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

Physical Review A

Transition to quantum turbulence in a Bose-Einstein condensate through the bending-wave instability of a single-vortex ring

Tzyy‐Leng Horng, C.-H. Hsueh, Shih-Chuan Gou

Published Jun 30, 2008• 32 citations
Publisher

Abstract

We investigate the dynamics of an unstable vortex ring in a pancake-shaped Bose-Einsten condensate by solving the Gross-Pitaevskii equation numerically. It is found that a quasisteady turbulent state with long relaxation time can be achieved through the disruption of a perturbed vortex ring in the condensate owing to the bending-wave instability. We verify that this quantum turbulent state is characterized by Kolmogorov energy spcetrum.

DOI
10.1103/physreva.77.063625

Related papers

Two-dimensional quantum turbulence in a nonuniform Bose-Einstein condensate

Tzyy‐Leng Horng, C.-H. Hsueh, Shih-Wei Su +2 more

We investigate the dynamics of turbulent flow in a two-dimensional trapped Bose-Einstein condensate by solving the Gross-Pitaevskii equation numerically. The development of the quantum turbulence is activated by the disruption of an initially embedded vortex quadrupole. By calculating the incompressible kinetic-energy spectrum of the superflow, we conclude that this quantum turbulent state is characterized by the Kolmogorov-Saffman scaling law in the wave-number space. Our study predicts the coexistence of two subinertial ranges responsible for the energy cascade and enstrophy cascade in this prototype of two-dimensional quantum turbulence.

Physical Review A•Aug 24, 2009•62 citations

Bending-wave instability of a vortex ring in a trapped Bose-Einstein condensate

Tzyy‐Leng Horng, Shih-Chuan Gou, Tai‐Chia Lin

Using a velocity formula derived by matched asymptotic expansion, we study the dynamics of a vortex ring in an axisymmetric Bose-Einstein condensate in the Thomas-Fermi limit. The trajectory for an axisymmetrically placed and oriented vortex ring shows that it generally precesses in a condensate. The linear instability due to bending waves is investigated both numerically and analytically. General stability boundaries for various perturbed wave numbers are computed. Our analysis suggests that a slightly oblate trap is needed to prevent the vortex ring from becoming unstable.

arXiv:cond-mat/0604009•Physical Review A•Oct 18, 2006•48 citations

Quantum turbulence by vortex stirring in a spinor Bose-Einstein condensate

Bruno Villasenor, Roberto Zamora-Zamora, Damián Bernal +1 more

We introduce a mechanism to develop a turbulent flow in a spinor Bose-Einstein condensate, consisting in the stirring of a single line vortex by means of an external magnetic field. We find that density and velocity fluctuations have white-noise power spectra at large frequencies and that the energy spectrum obeys Kolmogorov 5/3 law in the turbulent region. As the stirring is turned off, the flow decays to an agitated nonequilibrium state that shows an energy bottleneck crossover at small length scales. We demonstrate our findings by numerically solving two-state spinor coupled three-dimensional Gross-Pitaevskii equations. We suggest that this mechanism may be experimentally implemented in spinor ultracold gases confined by optical traps.

arXiv:1309.6218•Physical Review A•Mar 10, 2014•17 citations

Quantum turbulence in a trapped Bose-Einstein condensate

Michikazu Kobayashi, Makoto Tsubota

We study quantum turbulence in trapped Bose-Einstein condensates by numerically solving the Gross-Pitaevskii equation. Combining rotations around two axes, we successfully induce quantum turbulent state in which quantized vortices are not crystallized but tangled. The obtained spectrum of the incompressible kinetic energy is consistent with the Kolmogorov law, the most important statistical law in turbulence.

arXiv:cond-mat/0703603•Physical Review A•Oct 31, 2007•141 citations

Turbulence and far-from-equilibrium equation of state of Bogoliubov waves in Bose-Einstein condensates

Ying Zhu, Giorgio Krstulovic, Sergey Nazarenko

Abstract Bogoliubov waves are fundamental excitations of Bose-Einstein condensates. They emerge from a perturbed ground state and interact nonlinearly, triggering turbulent cascades. Here, we study turbulent Bose-Einstein condensates theoretically and numerically using the three-dimensional Gross-Pitaevskii model and its associated wave-kinetic equations. We derive a Kolmogorov-like stationary spectrum for short Bogoliubov waves and find a complete analytical expression for the spectrum in the long-wave acoustic regime. We then use our predictions to explain the far-from-equilibrium equation of state observed in recent turbulent quantum gas experiments, and to suggest future experimental settings.

arXiv:2408.15163•Communications Physics•Jul 8, 2026•1 citation

Slowing down of vortex rings in Bose-Einstein condensates

J. L. Helm, Carlo F. Barenghi, Anthony J. Youd

We consider vortex rings moving in a Bose--Einstein condensate. By numerically solving the Gross--Pitaevskii equation, we show that if the circular shape of the ring is perturbed by helical Kelvin waves of given amplitude and azimuthal wave number, the translational self-induced velocity of the vortex ring is reduced; at large amplitude, the vortex ring halts.

Physical Review A•Apr 8, 2011•19 citations
We investigate the dynamics of an unstable vortex ring in a pancake-shaped Bose-Einsten condensate by solving the Gross-Pitaevskii equation numerically. It is found that a quasisteady turbulent state with long relaxation time can be achieved through the disruption of a perturbed vortex ring in the condensate owing to the bending-wave instability. We verify that this quantum turbulent state is characterized by Kolmogorov energy spcetrum.
We investigate the dynamics of turbulent flow in a two-dimensional trapped Bose-Einstein condensate by solving the Gross-Pitaevskii equation numerically. The development of the quantum turbulence is activated by the disruption of an initially embedded vortex quadrupole. By calculating the incompressible kinetic-energy spectrum of the superflow, we conclude that this quantum turbulent state is characterized by the Kolmogorov-Saffman scaling law in the wave-number space. Our study predicts the coexistence of two subinertial ranges responsible for the energy cascade and enstrophy cascade in this prototype of two-dimensional quantum turbulence.
Using a velocity formula derived by matched asymptotic expansion, we study the dynamics of a vortex ring in an axisymmetric Bose-Einstein condensate in the Thomas-Fermi limit. The trajectory for an axisymmetrically placed and oriented vortex ring shows that it generally precesses in a condensate. The linear instability due to bending waves is investigated both numerically and analytically. General stability boundaries for various perturbed wave numbers are computed. Our analysis suggests that a slightly oblate trap is needed to prevent the vortex ring from becoming unstable.
We introduce a mechanism to develop a turbulent flow in a spinor Bose-Einstein condensate, consisting in the stirring of a single line vortex by means of an external magnetic field. We find that density and velocity fluctuations have white-noise power spectra at large frequencies and that the energy spectrum obeys Kolmogorov 5/3 law in the turbulent region. As the stirring is turned off, the flow decays to an agitated nonequilibrium state that shows an energy bottleneck crossover at small length scales. We demonstrate our findings by numerically solving two-state spinor coupled three-dimensional Gross-Pitaevskii equations. We suggest that this mechanism may be experimentally implemented in spinor ultracold gases confined by optical traps.
Abstract Bogoliubov waves are fundamental excitations of Bose-Einstein condensates. They emerge from a perturbed ground state and interact nonlinearly, triggering turbulent cascades. Here, we study turbulent Bose-Einstein condensates theoretically and numerically using the three-dimensional Gross-Pitaevskii model and its associated wave-kinetic equations. We derive a Kolmogorov-like stationary spectrum for short Bogoliubov waves and find a complete analytical expression for the spectrum in the long-wave acoustic regime. We then use our predictions to explain the far-from-equilibrium equation of state observed in recent turbulent quantum gas experiments, and to suggest future experimental settings.