A universal growth dynamics is revealed that for different quenches, the experimental data of quasi-condensate collapse onto a single curve as a function of evolving time rescaled by characteristic coherence-formation time. Moreover, we find that for a wide range of quenches, the dependence of the vortex density on the quasi-condensate formation time, rather than the ramping time, is well described by the celebrated the Kibbble-Zurek mechanism. Our work paves the way to study the complex vortex dynamics in vortex turbulence systems.
In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in 3 He-B, that q = α/(1 − α') < 1.3, where α and α' are mutual friction parameters. The authors put forward a qualitative argument that q is the ratio of dissipative and inertial forces on the superfluid, so for q < 1 inertial forces should overcome the dissipative forces and cause turbulence. Thus 1/ q would play, for a quantum fluid, the same role played in classical fluid dynamics by the Reynolds number (the ratio of inertial forces and dissipative forces in the Navier-Stokes equation). The aim of this work is to supplement this qualitative condition q = 1 with a quantitative calculation. By analysing both axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid, we find that in the long axial wavelength limit the condition q = 1 is the crossover between damped and propagating Kelvin waves; thus, for q > 1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. Besides the relevance to the experiment of Finne et al. , the spectrum of oscillations which we find is relevant to the study of torsional oscillations of a rotating superfluid and generalises to three dimensions the spectrum of Kelvin waves on an isolated vortex line.
We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q −1 playing the same role as the Reynolds number Re= UR/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re≫1 in classical hydrodynamics, and q ≪1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Re s = UR/κ , which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. A phase diagram of the dynamical vortex states is suggested.