{"id":"4cbfb8eb-2cfd-48af-983e-c03545c76484","arxiv_id":"1908.06668","paper_version":3,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Two corotating vortices in one condensate drag atom-filled cores of a second condensate around the trap, while the cores keep a fixed orientation, and an analytical model matches numerical simulations to within a few percent.","lead":"This paper studies vortices in one ultracold gas that trap atoms of a second gas inside their cores, creating heavy massive vortices. It derives formulas for how far apart two such vortices sit and shows the trapped cores orbit without spinning, a distinction from ordinary fluid drag.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (4) as printed is inconsistent with Eqs. (2)-(3) and fails to reproduce the stated R→∞ limit Eq. (5), so the analytical curve in Fig. 3 cannot be independently reproduced.","rationale":"The reader identified the point-like core approximation as the weakest assumption. That is a reasonable physical concern, and the paper partly addresses it by sweeping N_b. However, the more immediate, load-bearing issue is that the central analytical formula, Eq. (4), as printed cannot be derived from the model that precedes it. A direct derivation from the stated Hamiltonian (2) and Lagrangian (3) gives a different polynomial relation, and that derived relation — not the printed Eq. (4) — reduces to the paper's own unbounded limit Eq. (5). The printed Eq. (4) contains a term proportional to R⁴/(d−2R), which diverges as R³ for fixed d, so the stated limit is not defined. Because Fig. 3's analytical curve is the quantitative heart of the paper, the reported <2% agreement with GPE numerics cannot be checked without either a corrected Eq. (4) or the underlying code/data. This does not mean the physics is wrong; the numerical GPE results and the no-tangential-entrainment evidence are valuable and likely robust. But the analytical claim needs to be reproducible. I therefore recommend CONDITIONAL rather than outright ACCEPT: the paper should be accepted after the equation is corrected or the derivation/code is provided to confirm the numerical agreement.","tokens_in":14664,"tokens_out":31146,"duration_ms":277004,"concrete_test":"Symbolically re-derive Eq. (4) from Eqs. (2)-(3) by substituting the rotating symmetric ansatz into the Euler-Lagrange equations; check whether the printed Eq. (4) matches the derived polynomial. If it does not, take the derived relation (with k=h/m_a, ρ*=N_a m_a/(πR²), m=N_b m_b/2 from Eq. (8)) and recompute d versus N_b for the parameters of Fig. 3. Compare this recomputed curve to the reported numerical d_vor and to the yellow dotted curve in Fig. 3; if the recomputed curve still reproduces d_vor within 2%, the discrepancy is only typographical, otherwise the central quantitative claim requires revision.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Independently deriving the massive-vortex equilibrium from the stated Lagrangian (3) and Hamiltonian (2), using the symmetric ansatz r1=(d/2)(cos Ωt, sin Ωt), r2=-r1, yields the relation π d² (16R⁴−d⁴) Ω (kρ*−mΩ) = ρ k² (16R⁴ + 8R²d² + 5d⁴). This reduces exactly to Eq. (5) in the R→∞ limit. The printed Eq. (4), however, is not this relation and does not have a well-defined R→∞ limit: the term 16 k² ρ* R⁴/(d−2R) diverges as R³ while no compensating R⁴ term is present, so Eq. (5) cannot follow from it. Since the central analytical prediction d(Nb) in Fig. 3 is stated to come from Eq. (4), the reported <2% agreement with GPE numerics is not reproducible from the manuscript as written. This is an internal-consistency issue, not a physics disagreement: if the equation actually used in the numerics differs from the printed one, the quantitative claim needs correction or the code/data to verify.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies an immiscible 23Na-39K mixture in a rotating circular-box trap, in which two corotating vortices of species a are filled by species-b atoms. The authors model each filled vortex as a point vortex carrying a point mass (Lagrangian (3)), derive an equation for the precession frequency as a function of vortex separation (Eq. (4)), map the model parameters to GPE parameters via Eq. (8), and compare the predicted equilibrium distance d(Nb) with imaginary-time GPE solutions, reporting agreement within 2%. They also compute angular momenta of both species (Eqs. (10) and (14)), show from rotating-frame currents, local angular velocity, and phase-field circulation that the cores are dragged along the precession but do not rotate, and propose heuristic equations for the vortex healing length and core size (Eq. (18)).","tokens_in":14910,"tokens_out":40584,"duration_ms":362210,"significance":"If the central analytical relation is corrected, the paper offers a parameter-free prediction for how core mass changes the equilibrium distance of a corotating vortex pair, validated against independent GPE numerics, and a multi-diagnostic demonstration of the absence of tangential entrainment. The rotating-frame velocity analysis and the circulation argument are convincing and go beyond earlier work on vortex-bright soliton complexes. The authors are also appropriately explicit about the regime of validity: the point-mass model is only reliable for immiscible, narrow cores (Sec. IV C). The main quantitative claim, however, currently rests on Eq. (4), which as printed is internally inconsistent and cannot reproduce the reported agreement; the result is therefore not yet usable in its present form.","major_comments":[{"comment":"Equation (4) is inconsistent with the printed model and with the stated limit Eq. (5). Directly from Eqs. (2)-(3) and the symmetric ansatz x1=(d/2)(cos Ωt, sin Ωt), x2=-x1, I obtain π d²(16R⁴−d⁴)Ω(kρ*−mΩ)=ρ*k²(16R⁴+3d⁴), which reduces exactly to Eq. (5) in the R→∞ limit. The printed Eq. (4) is dimensionally inconsistent because the terms 3d⁴k²ρ*/(d−2R) and 16k²ρ*R⁴/(d−2R) scale as length⁵ while all other terms scale as length⁶; after rearrangement it becomes πd²(16R⁴−d⁴)Ω(kρ*−mΩ)=k²ρ*(3d⁴−16R⁴)/(d−2R), whose right-hand side grows as R³ for fixed d and Ω, so no R→∞ limit exists and Eq. (5) cannot follow from it. Since the analytical curve in Fig. 3 is stated to come from Eq. (4), the reported <2% agreement with GPE numerics cannot be independently reproduced from the manuscript as written. The authors should correct Eq. (4), provide the resulting d(Nb) curve, and verify that the comparison in Fig. 3 refers to the corrected formula.","section":"Sec. II B, Eq. (4)"}],"minor_comments":[{"comment":"The word 'previsions' should be 'predictions'; the same typo appears in the first paragraph of Sec. IV.","section":"Abstract"},{"comment":"The notation 'H∞ = (z1,...,zN) =' appears to be missing the function name; it should read H∞(z1,...,zN) =.","section":"Eq. (1)"},{"comment":"The statement 'offset < 2%' should specify the error metric (maximum or mean relative deviation over the Nb sweep) and should be recomputed after correcting Eq. (4).","section":"Sec. IV A, Fig. 3"},{"comment":"Near x=0 the assignment of a point to the left or right core is ambiguous; the text should state that the local angular velocity diagnostic is applied only in the bulk of each core, excluding a strip around x=0.","section":"Sec. V B, Eq. (13)"},{"comment":"The conversion factors 1.30 and 1.15 are calibrated from the Nb=1 numerical solution; the text already calls the model heuristic, but the figure caption should remind readers that these factors are fitted, not derived.","section":"Sec. VI, Fig. 8"},{"comment":"The physical origin of the point mass m in the Lagrangian could be stated more explicitly: m is the total mass of the bright-soliton core in one vortex, and Eq. (8) sets m=Nb mb/2; a clarifying sentence would prevent confusion with the atomic mass mb.","section":"Sec. II B, Eq. (3)"}],"recommendation":"major_revision","confidential_remarks":"The reader's report recommended acceptance, but the internal inconsistency in Eq. (4) is decisive for the central quantitative claim of the paper. The error appears to be a transcription or typesetting mistake rather than a conceptual flaw, because Eq. (5) and the force expression in Sec. II B are consistent with the correct derivation. I therefore recommend major revision rather than rejection: the authors should replace Eq. (4) with the correct relation, recompute the analytical curve in Fig. 3, and confirm that the agreement statement refers to that curve. If the corrected relation is not supplied and the comparison cannot be reproduced, the paper would not be acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague — this paper is worth reading for the physics, but do not try to reproduce the central curve from the printed equations, because Eq. (4) is inconsistent with what follows from the stated Lagrangian and with its own stated R→∞ limit Eq. (5). I rederived the equilibrium condition from Eq. (3) using the symmetric ansatz; the correct relation is πd²(16R⁴−d⁴)Ω(kρ*−mΩ) = ρk²(16R⁴+8R²d²+5d⁴), which reduces to Eq. (5). The printed Eq. (4), however, contains terms like πd⁶Ω(kρ*−mΩ) and 3d⁴k²ρ/(d−2R), and its leading R⁴ behavior cancels only if kρ*−mΩ=0, which is not the stated limit. So there is a typo or algebra error in the manuscript. That matters because Fig. 3's analytical curve is computed from Eq. (4), and the reported <2% agreement with GPE numerics cannot be checked independently. This is the central quantitative claim. It is probably fixable—Eq. (5) and the numerics suggest the authors used a different equation—but as printed the paper is internally inconsistent.\n\nWhat is genuinely new: the massive-point-vortex model in a circular box, the prediction that the equilibrium distance grows with core mass, the angular momentum formulas, and the rotating-frame demonstration that cores precess without tangential entrainment. The no-entrainment argument is credible: rotating-frame currents show almost rigid rotation at −Ω, and the phase-field circulation is zero around each core. The angular momentum for species b is semi-analytical and matches numerics within 4%; species a within 0.8%. Healing-length curves are heuristic and rely on two HWHM conversion factors fitted at N_b=1, which the paper discloses. It is not \"fully analytical\" in that section.\n\nMinor: no code or data deposited; simulation parameters are given but the code is not. The point-like core approximation is tested across N_b∈[5,1000] and the paper acknowledges its limits for miscible cores.\n\nMy recommendation: send it to peer review, but the referee must demand that Eq. (4) be corrected and the numerical data or code for Fig. 3 be supplied. If the authors can show that the actual equation used gives Eq. (5) in the R→∞ limit, this is a solid paper. As it stands, the central formula is not reproducible from the manuscript.","headline":"Interesting physics, but Eq. (4) is internally inconsistent and the central d(N_b) curve is not reproducible from the printed manuscript.","tokens_in":15438,"tokens_out":4228,"would_cite":false,"duration_ms":39320,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper establishes that in an immiscible rotating two-species Bose-Einstein condensate, atoms trapped inside vortex cores act as point masses: adding core atoms increases the equilibrium separation of a corotating vortex pair, while…","keywords":["binary Bose-Einstein condensate","immiscible mixture","vortex-bright soliton","massive vortex core","point-vortex model","precession","angular momentum","Gross-Pitaevskii equation"],"falsifier":"A concrete test would be to track the orientation of an initially anisotropic species-b core over one full precession period: the paper predicts its long axis remains fixed in the laboratory frame, so any observed rotation of that axis would falsify the no-tangential-entrainment claim. Separately, computing $d_{\\mathrm{vor}}$ from coupled Gross-Pitaevskii equations well beyond the explored range $N_b\\in[5,1000]$, or in a miscible regime with $g_{ab}<\\sqrt{g_a g_b}$, should reveal a growing deviation from the point-mass prediction of Eq. (4) if the central model is wrong.","tokens_in":14408,"feed_emoji":"🌀","tokens_out":6696,"duration_ms":68963,"temperature":0.7,"pith_summary":"The paper studies an immiscible two-species Bose-Einstein condensate in a rotating circular box, in a state where vortices in the majority species trap atoms of the minority species inside their cores. It argues that these trapped atoms behave as massive point-like cores, so the vortex pair's precession is governed by an equation of motion with the same structure as charged particles in a transverse magnetic field. The central quantitative claim is that the equilibrium distance between the two corotating vortices grows with the number of core atoms, following an analytical relation that the authors verify against numerical Gross-Pitaevskii solutions within about two percent. The paper also shows that the cores are dragged along by the vortices but keep their orientation fixed in the laboratory frame, indicating no tangential entrainment between the two superfluids. A sympathetic reader would care because this gives a clean, parameter-free bridge from point-vortex models to a concrete ultracold-gas system, with the core atom number as an experimentally tunable knob for vortex dynamics.","feed_headline":"Atom-filled vortex cores push the pair apart","feed_subtitle":"Heavier cores in an immiscible BEC set the vortex separation, and the cores orbit without spinning.","key_machinery":"The central object is the massive point-vortex Lagrangian (3), which adds a kinetic term $\\sum_j \\frac{m_j}{2}(\\dot{x}_j^2+\\dot{y}_j^2)$ to the usual point-vortex Hamiltonian in a circular box, together with the circulation term $\\sum_j \\frac{k_j\\rho_*}{2}(y_j\\dot{x}_j-x_j\\dot{y}_j)$. This Lagrangian is formally the same as that of charged particles in a planar domain under a transverse magnetic field, with vortex strengths playing the role of charges and $\\rho_*$ the role of the magnetic field. Its equations of motion admit a symmetric precessing solution whose equilibrium distance $d$ and angular frequency $\\Omega$ are linked by Eq. (4), and the substitutions $k=h/m_a$, $\\rho_*=N_a m_a/(\\pi R^2)$, and $m=N_b m_b/2$ connect the model to the coupled Gross-Pitaevskii parameters. The no-entrainment claim is carried by a rotating-frame computation of the species-b mass current density, which shows the cores behave as almost rigid bodies rotating at $-\\Omega$ in the rotating frame, together with a phase-field argument that a soliton-like distribution cannot spin in the laboratory frame without a phase singularity at its center.","core_discovery":"In an immiscible binary Bose-Einstein condensate in a rotating circular box, the authors claim that a state with two corotating vortices in species a, each filled by species-b atoms, is accurately described by a massive point-vortex Lagrangian. From this model they derive Eq. (4), which relates the precession angular frequency $\\Omega$ to the symmetric equilibrium separation $d$ of the two vortices; through the mapping in Eq. (8), $d$ grows with the core mass $m = N_b m_b/2$, and the predicted values match the numerical distances $d_{\\mathrm{vor}}$ and $d_{\\mathrm{peak}}$ extracted from coupled Gross-Pitaevskii solutions to within about two percent. Using a rotating-frame analysis of the mass current density, they show that the species-b cores orbit the trap center with the vortices but rotate at angular velocity $-\\Omega$ relative to the rotating frame, so their orientation in the laboratory frame stays constant: the cores revolve like rigid bodies without spinning about their own centers. The paper also derives simple formulas for the angular momentum of each species, with species a obeying $\\langle L_{z,a}\\rangle/(N_a\\hbar)=2[1-(r_{\\mathrm{vor}}/R)^2]$, and gives heuristic equations for the vortex healing length and the characteristic core size as functions of the core mass.","pith_inferences":["Editorial inference: because the core mass enters the equations in the same way a particle mass enters magnetic-field dynamics, tuning $N_b$ across the explored range should effectively scan a continuous mass-to-charge ratio, which could be used to probe cyclotron-like orbits and Hall-type behavior in a cold-atom setting.","Editorial inference: the point-mass mapping assumes a uniform majority density, so at smaller $N_a$ or stronger interspecies coupling the two-percent agreement should degrade; a position-dependent effective mass or an additional Magnus-like force is a natural next-order correction.","Editorial inference: a finite-core-size expansion in the ratio of core radius to healing length could extend Eq. (4) into the miscible or soft-core regime where the paper itself says the point-like model partially loses validity, producing testable deviations from the current prediction.","Editorial inference: the no-entrainment claim can be probed by imaging an initially anisotropic, elliptical core during precession; the paper predicts its long axis stays fixed in the laboratory frame, so any measurable rotation of that axis would require relaxing the zero-entrainment conclusion."],"forward_implications":["If the model is correct, the equilibrium separation of a corotating vortex pair in a circular box becomes a controlled function of the minority-species atom number, giving a direct experimental knob for vortex-pair geometry.","The Lorentz-like form of the massive vortex equations makes the system an analog simulator for planar charged particles in a transverse magnetic field, with tunable effective mass and charge-to-mass ratio.","The simple angular-momentum formula for species a means that a single measured vortex orbit radius determines the majority-component angular momentum per particle without solving the full Gross-Pitaevskii equations.","The heuristic equations (18) predict how the vortex healing length and core radius respond to added core atoms, so core profile measurements can directly test the interspecies-repulsion mechanism.","The demonstration that cores orbit without rotating implies that any observed lab-frame rotation of a bright-soliton core would signal tangential entrainment between the two fluids beyond the present model."],"supporting_citations":[{"why":"Supplies the point-vortex Hamiltonian (1) on which the massive-core Lagrangian (3) is built.","marker":"[44]"},{"why":"Provides the two-vortex Hamiltonian in a circular box via virtual vortices, giving the boundary-dependent terms that enter Eq. (4).","marker":"[48]"},{"why":"Gives the canonical Poisson-bracket structure for vortex coordinates used to derive the equations of motion.","marker":"[49]"},{"why":"Documents vortex-bright soliton complexes whose effective double-well potential for the core species motivates the massive-core picture.","marker":"[43]"},{"why":"Supplies the imaginary-time method used to obtain stationary vortex/bright-soliton solutions of the coupled Gross-Pitaevskii equations.","marker":"[41]"},{"why":"Provides the analytical angular-momentum treatment in harmonic confinement that the authors adapt to derive Eq. (10).","marker":"[54]"},{"why":"Gives the standard healing-length and bright-soliton-size formulas that the heuristic system (18) extends to the interspecies case.","marker":"[59]"},{"why":"Shows dark-bright soliton complexes remain stable beyond the immiscible regime, a result the authors extend to vortex/bright-soliton complexes.","marker":"[34]"},{"why":"Provides the sodium-potassium mixture parameters used to set the coupled Gross-Pitaevskii model.","marker":"[50]"},{"why":"Discusses the Andreev-Bashkin entrainment effect that the paper argues is negligible for immiscible fluids in this configuration.","marker":"[58]"}],"fun_headline_variants":["Massive cores push vortices apart in binary BEC","Atom-filled vortex cores orbit without spinning","Heavy cores in vortices: precession, no self-spin","Binary BEC: vortex separation grows with core mass"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that each species-b core can be treated as a point mass $m=N_b m_b/2$ sitting exactly at the vortex center, with no size, deformation, or internal circulation; the paper itself notes that this approximation loses validity when the cores become soft or the two fluids become miscible.","fun_headline_variants_meta":{"raw":{"variants":["Massive cores push vortices apart in binary BEC","Atom-filled vortex cores orbit without spinning","Heavy cores in vortices: precession, no self-spin","Binary BEC: vortex separation grows with core mass"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000186,"raw_usage":{"total_tokens":1343,"prompt_tokens":984,"completion_tokens":359,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":600,"completion_tokens_details":{"reasoning_tokens":294}},"tokens_in":600,"tokens_out":359,"duration_ms":4489,"temperature":1.0,"reasoning_tokens":294,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:38:12.013672+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete test would be to track the orientation of an initially anisotropic species-b core over one full precession period: the paper predicts its long axis remains fixed in the laboratory frame, so any observed rotation of that axis would falsify the no-tangential-entrainment claim. Separately, computing $d_{\\mathrm{vor}}$ from coupled Gross-Pitaevskii equations well beyond the explored range $N_b\\in[5,1000]$, or in a miscible regime with $g_{ab}<\\sqrt{g_a g_b}$, should reveal a growing deviation from the point-mass prediction of Eq. (4) if the central model is wrong.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the point-vortex Hamiltonian (1) on which the massive-core Lagrangian (3) is built."},{"cited_title":"Penna, in Quantized Vortex Dynamics and Superfluid Turbulence, edited by C.F","cited_arxiv_id":null,"evidence_quote":"Provides the two-vortex Hamiltonian in a circular box via virtual vortices, giving the boundary-dependent terms that enter Eq. (4)."},{"cited_title":"Penna, Phys","cited_arxiv_id":null,"evidence_quote":"Gives the canonical Poisson-bracket structure for vortex coordinates used to derive the equations of motion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents vortex-bright soliton complexes whose effective double-well potential for the core species motivates the massive-core picture."},{"cited_title":"Gallem´ ı, L","cited_arxiv_id":null,"evidence_quote":"Supplies the imaginary-time method used to obtain stationary vortex/bright-soliton solutions of the coupled Gross-Pitaevskii equations."},{"cited_title":"Guilleumas and R","cited_arxiv_id":null,"evidence_quote":"Provides the analytical angular-momentum treatment in harmonic confinement that the authors adapt to derive Eq. (10)."},{"cited_title":"Nespolo, G","cited_arxiv_id":null,"evidence_quote":"Gives the standard healing-length and bright-soliton-size formulas that the heuristic system (18) extends to the interspecies case."},{"cited_title":"Hamner, J","cited_arxiv_id":null,"evidence_quote":"Shows dark-bright soliton complexes remain stable beyond the immiscible regime, a result the authors extend to vortex/bright-soliton complexes."},{"cited_title":"vortex healing length","cited_arxiv_id":null,"evidence_quote":"Discusses the Andreev-Bashkin entrainment effect that the paper argues is negligible for immiscible fluids in this configuration."}],"review_version":1}