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. E

Relaxation of twist helicity in the cascade process of linked quantum vortices

Simone Zuccher, Renzo L. Ricca

Published May 18, 2017• 24 citations
Publisher

Abstract

By numerically solving the three-dimensional Gross-Pitaevskii equation we analyze the cascade process associated with the evolution and decay of a pair of linked vortex rings. The system decays through a series of reconnections to produce finally three unlinked, unfolded, almost planar vortex loops. Total helicity, initially zero, remains unchanged throughout the process. The gradual transfer from writhe (due to initial linking) to twist helicity, followed by a continuous relaxation of twist across scales during the evolution is shown to be a generic mechanism that consistently takes place on each individual component.

DOI
10.1103/physreve.95.053109

Related papers

Topological cascade of quantum Borromean rings

Hao Guan, Simone Zuccher, Xin Liu

The evolution and the topological cascade of quantum vortices forming Borromean rings are studied for the first time. The initial configuration of the system is given by three elliptical planar loops linked together, and the evolution is governed by the numerical implementation of the Gross–Pitaevskii equation. It is found that the topological cascade is not unique, but it depends crucially on the initial geometric configuration. Quantum vortices undergo a series of spontaneous reconnections, resulting in various degenerative pathways characterized by different topology and structural complexity triggered by the different inclination of one of the initial ellipses. Typical decaying routes are given by the successive creation of a Whitehead link, a connected sum of two Hopf links, a trefoil knot, a Hopf link, and the final formation of unknotted, unlinked loops. By structural complexity analysis, we show that the generic trend of the vortex decay goes through a series of topological simplifications, resulting in the formation of small-scale planar loops (rings). During the later stage of evolution, the inverse cascade and topological cycles involving the interaction of unknotted loops become more common, remaining sub-dominant to the overall topological simplification process. These results pave the way to investigate the fundamental relations between structural complexity and energy contents.

Physics of Fluids•Feb 1, 2025•3 citations

Helicity transfer during quantised vortex reconnection

Andrew William Baggaley

We consider the reconnection of two untwisted, linked quantised vortex rings in a Bose-Einstein condensate. We show that the reconnection is capable of transferring helicity, from the links present in the initial configuration, to a twisting of the resulting vortex ring, and hence a rotation of the phase plane along the vortex ring. As velocities in a quantum fluid are the gradient of the phase, a twisting of the phase along the vortices leads to an axial flow along the vortices. Hence one would expect that the dynamics of quantum turbulence are strongly influence by the helicity of the initial conditions or the system forcing. Our results also provide an important link between quantised vortex reconnections and reconnections in classical and magnetised fluids.

arXiv:1403.8121•Mar 31, 2014•1 citation

Vortex loops cascade as a channel of quantum turbulence decay

Miron B. Kursa, Konrad Bajer, Tomasz Lipniacki

We demonstrate that a single reconnection of two quantum vortices can lead to the creation of a cascade of vortex rings. Our analysis, motivated by the analytical results in localized induction approximation, involved high resolution Biot-Savart and Gross-Pitaevskii simulations. The latter showed that the rings cascade starts on the atomic scale, with rings diameters orders of magnitude smaller than the characteristic line spacing in the tangle, and thus capable of penetrating the tangle and annihilating on the boundaries. That way such process can be an efficient decay mechanism for sparse or moderately dense vortex tangle at very low temperatures.

Journal of Physics Conference Series•Dec 22, 2011•0 citations

Quantum vortex reconnections mediated by trapped particles

Umberto Giuriato, Giorgio Krstulovic

Reconnections between quantum vortex filaments in the presence of trapped particles are investigated using numerical simulations of the Gross-Pitaevskii equation. Particles are described with classical degrees of freedom and modeled as highly repulsive potentials which deplete the superfluid. First, the case of a vortex dipole with a single particle trapped inside one of the vortices is studied. It is shown that the reconnection takes place at the position of the particle as a consequence of the symmetry breaking induced by it. The separation rate between the reconnecting points is compatible with the known dynamics of quantum vortex reconnections, and it is independent of the particle mass and size. After the reconnection, the particle is pushed away with a constant velocity, and its trajectory is deflected because of the transverse momentum exchange with the vortex filaments. The momentum exchanges between the particle, the vortex, and a density pulse are characterized. Finally, the reconnection of two linked rings, each of them with several initially randomly distributed particles, is studied. It is observed that generically, reconnections take place at the location of trapped particles. It is shown that reconnection dynamics is unaffected for light particles.

arXiv:2007.10008•Physical review. B./Physical review. B•Sep 8, 2020•7 citations

Twist effects in quantum vortices and phase defects

Simone Zuccher, Renzo L. Ricca

Abstract In this paper we show that twist, defined in terms of rotation of the phase associated with quantum vortices and other physical defects effectively deprived of internal structure, is a property that has observable effects in terms of induced axial flow. For this we consider quantum vortices governed by the Gross–Pitaevskii equation (GPE) and perform a number of test cases to investigate and compare the effects of twist in two different contexts: (i) when this is artificially superimposed on an initially untwisted vortex ring; (ii) when it is naturally produced on the ring by the simultaneous presence of a central straight vortex. In the first case large amplitude perturbations quickly develop, generated by the unnatural setting of the initial condition that is not an analytical solution of the GPE. In the second case much milder perturbations emerge, signature of a genuine physical process. This scenario is confirmed by other test cases performed at higher twist values. Since the second setting corresponds to essential linking, these results provide new evidence of the influence of topology on physics.

Fluid Dynamics Research•Jul 21, 2017•12 citations

Dynamical evolution and decay of multi-charged quantum vortex in a Bose–Einstein condensate

Gustavo Deczka Telles, P. E. S. Tavares, A. R. Fritsch +2 more

Abstract We report the observation of the twisted decay of quadruply charged vortices taking place in an atomic Bose–Einstein condensate. Supporting numerical simulations show that the singly-charged vortices, which result from the decay of a multi-charged vortex, twist around intertwined in the shape of helical Kelvin waves.

arXiv:1505.00616•Laser Physics Letters•Dec 6, 2021•14 citations
By numerically solving the three-dimensional Gross-Pitaevskii equation we analyze the cascade process associated with the evolution and decay of a pair of linked vortex rings. The system decays through a series of reconnections to produce finally three unlinked, unfolded, almost planar vortex loops. Total helicity, initially zero, remains unchanged throughout the process. The gradual transfer from writhe (due to initial linking) to twist helicity, followed by a continuous relaxation of twist across scales during the evolution is shown to be a generic mechanism that consistently takes place on each individual component.
The evolution and the topological cascade of quantum vortices forming Borromean rings are studied for the first time. The initial configuration of the system is given by three elliptical planar loops linked together, and the evolution is governed by the numerical implementation of the Gross–Pitaevskii equation. It is found that the topological cascade is not unique, but it depends crucially on the initial geometric configuration. Quantum vortices undergo a series of spontaneous reconnections, resulting in various degenerative pathways characterized by different topology and structural complexity triggered by the different inclination of one of the initial ellipses. Typical decaying routes are given by the successive creation of a Whitehead link, a connected sum of two Hopf links, a trefoil knot, a Hopf link, and the final formation of unknotted, unlinked loops. By structural complexity analysis, we show that the generic trend of the vortex decay goes through a series of topological simplifications, resulting in the formation of small-scale planar loops (rings). During the later stage of evolution, the inverse cascade and topological cycles involving the interaction of unknotted loops become more common, remaining sub-dominant to the overall topological simplification process. These results pave the way to investigate the fundamental relations between structural complexity and energy contents.
We consider the reconnection of two untwisted, linked quantised vortex rings in a Bose-Einstein condensate. We show that the reconnection is capable of transferring helicity, from the links present in the initial configuration, to a twisting of the resulting vortex ring, and hence a rotation of the phase plane along the vortex ring. As velocities in a quantum fluid are the gradient of the phase, a twisting of the phase along the vortices leads to an axial flow along the vortices. Hence one would expect that the dynamics of quantum turbulence are strongly influence by the helicity of the initial conditions or the system forcing. Our results also provide an important link between quantised vortex reconnections and reconnections in classical and magnetised fluids.
We demonstrate that a single reconnection of two quantum vortices can lead to the creation of a cascade of vortex rings. Our analysis, motivated by the analytical results in localized induction approximation, involved high resolution Biot-Savart and Gross-Pitaevskii simulations. The latter showed that the rings cascade starts on the atomic scale, with rings diameters orders of magnitude smaller than the characteristic line spacing in the tangle, and thus capable of penetrating the tangle and annihilating on the boundaries. That way such process can be an efficient decay mechanism for sparse or moderately dense vortex tangle at very low temperatures.
Reconnections between quantum vortex filaments in the presence of trapped particles are investigated using numerical simulations of the Gross-Pitaevskii equation. Particles are described with classical degrees of freedom and modeled as highly repulsive potentials which deplete the superfluid. First, the case of a vortex dipole with a single particle trapped inside one of the vortices is studied. It is shown that the reconnection takes place at the position of the particle as a consequence of the symmetry breaking induced by it. The separation rate between the reconnecting points is compatible with the known dynamics of quantum vortex reconnections, and it is independent of the particle mass and size. After the reconnection, the particle is pushed away with a constant velocity, and its trajectory is deflected because of the transverse momentum exchange with the vortex filaments. The momentum exchanges between the particle, the vortex, and a density pulse are characterized. Finally, the reconnection of two linked rings, each of them with several initially randomly distributed particles, is studied. It is observed that generically, reconnections take place at the location of trapped particles. It is shown that reconnection dynamics is unaffected for light particles.
Abstract In this paper we show that twist, defined in terms of rotation of the phase associated with quantum vortices and other physical defects effectively deprived of internal structure, is a property that has observable effects in terms of induced axial flow. For this we consider quantum vortices governed by the Gross–Pitaevskii equation (GPE) and perform a number of test cases to investigate and compare the effects of twist in two different contexts: (i) when this is artificially superimposed on an initially untwisted vortex ring; (ii) when it is naturally produced on the ring by the simultaneous presence of a central straight vortex. In the first case large amplitude perturbations quickly develop, generated by the unnatural setting of the initial condition that is not an analytical solution of the GPE. In the second case much milder perturbations emerge, signature of a genuine physical process. This scenario is confirmed by other test cases performed at higher twist values. Since the second setting corresponds to essential linking, these results provide new evidence of the influence of topology on physics.