Splitting dynamics of quantized composite vortices in holographic miscible binary superfluids

Li Li; Yuping An

REVIEW 3 major objections 6 minor 1 cited by

Splitting dynamics of quantized composite vortices in holographic miscible binary superfluids

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read In strongly interacting binary superfluids at finite temperature, composite vortices split into fundamental singly quantized vortices, and strong dissipation prevents extra vortex pairs from surviving.

desk verdict First holographic study of composite vortex splitting in miscible binary superfluids; genuinely new temperature-dependent dynamics versus GPE, but the 'no long-lived vortices' universality claim needs sharper numerical support. read the letter →

arxiv 2501.03561 v1 pith:ZFICO6KR submitted 2025-01-07 hep-th cond-mat.quant-gasnlin.PS

Yuping An , Li Li This is my paper · ORCID

classification hep-thcond-mat.quant-gasnlin.PS

keywords compositevorticesbinarysuperfluidsholographicdynamicalinstabilityquasinormalmodesdissipationvortexsplittingtemperaturetransitions

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 studies what happens to multiply wound composite vortices in a strongly interacting, finite-temperature binary superfluid. Using a holographic model that naturally incorporates dissipation, the authors find that every unstable composite vortex eventually decays into fundamental singly quantized vortices, one per unit of winding number. They identify temperature-driven changes in which splitting mode dominates, and they show that strong dissipation suppresses the long-lived extra vortex-antivortex pairs seen in zero-temperature Gross-Pitaevskii calculations. The result matters because it predicts a qualitative difference between weakly interacting cold-atom superfluids and strongly interacting dissipative ones.

What carries the argument

The central object is the composite vortex, a pair of winding numbers $(S_1,S_2)$ for the two superfluid condensates sharing a common core, either co-rotating or counter-rotating. The argument runs through the holographic duality: a two-component charged scalar action in a fixed Schwarzschild-AdS black brane background (the probe limit), where the black hole supplies the temperature and dissipation. Linear stability is read off from the quasinormal spectrum of the dual black hole—an imaginary frequency with $\operatorname{Im}(\omega)>0$ signals a splitting instability—and the nonlinear outcome is obtained by full time evolution of the bulk equations. The comparison baseline is the zero-temperature, dissipation-free Gross-Pitaevskii description, whose predictions for these same vortex configurations were computed elsewhere.

What would settle it

Run a fully backreacted holographic simulation (or a finite-temperature dissipative Gross-Pitaevskii simulation) of a $(2,-2)$ composite vortex and count the late-time vortices; the paper's claim fails if more than two $(1,0)$ and two $(0,-1)$ vortices survive for long times. Alternatively, in an experiment with a strongly interacting binary superfluid, prepare a doubly charged composite vortex and observe whether any extra vortex-antivortex pair outlives the initial splitting.

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Extended reading notes

Core claim

The central claim is that, in a holographic miscible binary superfluid with strong coupling and finite temperature, the final state of any composite vortex labeled by windings $(S_1,S_2)$ is generically $S_1$ copies of the $(1,0)$ vortex and $|S_2|$ copies of the $(0,\pm1)$ vortex, with no additional long-lived vortex created. The instability channels and their growth rates are temperature dependent, producing dynamical transitions for the $(1,1)$, $(2,\pm1)$, and $(2,2)$ vortices; for example, $(1,1)$ becomes stable at low temperature while $(1,-1)$ is always unstable. This contrasts with Gross-Pitaevskii dynamics, where extra vortex pairs can survive, and the authors attribute the difference to strong dissipation in holographic superfluids. The claim is established by solving quasinormal modes around stationary vortex solutions and then integrating the full nonlinear time evolution.

Load-bearing premise

The matter fields are treated in the probe limit, so they do not react back on the spacetime geometry; if backreaction or a dynamical normal fluid were included, the instability strengths and final splitting patterns could change.

Editorial extensions

If this is right

Temperature, not just interaction strength, selects which splitting mode ($p=1,2,3$) dominates, so cooling a sample can switch the decay pattern.
The $(1,1)$ vortex is stable at low temperatures while $(1,-1)$ is not, implying an effective short-range attraction between a $(1,0)$ and a $(0,1)$ vortex and repulsion between counter-rotating partners.
Final states are universal fundamental vortices, so measuring the late-time vortex count gives a direct probe of dissipation strength in strongly interacting superfluids.
The absence of long-lived extra vortices distinguishes strongly coupled dissipative superfluids from weakly coupled zero-temperature gases, offering a clean experimental signature.

Reading between the lines

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

If the dissipation-truncation picture holds, then at even higher winding numbers one expects the same 'one fundamental vortex per unit winding' final state, but with intermediate multi-vortex clusters that never survive.
The effective two-vortex interaction picture (attraction for co-rotating, repulsion for counter-rotating) suggests the possibility of vortex-cluster bound states in two-component superfluids, which the authors mention but do not explore.
The temperature-dependent transition for the $(2,1)$ vortex hints that a singly quantized vortex in one component can act as a stabilizer of a doubly quantized vortex in the other at low temperature, analogous to vortex-bright solitons in immiscible fluids.
A testable extension: quench a miscible binary superfluid across the transition temperature and monitor whether the leading splitting channel changes as predicted by the $\operatorname{Im}(\omega)$ curves.

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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

First holographic study of composite-vortex splitting in miscible binary superfluids, and a decent one. The real content is the temperature dependence: the (1,1) vortex stabilizes at low T, the dominant mode switches between p=1 and p=2 for (2,1), and the p=3 channel is unstable for (2,−1) where GPE says it is stable. The sharpest physics is the contrast with zero-temperature GPE on the (2,−2) vortex, where the weakly coupled theory predicts extra surviving vortices and the holographic evolution does not. Figure 12 — p=3 explicitly seeded, extra vortex pairs appear and annihilate — is the right kind of evidence for that claim, and it is the paper's strongest moment.

The equations, boundary conditions, and spectrum extraction are stated clearly, and the quasinormal-mode analysis is standard for this literature. The citation pattern is fine; the self-citations are to the same model and the same numerical scheme, which is legitimate.

Soft spots, in order of how much they matter. First, 'long living' is never quantified, and the nonlinear runs are finite-time with no convergence tests or error estimates. The conclusion that all composite vortices decay to singly quantized fundamentals under generic perturbations is an extrapolation from a finite set of simulations, not something the numerics strictly prove. I do not think this kills the paper — the pattern is consistent across every case shown — but the universality claim is stated more strongly than the evidence supports. Second, the p≤3 truncation is asserted, not demonstrated: 'numerical evidence indicates that only p=1,2,3 modes are sufficient,' with no spectrum shown for p≥4. For S=2 vortices I would expect the higher multipoles to be stable, so the assertion is probably correct, but it is cheap to verify and a referee should ask for it. The probe limit freezes the normal-fluid dynamics; the authors flag it themselves, and it is the standard first pass. It could shift quantitative instability strengths, but I would be surprised if it changed the qualitative picture. That is a scope condition, not a flaw.

One thing the reader's report underplays: the dynamical transitions (e.g., (1,1) merging at low T, (2,1) stabilization) are themselves interesting and testable predictions, and they make the paper more than a dry numerical exercise.

Who this is for: people in holographic superfluids and multicomponent vortex dynamics. It deserves a serious referee. Ask for convergence checks, a p≥4 spot-check, and a quantified statement about lifetimes; then the universality claim can go in as a robust statement instead of a slogan. Recommendation: send to review, conditional on tightening the final-state claim and reporting the numerical checks.

Referee Report

3 major / 6 minor

Summary. This paper studies the fate of composite vortices in a holographic model of a miscible binary superfluid at finite temperature. The authors construct stationary axisymmetric vortex solutions with winding pairs (S1,S2), compute quasinormal-mode spectra for azimuthal perturbation channels p=1,2,3 as functions of T/Tc and inter-component coupling, and integrate the nonlinear bulk equations to show that unstable composite vortices split into singly quantized fundamental vortices. They report temperature-dependent transitions and claim that, unlike zero-temperature Gross-Pitaevskii dynamics, holographic dissipation prevents the formation of long-lived additional vortex pairs.

Significance. If correct, the central result constitutes an explicit finite-temperature, strong-coupling extension of the GPE vortex-splitting phenomenology and gives falsifiable predictions about the absence of long-lived extra vortices. The manuscript is clear and self-contained: the bulk action, boundary conditions, scaling conventions, and numerical scheme are stated, and the comparison with GPE results (e.g., the p=3 instability of (2,-1) and the extra vortices in (2,-2)) is concrete. The probe-limit approximation is acknowledged in Section 2 and is a standard first step. However, the universal conclusion ('all composite vortices... no additional long living vortex') rests on two pieces of evidence that are not fully quantified: completeness of the unstable mode set and finite simulation duration. These gaps are addressable.

major comments (3)

[Section 4, after Eq. (4.3)] The restriction to p=1,2,3 is asserted rather than demonstrated. The sentence "In principle we should consider all integer values of p, numerical evidence indicates that only p=1,2,3 modes are sufficient since other modes are all stable" is not accompanied by spectra for p>=4 or by a selection rule that excludes higher multipoles. Since the abstract and Section 5 state a universal claim over "all composite vortices" and "generic perturbations", an unstable p>=4 mode in the parameter range of Figures 4-5 would create additional vortex pairs not covered by the simulations. Please provide either an analytic argument limiting instability to low p or numerical spectra for p=4 and p=5 across the studied T/Tc and nu range, or restrict the claim accordingly.
[Sections 4.1-4.4 and Figures 6-12] The nonlinear evolutions are finite-time runs without convergence tests, error estimates, or a statement of how the integration duration compares with the dissipation/annihilation timescale. The conclusion's phrase "long living" is never quantified. As written, "we do not see additional long-lived vortices" is an extrapolation from finite simulations. Please report the total simulated time, grid spacing and time-step convergence, and compare run duration with the QNM decay rates or vortex-antivortex annihilation timescale; alternatively, soften the claim to "within the simulated time window".
[Section 5, first paragraph] The statement that the final state is obtained "regardless the initial perturbations" is stronger than the evidence presented. The simulations in Figures 6-12 start from the stationary solution plus small perturbations with specific p-modes, including one case where the p=3 mode is manually enhanced. No random-phase or multi-mode generic perturbation ensemble is shown. To support the universal wording, either demonstrate that the final state is independent of perturbation amplitudes and phases, or rephrase the conclusion to refer to the perturbations considered.

minor comments (6)

[Abstract] The phrase "The composite vortices is classified" should use the plural verb: "are classified".
[Section 4.2] The sentence "the decay of the vortiex in to a (1,0) and a (0,-1) vortex" contains typos: "vortiex" should be "vortex" and "in to" should be "into".
[Section 4.2] The reference "See Figure 4(b)&(c) and Figure 4" appears to have an incomplete second citation; likely "Figure 5" is intended.
[Section 4.4] The phrase "This is in consistence with" should be "consistent with".
[Section 5] The word "Addtional" should be "Additional".
[References, [25]] Reference [25] is incomplete: "2409.08310" should be formatted as "arXiv:2409.08310".

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the holographic derivation is self-contained and the final-state claim is an unforced output of the simulations.

full rationale

The paper's derivation chain is self-contained. Section 2 fixes the probe-limit action (2.1) and the Schwarzschild-AdS background (2.2) with parameters m_i^2=-2 and e_i=1 taken from standard holographic superfluidity; no target result is used to set these parameters. Section 3 solves the stationary equations of motion (3.2)-(3.4) for the composite vortex profiles, and Section 4 obtains the instability spectra from the generalized eigenvalue problem (4.3), which is solved independently of the subsequent nonlinear evolution. The nonlinear splitting dynamics in Figures 6-12 are full time integrations of the bulk EoMs using the numerical scheme of [25]; that self-citation is a code/method citation, not a load-bearing appeal to the paper's own conclusions. The central claim that generic unstable composite vortices end in singly quantized fundamental vortices without additional long-lived vortex-antivortex pairs is presented as an observed output of these simulations and is explicitly contrasted with GPE results from [16,20,24]; it is not encoded in the ansatz, in any fitted parameter, or in the definition of the composite vortex. The only identified limitations are evidential completeness issues (the assertion that p=1,2,3 modes are sufficient, and the unquantified meaning of 'long living'), but those are matters of evidence strength rather than circularity. No step in the paper equates a prediction with its input by construction, so no circular step is recorded.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The model uses standard holographic superconductor ingredients (bulk scalars, U(1) gauge field, Schwarzschild-AdS black brane), no new entities are introduced. The free parameters are coupling and temperature, both physical in the model. The main assumptions are the probe limit, identical components, and the axisymmetric vortex ansatz.

free parameters (3)

Inter-component coupling ν = -0.1 and -0.2 (fixed values)
This coupling controls miscibility and interaction strength between the two superfluids; values are chosen by hand to lie in the miscible regime (ν<0) and are not fitted to data.
Temperature T/Tc = Varied, e.g., 0.339 and 0.677
Temperature is a physical state variable, but the specific values used in simulations are chosen by hand to explore different regimes; it is a parameter of the calculation.
Critical chemical potential μc = Approximately 4.064
Determined numerically as the phase transition point for the holographic model; it is a computed property, not fitted to the vortex dynamics results.

assumptions (5)

domain assumption Probe limit: matter fields do not backreact on the spacetime metric.
Stated in Section 2: 'We work in the probe limit by neglecting the back-reaction of matter content to the geometry'. This freezes the normal fluid and metric dynamics.
domain assumption The two superfluid components are identical: m1^2=m2^2=-2, e1=e2=1.
Used in Section 2 to define the model; this symmetry simplifies the equations and may affect the generality of the results.
domain assumption Stationary axisymmetric vortex ansatz with phase windings S_i θ.
Equation (3.1) assumes the vortex profile is axisymmetric with a single winding number per component; this is the class of solutions studied.
ad hoc to paper Only excitation channels with p=1,2,3 are considered.
Section 4 states 'numerical evidence indicates that only p=1,2,3 modes are sufficient since other modes are all stable'; this claim is not shown in detail.
domain assumption In-going boundary condition at the horizon and source-free condition at the AdS boundary for quasinormal modes.
Standard holographic prescription for computing the spectrum of the dual system, described in Section 4.

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Pith. "Pith review of Splitting dynamics of quantized composite vortices in holographic miscible binary superfluids." pith.science (2026). https://pith.science/paper/ZFICO6KR

@misc{pith2026250103561,
  author       = {Pith},
  title        = {Pith review of: Splitting dynamics of quantized composite vortices in holographic miscible binary superfluids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZFICO6KR}},
  note         = {Machine review of arXiv:2501.03561}
}

abstract

The stability properties and splitting dynamics of multiply quantized vortices are the subject of interest in both theoretical and experimental investigations. Going beyond the regime of validity of Gross-Pitaevskii equation (GPE), we study the composite vortices in miscible strongly interacting binary superfluids by employing a holographic model that naturally incorporate finite temperature and dissipation. The composite vortices is classified in terms of an integer pair $(S_1, S_2)$ of phase winding numbers and can share the same vortex core, while either co-rotating or counter-rotating, leading to very diverse vortex structures. We uncover different dynamical behaviors compared to results from GPE that is valid in weak coupling limit and zero temperature. In particular, we show that the occurrence of dynamic instabilities and the instability strength are sensitive to the temperature. We identify several temperature dependent dynamical transitions in $(1,1)$, $(2,\pm 1)$ and $(2,2)$ vortices. The splitting behaviors associated with different multipolarities are demonstrated by solving the full-time evolution for slightly perturbed composite vortices. We find that the final states of all composite vortices are generally singly quantized vortices, and no additional long living vortex is formed due to strong dissipation. Our results highlight the important role of temperature and the distinction between dynamics of composite vortices in weakly interacting superfluids without dissipation and strongly interacting case with dissipation, shedding a new light on the understanding of quantum vortex and dynamical instabilities in multicomponent superfluids.

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Hartnoll, C.P

S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601

work page 2008

[2] [2]

Holographic model of superfluidity

C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [ 0809.4870]

work page Pith review arXiv 2009

[3] [3]

Kawaguchi and T

Y. Kawaguchi and T. Ohmi, Splitting instability of a multiply charged vortex in a bose-einstein condensate, Physical Review A 70 (2004) 043610

work page 2004

[4] [4]

Kuopanportti, E

P. Kuopanportti, E. Lundh, J.A.M. Huhtam¨ aki, V. Pietil¨ a and M. M¨ ott¨ onen,Core sizes and dynamical instabilities of giant vortices in dilute bose-einstein condensates, Physical Review A 81 (2010) 023603

work page 2010

[5] [5]

Middelkamp, P.G

S. Middelkamp, P.G. Kevrekidis, D.J. Frantzeskakis, R. Carretero-Gonz´ alez and P. Schmelcher, Bifurcations, stability, and dynamics of multiple matter-wave vortex states, Physical Review A 82 (2010) 013646

work page 2010

[6] [6]

R¨ abin¨ a, P

J. R¨ abin¨ a, P. Kuopanportti, M.I. Kivioja, M. M¨ ott¨ onen and T. Rossi,Three-dimensional splitting dynamics of giant vortices in bose-einstein condensates, Physical Review A 98 (2018) 023624

work page 2018

[7] [7]

Ewerz, A

C. Ewerz, A. Samberg and P. Wittmer, Dynamics of a vortex dipole in a holographic superfluid, Journal of High Energy Physics 2021 (2021) 199

work page 2021

[8] [8]

Ker¨ anen, E

V. Ker¨ anen, E. Keski-Vakkuri, S. Nowling and K.P. Yogendran,Inhomogeneous structures in holographic superfluids. ii. vortices, Physical Review D 81 (2010) 126012

work page 2010