Nonlinear dynamics of Josephson vortices in merging superfluid rings

Alexander Yakimenko; Artem Oliinyk; Boris Malomed

REVIEW 3 major objections 5 minor 50 references

Nonlinear dynamics of Josephson vortices in merging superfluid rings

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The final state of two merging superfluid rings is decided by their population imbalance and trap shape.

desk verdict Solid new 3D simulation results with a real gap: the threshold Pcr and stable hybrids are plausible, but the paper's asserted insensitivity to the dissipation rate γ needs to be shown before publication. read the letter →

arxiv 1908.02468 v2 pith:RJ2NVEHR submitted 2019-08-07 cond-mat.quant-gas nlin.PS

Artem Oliinyk , Boris Malomed , Alexander Yakimenko This is my paper · ORCID

classification cond-mat.quant-gasnlin.PS PACS 03.75.Lm67.85.De

keywords JosephsonvorticesBose-EinsteincondensatestoroidaltrapspersistentcurrentspopulationimbalanceGross-PitaevskiiequationKelvin-Helmholtzinstabilityhybridvortexstructures

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks what happens when two parallel ring-shaped Bose-Einstein condensates carrying different amounts of circulation are encouraged to merge by lowering the barrier between them. It claims the final state is set by the initial population imbalance between the rings and by the shape of the three-dimensional trap. In flat (pancake) traps, a ring carrying a single-quantum persistent current drags an initially non-rotating ring into the same rotating state only if its population is large enough; below a threshold $P_{\rm cr}\approx 0.21$, the merged condensate relaxes to zero angular momentum. In axially elongated traps, the merger instead produces long-lived three-dimensional hybrid vortex structures, which become completely stable when a weak residual barrier pins the Josephson vortices, and their angular momentum per particle can be tuned continuously. Because the dynamics are driven by the splitting, bending, and drift of Josephson vortices, the result connects persistent currents, collective vortex motion, and the fate of superflows after merging.

What carries the argument

The load-bearing object is the Josephson vortex, a rotational fluxon that appears in the low-density barrier between two superflows with different topological charges because the tunneling current has azimuthal periodicity. The argument runs on the three-dimensional weakly dissipative Gross-Pitaevskii equation with a single dissipation constant $\gamma=0.03$, a toroidal trapping potential whose aspect ratio $A=\omega_z/\omega_r$ is either large (pancake) or small (elongated), and a time-dependent sheet barrier that vanishes linearly in time. The fluxon's fate—bending and splitting into vertically oriented vortex-antivortex pairs in pancake traps, or staying radially oriented in elongated traps—is what determines whether the final condensate acquires, keeps, or loses the angular momentum of the initially dominant ring. A geometric energy argument based on the ratio of Thomas-Fermi widths explains why the radial orientation is favored in elongated traps.

What would settle it

Prepare a double-ring condensate with vorticities $(m_1,m_2)=(1,0)$ and a pancake trap, ramp the barrier off, and measure the final angular momentum per particle for imbalances below and above $P=0.21$. Observing a gradual rather than steplike change of $L_p$ with $P$, or finding that the threshold shifts with the dissipation rate $\gamma$, would contradict the claim. Conversely, a direct measurement of a stable hybrid in an elongated trap with a residual barrier, whose $L_p$ changes when the barrier position is moved, would confirm the central prediction.

Watch

Extended reading notes

Core claim

The paper's central claim is that the merger of two toroidal condensates with different vorticities is controlled by the nonlinear three-dimensional dynamics of Josephson vortices (rotational fluxons) that form in the tunneling barrier between the rings. For a pancake-shaped trap with initial vorticities $(m_1,m_2)=(1,0)$, the angular momentum per particle after relaxation is a step function of the initial population imbalance $P$: zero for $P<P_{\rm cr}$ and one quantum for $P>P_{\rm cr}$, with $0.20<P_{\rm cr}<0.22$. For $(m_1,m_2)=(2,0)$ the same logic selects a final state with either $m=0$ or $m=2$, never $m=1$, with $P_{\rm cr}\approx 0.29$. In an axially elongated trap with $m_1=1$, $m_2=-1$, the fluxons keep a horizontal (radial) orientation, the Kelvin-Helmholtz instability does not develop, and the long-lived hybrid state—two axially separated parts with different vorticities connected by radially oriented Josephson vortices—emerges. Keeping a nonzero residual barrier pins the fluxons and turns the hybrid into a completely stable stationary vortex complex whose angular momentum per particle can be tuned anywhere in $m_1<L_p<m_2$.

Load-bearing premise

The load-bearing assumption is that one small, spatially uniform friction parameter (set to 0.03 in the simulations) faithfully describes how real vortex lines drift and annihilate after the rings merge; the paper asserts without showing evidence that the outcomes do not depend on the exact value.

Editorial extensions

If this is right

In pancake traps, the final angular momentum of a merged $(1,0)$ double ring is a sharply quantized switch: zero below $P_{\rm cr}\approx 0.21$, one quantum above it.
A $(2,0)$ input cannot settle at $m=1$; symmetry forces the final state to either $m=0$ or $m=2$, with threshold $P_{\rm cr}\approx 0.29$.
In elongated traps with $m_1=1,m_2=-1$, the 3D vortex lattice does not roll up into Kelvin-Helmholtz turbulence, even under noise of a few percent, so long-lived hybrids rather than turbulent decay are the expected outcome.
Retaining a residual barrier pins the Josephson vortices and yields completely stable 3D hybrid vortex complexes with tunable angular momentum per particle over $m_1<L_p<m_2$.
Tuning the barrier position after the hybrid forms changes $L_p$ dynamically, providing an in-situ control knob rather than only an initial-condition effect.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the central claim is right, a direct measurement of the step in $L_p$ at $P\approx 0.21$ in a pancake trap would be a clean experimental test, and the step location should be independent of ramp speed if the dissipation assumption is correct.
The fluxon-splitting picture suggests that similar merger thresholds should appear in atomtronic circuits whenever two current-carrying loops with different circulation are connected by a tunable junction.
If real dissipation is spatially nonuniform, the threshold $P_{\rm cr}$ likely becomes geometry-dependent rather than a universal number; varying the temperature of the thermal cloud could expose this.
The completely stable hybrid with two axial vorticities and pinned fluxons is a natural platform for topologically protected information storage, since its two sectors carry distinct integer charges joined by Josephson vortices.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

What you should know: this paper reports a genuinely new numerical result. It goes beyond the existing 2D counterflow and static fluxon studies by simulating the full 3D dissipative merger of two toroidal BECs with different vorticities. The two headline findings are (i) a threshold in initial population imbalance Pcr ≈ 0.21 for the (m1,m2)=(1,0) case (and ≈0.29 for (2,0)) that determines whether the final condensate has zero or unit circulation, and (ii) long-lived 3D hybrid vortex states in axially elongated traps, which can be made stationary by a residual barrier and whose angular momentum per particle is tunable between integer vorticities. Both are concrete predictions an experimental group could attempt to test.

The modeling is standard: a weakly dissipative Gross-Pitaevskii equation with uniform γ = 0.03 and a time-dependent barrier. The initial states are prepared cleanly by imaginary-time propagation with imprinted phases. The paper also gives a useful energy argument for why horizontally oriented fluxons are preferred in elongated traps, and it is honest that the hybrids are transients unless pinned.

The soft spots are real but not fatal. The biggest is the asserted insensitivity to γ. The words “we have verified that results reported below do not essentially depend on a specific value of γ ≪ 1” appear in Section II, but no scan, plot, or data is shown. That matters because the relaxation path—vortex drift, annihilation, fluxon bending—is driven by this dissipation. A spatially nonuniform γ, or a different value, could move Pcr outside the quoted 0.20–0.22 interval. The stress-test note has this right. The fix is simple: show Lp(t) for γ = 0.01, 0.05, 0.1, and preferably a spatially dependent γ test.

Second, the paper gives no numerical convergence details: grid spacing, time step, domain size, or resolution checks. The Pcr intervals are determined from sparse points on an inset plot. Third, “completely stable” hybrids are demonstrated only for finite times and a single barrier configuration; more evidence is needed to distinguish a long-lived transient from a genuinely stable state. The claim that Lp can be tuned to any value between m1 and m2 rests on a few data points in Fig. 8. The qubit suggestion is speculative, but clearly labeled as such.

All that said, the central scenario is plausible and internally consistent. The citation pattern is fine; the authors build on their own earlier fluxon work, which is appropriate. This is not a desk-reject. It deserves a serious referee, and the revision should be moderate: add the γ-sensitivity evidence, the numerical methods, and tighten the stability language. I would cite it if I worked on persistent currents in toroidal BECs.

Referee Report

3 major / 5 minor

Summary. The paper studies the nonlinear merger dynamics of two vertically separated toroidal Bose-Einstein condensates carrying different initial vorticities, modeled by a three-dimensional weakly dissipative Gross-Pitaevskii equation with a gradually eliminated Gaussian barrier. For pancake-shaped traps with vorticities (m1,m2)=(1,0), the authors report a threshold initial population imbalance, Pcr in the interval 0.20<Pcr<0.22, below which the merged condensate relaxes to zero angular momentum and above which it relaxes to a single-charged persistent current; for (2,0) they report Pcr≈0.29 and no final m=1 state. For elongated (prolate) traps with m1=1, m2=-1, the simulations produce long-lived hybrid vortex structures with horizontal Josephson vortices, and the authors claim that a residual nonvanishing barrier pins these fluxons and makes the hybrids completely stable, with tunable angular momentum per particle.

Significance. If the reported effects hold, the paper contributes interesting and potentially testable predictions for persistent-current dynamics in atomtronic devices: a dominant superfluid ring can impose its vorticity on a less populated ring, and the final vorticity is controlled by the initial population imbalance and the trap aspect ratio. The model is standard and physically motivated, the explored regimes are clearly separated in parameter space, and the central claims are falsifiable by experiment and by direct simulation. The comparison with earlier 2D studies of Kelvin-Helmholtz instability is useful. However, the quantitative thresholds and the stability statements rest on numerical evidence that is not fully documented, and the asserted insensitivity to the dissipation parameter is not demonstrated.

major comments (3)

[Section II, Eq. (1) and text after Eq. (1)] The paper states that "we have verified that results reported below do not essentially depend on a specific value of gamma << 1" but presents no data, figure, or table supporting this claim. This is load-bearing because the relaxation mechanism itself—vortex drift, fluxon bending and splitting, antivortex annihilation, and the vertical drift of fluxons—is explicitly described in Sections III.A and III.B as driven by gamma. A spatially uniform gamma=0.03 is a particular choice, and the threshold Pcr and the claimed hybrid lifetimes are dynamical outcomes that can in principle shift with gamma. Please provide a scan over gamma (e.g., final Lp versus P for gamma=0.01, 0.03, 0.06) or otherwise quantitatively demonstrate the insensitivity asserted in the text.
[Section III.A, Figs. 4 and 5] The critical intervals 0.20<Pcr<0.22 for (m1,m2)=(1,0) and Pcr≈0.29 for (2,0) are determined from very sparse data: Fig. 4 shows only two evolution curves and its inset shows a handful of final points, while Fig. 5 shows four curves. No grid spacing, time step, domain size, or convergence tests are reported anywhere in the paper. Because the thresholds are central quantitative claims, the manuscript needs a statement of the numerical parameters and a demonstration that the threshold location is stable under resolution and time-step refinement, together with additional P values bracketing each threshold.
[Section III.B, Fig. 8] The claim that a residual barrier makes the hybrid "completely stable" is supported only by finite-time simulations at a single value of gamma and without a quantitative stability analysis. The text states that hybrids are transient and will eventually transform into ordinary states, yet later calls the pinned configuration completely stable; the distinction is not established. Please provide either longer-time simulations with a stated duration, a scan over residual barrier height and gamma, or a linear stability analysis around the pinned state before using the word "stable" rather than "long-lived on the simulated timescale."

minor comments (5)

[General/Introduction] There are several typos and inconsistent notations: "superﬂ uid" in the header, "ﬁled" in the Introduction, and "withm = 0" in the caption of Fig. 3 should be "with m2 = 0."
[Section II, Eqs. (1) and (8)] The wave function is denoted psi in Eq. (1) and Eq. (5) but Psi in Eq. (8); please use a single symbol or explicitly define the change. Also, Eq. (10) has a stray period after the closing brace.
[Section II, text after Eq. (10)] The asymmetry parameter P is defined through N1 and N2, but the text discussing "N1 > N2 for z0 > 0" would benefit from an explicit statement of how z0 is related to the barrier center and the ring populations, since z0 is also used as a possible shift of the barrier position.
[Section III.B, paragraph on hybrid decay] The sentences "they remain robust in the course of long evolution, and do not decay even being strongly perturbed" and "the emerging hybrid states are transient ones, as they will eventually transform into usual ones" are in tension; please clarify whether hybrids are finite-lifetime or effectively stable on experimental timescales.
[References] Reference [9] is cited as an arXiv preprint; if it has been published, the published version should be cited. Additionally, the experimental parameters quoted from Refs. [26,27] would be easier to check if the corresponding trap geometries were summarized in one place.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central thresholds and hybrid states are direct simulation outputs; the only self-citation is corroborative, not load-bearing.

full rationale

The paper's central quantitative claims—the threshold imbalance Pcr ≈ 0.21 for (m1,m2) = (1,0), Pcr ≈ 0.29 for (2,0), and the long-lived or stable 3D hybrids in elongated traps—are obtained by integrating the weakly dissipative Gross-Pitaevskii equation, Eq. (5), with fixed parameters and reading off the final angular momentum Lp from the simulated trajectories (Figs. 4, 5, 6, 8). No parameter is fitted to the target result, so the 'fitted input called prediction' pattern does not apply. The initial-state construction imprints integer vorticities m1 and m2 via Eq. (8), and the observed final states are genuinely different outputs (e.g., Lp = 0 versus Lp = 1 across Pcr). The one self-citation, Ref. [9], is used to assert that |m1 − m2| Josephson vortices form in the tunnel barrier, but the same section also states that this 'necessarily follows from the azimuthal periodicity of the condensate wave function', and the vortex structure is directly visible in the initial snapshots; hence the self-citation is corroborative rather than load-bearing. The hybrid Lp range m1 < Lp < m2 is consistent with the hybrid being composed of two domains of vorticities m1 and m2, but the stability and tunability of these hybrids are demonstrated numerically, not derived from that definition. The unsupported assertion of gamma-insensitivity (Section II) is a robustness assumption and a correctness risk, but it is not a circular reduction: varying gamma would affect the quantitative threshold, yet the threshold remains a simulation output rather than an input. Overall, the derivation chain is self-contained against direct numerical integration, so no circular step is identified.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central claims rest on the dissipative GPE model, the imaginary-time preparation of vortex states, and the specific trap geometry. Free parameters are the phenomenological dissipation gamma and the barrier protocol parameters, none of which are fitted to reproduce the claimed outcomes.

free parameters (3)

gamma (dissipation parameter) = 0.03
Phenomenological dissipation strength chosen from prior literature [12,19]; the paper asserts insensitivity to its value but shows no systematic scan.
td (barrier elimination time) = 0.015 s
Switching time for the separating barrier; chosen by hand and not varied, yet the merger dynamics could depend on it.
ub (initial barrier strength) = 80 (scaled)
Amplitude of the Gaussian sheet potential; set to a fixed value, not scanned.

assumptions (3)

domain assumption The 3D dissipative Gross-Pitaevskii equation with a single constant gamma models the coupled BEC dynamics.
Invoked in Section II, Eq. (1); the central relaxation dynamics and final states are simulated within this model.
domain assumption Imaginary-time propagation with the phase ansatz Eq. (8) converges to physical stationary states with the desired vorticities in each ring.
Section II, after Eq. (8); all initial states for simulations are prepared this way.
domain assumption The toroidal trapping potential of Eq. (2), with a harmonic radial minimum at rho0 and quadratic axial confinement, is an adequate representation of experimental double-ring traps.
Section II, Eq. (2); the aspect-ratio dependence is the central control parameter.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Nonlinear dynamics of Josephson vortices in merging superfluid rings." pith.science (2026). https://pith.science/paper/RJ2NVEHR

@misc{pith2026190802468,
  author       = {Pith},
  title        = {Pith review of: Nonlinear dynamics of Josephson vortices in merging superfluid rings},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RJ2NVEHR}},
  note         = {Machine review of arXiv:1908.02468}
}

read the original abstract

We consider merger of two parallel toroidal atomic Bose-Einstein condensates with different vorticities in a three-dimensional (3D) trap. In the tunnel-coupling regime, Josephson vortices (rotational fluxons) emerge in the barrier between the superflows. When the barrier is gradually eliminated, we observe essentially three-dimensional evolution of quantum vortices, which may include the development of the Kelvin-Helmholtz instability at the interface between the rings, in the framework of a weakly dissipative Gross-Pitaevskii equation. An initially more populated ring, carrying a persistent current, can drag an initially non-rotating less populated one into the same vortex state. The final state of the condensate crucially depends on an initial population imbalance in the double-ring set, as well as on the shape of the 3D trapping potential, oblate or prolate. In the prolate (axially elongated) configuration, robust 3D hybrid structures may appear as a result of the merger of persistent currents corresponding to different vorticities.

Figures

Figures reproduced from arXiv: 1908.02468 by the authors.

**Figure 2.** FIG. 2. (Color online) The evolution of the merging rings [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** FIG. 4. (Color online) The evolution of the total angular mo [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Figures from the paper (4 more)

**Figure 5.** Figure 5: FIG. 5. (Color online) Evolution of the total angular momen [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: FIG. 6. (Color online) Snapshots at three moments of time, il [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: FIG. 7. (a) Total energy of the hybrid vs. number of particles [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 8.** Figure 8: FIG. 8. Example of stable evolution of the vortex hybrid. The [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

50 extracted references · 45 canonical work pages

[1]

peanut-shaped

03 as in Refs. [12, 19]. Actually, we have veriﬁed that results reported below do not essentially depend on a speciﬁc value of γ ≪ 1. We consider a toroidal condensate, split by a blue- detuned sheet beam in upper and lower weakly coupled rings-shaped components. The respective total trapping potential is Vext(ρ,z,t ) = 1 2Mω 2 r(ρ −ρ0)2 + 1 2Mω 2 zz2 +Vb...

work page
[2]

V. M. Kaurov and A. B. Kuklov, Phys. Rev. A 71, 011601 (2005)

work page 2005
[3]

A. V. Ustinov, Physica D 123, 315 (1998)

work page 1998
[4]

and Guilleumas, M

Gallem ´ ı, A. and Guilleumas, M. and Mayol, R. and Ma- teo, A. Mu˜ noz, Phys. Rev. A 93, 033618 (2016)

work page 2016
[5]

V. M. Kaurov and A. B. Kuklov, Phys. Rev. A 73, 013627 (2006), cond-mat/0508342

work page Pith review arXiv 2006
[6]

Su, S.-C

S.-W. Su, S.-C. Gou, A. Bradley, O. Fialko, and J. Brand, Physical Review Letters 110, 215302 (2013)

work page 2013
[7]

Brand, T

J. Brand, T. J. Haigh, and U. Z¨ ulicke, Phys. Rev. A 80, 011602 (2009)

work page 2009
[8]

J. A. Gil Granados, A. Mu˜ noz Mateo, M. Guilleumas, and X. Vi˜ nas, New Journal of Physics21, 043036 (2019)

work page 2019

Show all 50 references

[9]

Christian Baals, Herwig Ott, Joachim Brand, Antonio Muoz Mateo, Phys. Rev. A 98, 053603 (2018)

2018
[10]

Driben, Y

R. Driben, Y. Kartashov, B. A. Malomed, T. Meier, and L. Torner, New J. Phys. 16, 063035 (2014)

2014
[11]

Oliinyk, A

A. Oliinyk, A. Yakimenko, and B. Malomed, arXiv e- prints (2019), arXiv:1901.06502 [cond-mat.quant-gas]

2019 arXiv
[12]

Tsubota, M

M. Tsubota, M. Kobayashi, H. Takeuchi, Phys. Rep. 522, 191 (2013)

2013
[13]

W. R. Peltier and C. P. Caulﬁeld, Ann. Rev. Fluid Mech. 35, 135 (2003)

2003
[14]

Takeuchi, N

H. Takeuchi, N. Suzuki, K. Kasamatsu, H. Saito, and M. Tsubota, Phys. Rev. B 81, 094517 (2010), arXiv:0909.2144 [cond-mat.quant-gas]

2010 arXiv
[15]

for |m1 −m2| = 20, hence the respective vortex street contained 40 vortex cores. As pointed out in [15], in the absence of perturbations the vortex streets survived for a long time; however, under the action of noisy perturba- tions (whose magnitude was less than one percent o...
[16]

Suzuki, H

N. Suzuki, H. Takeuchi, K. Kasamatsu, M. Tsub- ota, and H. Saito, Phys. Rev. A 82, 063604 (2010), arXiv:1009.1740 [cond-mat.quant-gas]. 9

2010 arXiv
[17]

Baggaley, N.G

A.W. Baggaley, N.G. Parker, Phys. Rev. A 97, 053608 (2018)

2018
[18]

A. I. Yakimenko, Yu. M. Bidasyuk, O.O. Prikhodko, S.I. Vilchinskii, E.A. Ostrovskaya, and Yu. S. Kivshar, Phys. Rev. A 88, 043637 (2013)

2013
[19]

S. J. Rooney, A. S. Bradley, and P. B. Blakie, Phys. Rev. A 81, 023630 (2010)

2010
[20]

Moulder, S

S. Moulder, S. Beattie, R. P. Smith, N. Tammuz, and Z. Hadzibabic, Phys. Rev. A 86, 013629 (2012)

2012
[21]

A. I. Yakimenko, Y. M. Bidasyuk, O. O. Prikhodko, S. I. Vilchinskii, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. A 88, 043637 (2013)

2013
[22]

A. J. Allen, E. Zaremba, C. F. Barenghi, and N. P. Proukakis, Phys. Rev. A 87, 013630 (2013)

2013
[23]

Y. M. Bidasyuk, A. V. Chumachenko, O. O. Prikhodko, S. I. Vilchinskii, M. Weyrauch, and A. I. Yakimenko, Phys. Rev. A 92, 053603 (2015)

2015
[24]

S. Choi, S. A. Morgan, and K. Burnett, Phys. Rev. A 57, 4057 (1998)

1998
[25]

N. P. Proukakis and B. Jackson, J. Phys. B: At. Mol. Opt. Phys. 41, 203002 (2008)

2008
[26]

Carretero-Gonzalez, N

R. Carretero-Gonzalez, N. Whitaker, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 77, 023605 (2008)

2008
[27]

Kasamatsu, M

K. Kasamatsu, M. Tsubota, and M. Ueda, Phys. Rev. A 67, 033610 (2003)

2003
[28]

K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, G. K. Campbell, Phys. Rev. Lett. 110, 025302 (2013)

2013
[29]

Jendrzejewski, S

F. Jendrzejewski, S. Eckel, N. Murray, C. Lanier, M. Ed- wards, C. J. Lobb, and G. K. Campbell, Phys. Rev. Lett. 113, 045305 (2014)

2014
[30]

Brtka, A

M. Brtka, A. Gammal, and B. A. Malomed, Phys. Rev. A 82, 053610 (2010)

2010
[31]

L. Wen, Y. Qiao, Y. Xu, and L. Mao, Phys. Rev. A 87, 033604 (2013)

2013
[32]

A. I. Yakimenko, K. O. Isaieva, S. I. Vilchinskii, and M. Weyrauch, Phys. Rev. A 88, 051602 (2013)

2013
[33]

Ishino, M

S. Ishino, M. Tsubota, and H. Takeuchi, Phys. Rev. A 88, 063617 (2013)

2013
[34]

Ishino, M

S. Ishino, M. Tsuboto, and H. Takeuchi, EPL 111, 30005 (2015)

2015
[35]

Hoashi, Y

M. Hoashi, Y. Nakamura, and Y. Yamanaka, Phys. Rev. A 93, 043622 (2016)

2016
[36]

Xu, Z.-Q

S.-L. Xu, Z.-Q. Wang, J.-R. He, L. Xue, and M. R. Belic, J. Mod. Opt. 65, 1542 (2018)

2018
[37]

Y. Li, Z. Chen, Z. Luo, C. Huang, H. Tan, W. Pang, and B. A. Malomed, Phys. Rev. A 98, 063602 (2018), arXiv:1801.10274 [cond-mat.quant-gas]

2018 arXiv
[38]

Z. Chen, Y. Li, N. P. Proukakis, and B. A. Malomed, New J. Phys. 21, 073058 (2019)

2019
[39]

Leykam, B

D. Leykam, B. Malomed, and A. S. Desyatnikov, J. Op- tics 82, 053610 (2013)

2013
[40]

J. R. Salgueiro, J. Optics 18, 074004 (2016)

2016
[41]

Mayteevarunyoo, B

T. Mayteevarunyoo, B. Malomed, and D. Skryabin, New J. Phys. 20, 113019 (2018)

2018
[42]

Beattie, S

S. Beattie, S. Moulder, R. J. Fletcher, and Z. Hadzibabi c, Phys.Rev. Lett. 110, 025301 (2013)

2013
[43]

We present animations of dynamics of vortices with smal l and big initial imballance P , degradation of hybrid sys- tem in time and pinning possibility in systems of hybrid type
[44]

For vertically oriented vortex lines (detected in z =const plane) we use red (vortices) and blue (antivortices) colors

To detect the vortex cores we use an algorithm of numeri- cal phase unwrapping at each point of the grid in diﬀerent planes: z =const, x =const or y =const. For vertically oriented vortex lines (detected in z =const plane) we use red (vortices) and blue (antivortices) colors. ...
[45]

A. I. Yakimenko, Y. M. Bidasyuk, M. Weyrauch, Y. I. Kuriatnikov, and S. I. Vilchinskii, Phys. Rev. A 91, 033607 (2015)

2015
[46]

Kanai, W

T. Kanai, W. Guo, and M. Tsubota, Phys. Rev. A 97, 013612 (2018)

2018
[47]

Kanai, W

T. Kanai, W. Guo, and M. Tsubota, Journal of Low Temperature Physics 195, 37 (2019)

2019
[48]

A. Ohta, R. Kashiwa, and H. Sakaguchi, Phys. Rev. A 82, 055602 (2010)

2010
[49]

Kasamatsu, M

K. Kasamatsu, M. Tsubota, Phys. Rev. A 79, 023606 (2009)

2009
[50]

Das Sarma, M

S. Das Sarma, M. Freedman, and C. Nayak, Phys. Rev. Lett. 94, 166802 (2005)

2005

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

peanut-shaped

03 as in Refs. [12, 19]. Actually, we have veriﬁed that results reported below do not essentially depend on a speciﬁc value of γ ≪ 1. We consider a toroidal condensate, split by a blue- detuned sheet beam in upper and lower weakly coupled rings-shaped components. The respective total trapping potential is Vext(ρ,z,t ) = 1 2Mω 2 r(ρ −ρ0)2 + 1 2Mω 2 zz2 +Vb...

work page

[2] [2]

V. M. Kaurov and A. B. Kuklov, Phys. Rev. A 71, 011601 (2005)

work page 2005

[3] [3]

A. V. Ustinov, Physica D 123, 315 (1998)

work page 1998

[4] [4]

and Guilleumas, M

Gallem ´ ı, A. and Guilleumas, M. and Mayol, R. and Ma- teo, A. Mu˜ noz, Phys. Rev. A 93, 033618 (2016)

work page 2016

[5] [5]

V. M. Kaurov and A. B. Kuklov, Phys. Rev. A 73, 013627 (2006), cond-mat/0508342

work page Pith review arXiv 2006

[6] [6]

Su, S.-C

S.-W. Su, S.-C. Gou, A. Bradley, O. Fialko, and J. Brand, Physical Review Letters 110, 215302 (2013)

work page 2013

[7] [7]

Brand, T

J. Brand, T. J. Haigh, and U. Z¨ ulicke, Phys. Rev. A 80, 011602 (2009)

work page 2009

[8] [8]

J. A. Gil Granados, A. Mu˜ noz Mateo, M. Guilleumas, and X. Vi˜ nas, New Journal of Physics21, 043036 (2019)

work page 2019