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:1410.1259

Approach and separation of quantum vortices with balanced cores

C. Rorai, Jack W. D. Skipper, Robert M. Kerr, Katepalli R. Sreenivasan

Published Oct 6, 2014• 3 citations
arXivHTMLPDF

Abstract

Using two innovations, smooth, but distinctly different, scaling laws for the numerical reconnection of pairs of initially orthogonal and anti-parallel quantum vortices are obtained using the three-dimensional Gross-Pitaevskii equations, the simplest mean-field non-linear Schrödinger equation for a quantum fluid. The first innovation suppresses temporal fluctuations by using an initial density profile that is slightly below the usual two-dimensional steady-state Padé approximate profiles. The second innovation is to find the trajectories of the quantum vortices from a pseudo-vorticity constructed on the three-dimensional grid from the gradients of the wave function. These trajectories then allow one to calculate the Frenet-Serret frames and the curvature of the vortex lines. For the anti-parallel case, the scaling laws just before and after reconnection obey the dimensional $δ\sim|t_r-t|^{1/2}$ prediction with temporal symmetry about the reconnection time $t_r$ and physical space symmetry about the $x_r$, the mid-point between the vortices, with extensions of the vortex lines formng the edges of an equilateral pyramid. For all of the orthogonal cases, before reconnection $δ_{in}\sim(t-t_r)^{1/3}$ and after reconnection $δ_{out}\sim(t-t_r)^{2/3}$, which are respectively slower and faster than the dimensional prediction. In these cases, the reconnection takes place in a plane defined by the directions of the curvature and vorticity. To define the structure further, lines are drawn that connect the four arms that extend from the reconnection plane, four angles $θ_i$ between these arms are found, then summed, giving $\sumθ_i>360^\circ$. This implies that the overall structure is convex or hyperbolic, as opposed to the acute angles of the anti-parallel pyramid.

DOI
10.48550/arxiv.1410.1259

Related papers

Approach and separation of quantised vortices with balanced cores

C. Rorai, Jack W. D. Skipper, Robert M. Kerr +1 more

The scaling laws for the reconnection of isolated pairs of quantised vortices are characterised by numerically integrating the three-dimensional Gross–Pitaevskii equations, the simplest mean-field equations for a quantum fluid. The primary result is the identification of distinctly different temporal power laws for the pre- and post-reconnection separation distances $\unicode[STIX]{x1D6FF}(t)$ for two configurations. For the initially anti-parallel case, the scaling laws before and after the reconnection time $t_{r}$ obey the dimensional $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/2}$ prediction with temporal symmetry about $t_{r}$ and physical space symmetry about the mid-point between the vortices $x_{r}$ . The extensions of the vortex lines close to reconnection form the edges of an equilateral pyramid. For all of the initially orthogonal cases, $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/3}$ before reconnection and $\unicode[STIX]{x1D6FF}\sim |t-t_{r}|^{2/3}$ after reconnection are respectively slower and faster than the dimensional prediction. For both configurations, smooth scaling laws are generated due to two innovations. The first innovation is to use an initial low-energy vortex-core density profile that suppresses unwanted density fluctuations as the vortices evolve in time. The other innovation is the accurate identification of the position of the vortex cores from a pseudo-vorticity constructed on the three-dimensional grid from the gradients of the wave function. These trajectories allow us to calculate the Frenet–Serret frames and the curvature of the vortex lines, secondary results that might hold clues for the origin of the differences between the scaling laws of the two configurations. Reconnection takes place in a reconnection plane defined by the average tangents $\boldsymbol{T}_{av}$ and curvature normal $\boldsymbol{N}_{av}$ directions of the pseudo-vorticity curves at the points of closest approach, at time $t\approx t_{r}$ . To characterise the structure further, lines are drawn that connect the four arms that extend from the reconnection plane, from which four angles $\unicode[STIX]{x1D703}_{i}$ between the lines are defined. Their sum is convex or hyperbolic, that is $\sum _{i=1,4}\unicode[STIX]{x1D703}_{i}>360^{\circ }$ , for the orthogonal cases, as opposed to the acute angles of the pyramid found for the anti-parallel initial conditions.

Journal of Fluid Mechanics•Nov 4, 2016•34 citations

Study of Reconnection and Acoustic Emission of Quantized Vortices in Superfluid by the Numerical Analysis of the Gross–Pitaevskii Equation

Shin-ichiro Ogawa, Makoto Tsubota, Yuji Hattori

We study numerically the reconnection of quantized vortices and the concurrent acoustic emission by the analysis of the Gross-Pitaevskii equation. Two quantized vortices reconnect following the process similar to classical vortices; they approach, twist themselves locally so that they become anti-parallel at the closest place, reconnect and leave separately.The investigation of the motion of the singular lines where the amplitude of the wave function vanishes in the vortex cores confirms that they follow the above scenario by reconnecting at a point. This reconnection is not contradictory to the Kelvin's circulation theorem, because the potential of the superflow field becomes undefined at the reconnection point. When the locally anti-parallel part of the vortices becomes closer than the healing length, it moves with the velocity comparable to the sound velocity, emits the sound waves and leads to the pair annihilation or reconnection; this phenomena is concerned with the Cherenkov resonance. The vortices are broken up to smaller vortex loops through a series of reconnection, eventually disappearing with the acoustic emission. This may correspond to the final stage of the vortex cascade process proposed by Feynman. The change in energy components, such as the quantum, the compressible and incompressible kinetic energy is analyzed for each dynamics. The propagation of the sound waves not only appears in the profile of the amplitude of the wave function but also affects the field of its phase, transforming the quantum energy due to the vortex cores to the kinetic energy of the phase field.

arXiv:cond-mat/0104255•Journal of the Physical Society of Japan•Mar 15, 2002•48 citations

Interactions and reconnections of four-dimensional quantum vortices

H. A. J. Middleton-Spencer, Ben McCanna, Davide Proment +1 more

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.

arXiv:2411.07943•Physical Review Fluids•Jul 13, 2026•0 citations

Quantum vortex reconnections

Simone Zuccher, Marco Caliari A, Andrew William Baggaley +1 more

We study reconnections of quantum vortices by numerically solving the governing Gross-Pitaevskii equation. We find that the minimum distance between vortices scales differently with time before and after the vortex reconnection. We also compute vortex reconnections using the Biot-Savart law for vortex filaments of infinitesimal thickness, and find that, in this model, reconnections are time symmetric. We argue that the likely cause of the difference between the Gross-Pitaevskii model and the Biot-Savart model is the intense rarefaction wave which is radiated away from a Gross-Pitaeveskii reconnection. Finally we compare our results to experimental observations in superfluid helium and discuss the different length scales probed by the two models and by experiments.

arXiv:1206.2498•Physics of Fluids•Dec 1, 2012•131 citations

Superfluid vortices in four spatial dimensions

Ben McCanna, Hannah M. Price

Quantum vortices in superfluids have been an important research area for many decades. Naturally, research on this topic has focused on two and three-dimensional superfluids, in which vortex cores form points and lines, respectively. Very recently, however, there has been growing interest in the quantum simulation of systems with four spatial dimensions; this raises the question of how vortices would behave in a higher-dimensional superfluid. In this paper, we begin to establish the phenomenology of vortices in 4D superfluids under rotation, where the vortex core can form a plane. In 4D, the most generic type of rotation is a "double rotation" with two angles (or frequencies). We show, by solving the Gross-Pitaesvkii equation, that the simplest case of equal-frequency double rotation can stabilise a pair of vortex planes intersecting at a point. This opens up a wide number of future research topics, including unequal-frequency double rotations; the stability and reconnection dynamics of intersecting vortex surfaces; and the possibility of closed vortex surfaces.

arXiv:2005.07485•Physical Review Research•May 10, 2021•12 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
Using two innovations, smooth, but distinctly different, scaling laws for the numerical reconnection of pairs of initially orthogonal and anti-parallel quantum vortices are obtained using the three-dimensional Gross-Pitaevskii equations, the simplest mean-field non-linear Schrödinger equation for a quantum fluid. The first innovation suppresses temporal fluctuations by using an initial density profile that is slightly below the usual two-dimensional steady-state Padé approximate profiles. The second innovation is to find the trajectories of the quantum vortices from a pseudo-vorticity constructed on the three-dimensional grid from the gradients of the wave function. These trajectories then allow one to calculate the Frenet-Serret frames and the curvature of the vortex lines. For the anti-parallel case, the scaling laws just before and after reconnection obey the dimensional δ∼∣tr−t∣1/2δ\sim|t_r-t|^{1/2}δ∼∣tr​−t∣1/2 prediction with temporal symmetry about the reconnection time trt_rtr​ and physical space symmetry about the xrx_rxr​, the mid-point between the vortices, with extensions of the vortex lines formng the edges of an equilateral pyramid. For all of the orthogonal cases, before reconnection δin∼(t−tr)1/3δ_{in}\sim(t-t_r)^{1/3}δin​∼(t−tr​)1/3 and after reconnection δout∼(t−tr)2/3δ_{out}\sim(t-t_r)^{2/3}δout​∼(t−tr​)2/3, which are respectively slower and faster than the dimensional prediction. In these cases, the reconnection takes place in a plane defined by the directions of the curvature and vorticity. To define the structure further, lines are drawn that connect the four arms that extend from the reconnection plane, four angles θiθ_iθi​ between these arms are found, then summed, giving ∑θi>360∘\sumθ_i>360^\circ∑θi​>360∘. This implies that the overall structure is convex or hyperbolic, as opposed to the acute angles of the anti-parallel pyramid.
The scaling laws for the reconnection of isolated pairs of quantised vortices are characterised by numerically integrating the three-dimensional Gross–Pitaevskii equations, the simplest mean-field equations for a quantum fluid. The primary result is the identification of distinctly different temporal power laws for the pre- and post-reconnection separation distances $\unicode[STIX]{x1D6FF}(t)$ for two configurations. For the initially anti-parallel case, the scaling laws before and after the reconnection time trt_{r}tr​ obey the dimensional $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/2}$ prediction with temporal symmetry about trt_{r}tr​ and physical space symmetry about the mid-point between the vortices xrx_{r}xr​ . The extensions of the vortex lines close to reconnection form the edges of an equilateral pyramid. For all of the initially orthogonal cases, $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/3}$ before reconnection and $\unicode[STIX]{x1D6FF}\sim |t-t_{r}|^{2/3}$ after reconnection are respectively slower and faster than the dimensional prediction. For both configurations, smooth scaling laws are generated due to two innovations. The first innovation is to use an initial low-energy vortex-core density profile that suppresses unwanted density fluctuations as the vortices evolve in time. The other innovation is the accurate identification of the position of the vortex cores from a pseudo-vorticity constructed on the three-dimensional grid from the gradients of the wave function. These trajectories allow us to calculate the Frenet–Serret frames and the curvature of the vortex lines, secondary results that might hold clues for the origin of the differences between the scaling laws of the two configurations. Reconnection takes place in a reconnection plane defined by the average tangents Tav\boldsymbol{T}_{av}Tav​ and curvature normal Nav\boldsymbol{N}_{av}Nav​ directions of the pseudo-vorticity curves at the points of closest approach, at time t≈trt\approx t_{r}t≈tr​ . To characterise the structure further, lines are drawn that connect the four arms that extend from the reconnection plane, from which four angles $\unicode[STIX]{x1D703}_{i}$ between the lines are defined. Their sum is convex or hyperbolic, that is $\sum _{i=1,4}\unicode[STIX]{x1D703}_{i}>360^{\circ }$ , for the orthogonal cases, as opposed to the acute angles of the pyramid found for the anti-parallel initial conditions.
We study numerically the reconnection of quantized vortices and the concurrent acoustic emission by the analysis of the Gross-Pitaevskii equation. Two quantized vortices reconnect following the process similar to classical vortices; they approach, twist themselves locally so that they become anti-parallel at the closest place, reconnect and leave separately.The investigation of the motion of the singular lines where the amplitude of the wave function vanishes in the vortex cores confirms that they follow the above scenario by reconnecting at a point. This reconnection is not contradictory to the Kelvin's circulation theorem, because the potential of the superflow field becomes undefined at the reconnection point. When the locally anti-parallel part of the vortices becomes closer than the healing length, it moves with the velocity comparable to the sound velocity, emits the sound waves and leads to the pair annihilation or reconnection; this phenomena is concerned with the Cherenkov resonance. The vortices are broken up to smaller vortex loops through a series of reconnection, eventually disappearing with the acoustic emission. This may correspond to the final stage of the vortex cascade process proposed by Feynman. The change in energy components, such as the quantum, the compressible and incompressible kinetic energy is analyzed for each dynamics. The propagation of the sound waves not only appears in the profile of the amplitude of the wave function but also affects the field of its phase, transforming the quantum energy due to the vortex cores to the kinetic energy of the phase field.
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.
We study reconnections of quantum vortices by numerically solving the governing Gross-Pitaevskii equation. We find that the minimum distance between vortices scales differently with time before and after the vortex reconnection. We also compute vortex reconnections using the Biot-Savart law for vortex filaments of infinitesimal thickness, and find that, in this model, reconnections are time symmetric. We argue that the likely cause of the difference between the Gross-Pitaevskii model and the Biot-Savart model is the intense rarefaction wave which is radiated away from a Gross-Pitaeveskii reconnection. Finally we compare our results to experimental observations in superfluid helium and discuss the different length scales probed by the two models and by experiments.
Quantum vortices in superfluids have been an important research area for many decades. Naturally, research on this topic has focused on two and three-dimensional superfluids, in which vortex cores form points and lines, respectively. Very recently, however, there has been growing interest in the quantum simulation of systems with four spatial dimensions; this raises the question of how vortices would behave in a higher-dimensional superfluid. In this paper, we begin to establish the phenomenology of vortices in 4D superfluids under rotation, where the vortex core can form a plane. In 4D, the most generic type of rotation is a "double rotation" with two angles (or frequencies). We show, by solving the Gross-Pitaesvkii equation, that the simplest case of equal-frequency double rotation can stabilise a pair of vortex planes intersecting at a point. This opens up a wide number of future research topics, including unequal-frequency double rotations; the stability and reconnection dynamics of intersecting vortex surfaces; and the possibility of closed vortex surfaces.
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.