{"id":"00e8fa11-97de-430f-8470-9651347623ca","arxiv_id":"2607.19840","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Increasing a density-dependent gauge potential in a toroidal condensate transforms a ring of singly quantized vortices into a giant vortex with higher circulation.","lead":"In a toroidal Bose-Einstein condensate, a density-dependent synthetic gauge field can drive the ground state from a ring-shaped lattice of ordinary vortices into a single giant vortex when the nonlinear-rotation strength is increased. The paper maps where this happens and how the excitation spectrum changes, which is useful for atomtronic devices that control superflow with light-induced gauge fields.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central transition claim rests on an unspecified numerical solver; without convergence tests or code, the giant-vortex state at C=12 could be a numerical artifact.","rationale":"The reader's weakest assumption identified the unspecified numerical solver as the key gap, and I agree that this is the most load-bearing concern. The central claim is entirely dependent on numerically generated ground states, and the lack of solver details prevents any independent check of convergence or stability. The concrete test I propose directly targets this concern by reproducing the critical state with documented methods and testing convergence and dynamical stability. If the test passes, the central claim gains credible support; if it fails, the transition may be spurious. The reader's verdict of CONDITIONAL is appropriate, so I do not change it.","tokens_in":21254,"tokens_out":7775,"duration_ms":78703,"concrete_test":"Reproduce the ground state for Fig. 1(a5) parameters (Ω=0.45, g=250, r0=4, C=12) using a fully specified numerical method. Use imaginary-time propagation with a finite-difference or split-step scheme on a 1024×1024 grid (Δx≈0.02) with time step Δt=10^-5, and run until the energy and central circulation converge to <0.1% change over 10^4 steps. Verify convergence by (i) doubling grid resolution (2048×2048), (ii) halving Δt, and (iii) comparing with an independent stationary solver (e.g., normalized gradient flow or Newton's method). Also compute the BdG spectrum of the converged state and check for negative eigenvalues (dynamical instability). If the central circulation is robustly 15 and the state is dynamically stable, the transition claim is supported; otherwise, the reported transition may be a numerical artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central assertion—that increasing nonlinear rotation strength C drives a structural transition from a ring-shaped vortex lattice (circulation 6) to a giant vortex (circulation 15) at C=12 with negative chemical potential (Sec. III, Figs. 1 and 5)—is based on ground-state solutions of Eq. (9). However, the numerical solver is never described: no grid size, time step, imaginary-time propagation scheme, convergence criterion, or boundary handling is provided. This is load-bearing because the transition occurs in a regime where the Thomas-Fermi analysis itself shows solutions terminate at a maximum C (Fig. 2), so the C=12 state lies near the boundary of admissible solutions and is especially sensitive to numerical resolution and convergence. If the grid is too coarse, vortex cores may be artificially merged into the central hole, inflating the circulation; if imaginary-time propagation is stopped early, the state may be a metastable local minimum rather than the true ground state. The paper's own BdG analysis is applied to these states but does not explicitly demonstrate stability of the C=12 giant vortex (e.g., no anomalous-mode check is reported for the toroidal geometry). Without code/data or detailed numerical evidence, the central transition claim cannot be independently verified.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a quasi-2D Bose-Einstein condensate in a toroidal trap, governed by the GP equation (9) with a density-dependent gauge potential that induces a nonlinear rotation term proportional to C n L_z. Ground states are computed for positive interaction strengths g = 250-1000 and rotation frequencies Omega = 0.45-0.9. The central claim is that increasing C drives a structural transition from a ring-shaped vortex lattice with total circulation six to a giant vortex with circulation fifteen at C = 12, accompanied by negative chemical potential (Figs. 1 and 5). The paper derives a Thomas-Fermi density (13), maps the allowed parameter region (Fig. 2), studies giant-vortex generation by atom removal and by a repulsive Gaussian beam (Figs. 6 and 7), computes collective excitations with BdG and hydrodynamic methods (Figs. 8-10), and analyzes the stability of multiply quantized vortices (Figs. 11 and 12). A violation of Kohn's theorem and mode softening across the transition are reported.","tokens_in":21515,"tokens_out":7032,"duration_ms":75080,"significance":"If the central transition is numerically robust, the result is significant: the density-dependent gauge field would provide a new control parameter for assembling high-circulation giant vortices in annular geometry. The analytic Thomas-Fermi solution-space mapping is explicit and useful, and the mutual consistency of the BdG and hydrodynamic spectra is a positive check. There is no fitting or prediction circularity. However, the central claim depends entirely on ground-state solutions whose numerical solver is not described, and the title's 'attractive interactions' is not supported by the simulations. The significance is therefore conditional on the numerical details and on corrected framing.","major_comments":[{"comment":"The numerical method used to solve Eq. (9) is never specified: no grid size or spacing, time step, imaginary-time or real-time propagation scheme, convergence criterion, or boundary treatment. This is load-bearing because the reported transition occurs near the upper termination of the Thomas-Fermi solutions for r0 = 4, where the circulation count (6 to 15 at C = 12) and the BdG frequencies are sensitive to numerical resolution. Please provide full numerical details and convergence tests, e.g., circulation and chemical potential versus grid spacing and time step, at least for the states in Fig. 1 and the spectra in Figs. 8 and 9. The reviewer agrees with the stress-test concern here.","section":"Sec. II after Eq. (9); Figs. 1, 5, 8, 9"},{"comment":"The title and parts of the text describe the problem as involving 'attractive interactions', but all simulations use repulsive contact interactions (g = 250, 500, 1000). The negative chemical potential shown in Fig. 5 is induced by rotation/nonlinear rotation, not by a negative scattering length. The manuscript should change the title/abstract or present actual negative-g results; otherwise the advertised attractive-interaction regime is not being studied.","section":"Title and Sec. III (Fig. 5)"},{"comment":"The l = 1 dipole mode is said to signal 'a deviation from Kohn's theorem'. Kohn's theorem applies to harmonic confinement, whereas the toroidal potential V = (r - r0)^2/2 is not a harmonic potential. A decreasing dipole frequency in this trap is therefore not a violation of a theorem that does not apply. Please remove this claim or define precisely which generalized Kohn theorem is being tested and why it should hold in the toroidal trap.","section":"Sec. V, Fig. 8"},{"comment":"The multiply-quantized-vortex stability analysis is explicitly performed for a harmonically trapped condensate, but the abstract and conclusion state the global/local stability result without that qualifier. Because the paper's main context is toroidal, this transfer is not automatic. A toroidal MQV calculation, or a clear qualifier that the result refers to harmonic traps, is required.","section":"Sec. VI, Fig. 11; Conclusion"}],"minor_comments":[{"comment":"The figures are referred to as 'Figure III' and 'Fig. III' in the text; the numbering should be corrected to Fig. 2.","section":"Fig. 2 captions"},{"comment":"The text says the BdG equations are obtained using the perturbation ansatz in Eq. (18); it should refer to Eqs. (19) and (20), since Eq. (18) defines the laser potential.","section":"Sec. V, after Eq. (22)"},{"comment":"The radial prefactors in Eq. (12) are typeset ambiguously. In addition, the term 'attractive regime' in the description of Fig. 2(c)-(f) should be replaced by 'negative chemical potential' to avoid implying negative g.","section":"Eq. (12) and Fig. 2(c)-(f)"},{"comment":"The conclusion says 'absorption techniques' while Section IV uses 'atom removal'; the terminology should be unified.","section":"Abstract and Sec. IV/Conclusion"}],"recommendation":"major_revision","confidential_remarks":"The main unresolved issue is the missing numerical method for the GP equation. If the authors can supply a full solver description and convergence tests, and correct the attractive-interaction wording and the Kohn-theorem claim, the paper could become publishable. I see no evidence of circularity or fabrication, but the central transition cannot be accepted on the current evidence."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is the first toroidal-geometry study of the density-dependent gauge potential, and it finds a ring-lattice-to-giant-vortex transition as the nonlinear rotation strength C grows. That is worth refereeing. But the paper as posted does not document its numerical solver, and the title oversells “attractive interactions” when the simulations use repulsive g=250.\n\nWhat is actually new: the model is not new—density-dependent gauge potentials and nonlinear rotation have been studied in harmonic traps—but the toroidal trap is. The central result, that increasing C drives a structural transition from a ring-shaped vortex lattice (circulation 6) to a giant vortex (circulation 15) at C=12, is a clean numerical observation that I do not think appears in prior literature. The Thomas-Fermi analysis gives a useful parameter-space map of where these solutions can exist, and the BdG and hydrodynamic spectra agree for the low-lying modes. That mutual consistency is real evidence. The MQV stability section, while set in a harmonic trap rather than the torus, does show a genuine and interesting effect: positive C lowers the free energy of multiply quantized vortices but does not remove the anomalous mode.\n\nWhere the soft spots are: the biggest is reproducibility. The numerical solver is never described—no grid size, no time step, no imaginary-time scheme, no convergence criterion. The stress-test note is right that this is load-bearing: the C=12 giant vortex sits near the boundary of the Thomas-Fermi solution regime, and without convergence tests an artificial merging of vortex cores into the central hole is exactly the kind of artifact you need to rule out. The paper’s own BdG analysis is applied to that state, but no anomalous-mode check is reported for the toroidal geometry. Second, the title and abstract say “attractive interactions,” but the GP equation has g>0 throughout. The giant vortex appears at negative chemical potential, which is not the same as a negative scattering length. That wording should be fixed. Third, the “violation of the Kohn theorem” is an overstatement in a toroidal trap; the dipole mode is not protected by Kohn’s theorem when the trap is anharmonic. Minor, but worth correcting. Fourth, Sec. VI is about a harmonic trap and is never connected to the toroidal geometry that frames the rest of the paper.\n\nThe flaws are identifiable and fixable, not fatal. Who is this for? People working on synthetic gauge fields and vortex states in annular geometries will find the parameter map and the transition useful. It deserves a serious referee, but the referee should ask for the numerical details and convergence tests, and the authors should clarify the title and the harmonic-trap section. If those come back clean, I’d be happy to cite it.","headline":"A genuinely new geometry for the density-dependent gauge potential model, with a plausible giant-vortex transition—but the central numerical claim needs better support before I'd bet on it.","tokens_in":21997,"tokens_out":3771,"would_cite":false,"duration_ms":42622,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.75.Lm","03.75.Kk"],"model":"deepseek-v4-flash","headline":"Increasing the strength of nonlinear rotation in a toroidal condensate drives a structural transition from a ring-shaped vortex lattice to a giant vortex, with circulation rising from six to fifteen quanta.","keywords":["density-dependent gauge potential","nonlinear rotation","giant vortex","toroidal Bose-Einstein condensate","vortex lattice transition","Thomas-Fermi profile","collective excitations","multiply quantized vortex stability"],"falsifier":"Run an independent imaginary-time simulation of the two-dimensional Gross–Pitaevskii equation with fixed numerical parameters (grid spacing $\\leq 0.05$, time step $\\leq 10^{-5}$, and explicit boundary conditions) at $\\Omega=0.45$, $g=250$, $r_0=4$, and check whether the ground-state circulation rises from 6 at $\\tilde{C}=0$ to 15 at $\\tilde{C}=12$, with the phase accumulating $15 \\times 2\\pi$ around a single central core; failure to reproduce that jump would falsify the claimed transition.","tokens_in":21128,"feed_emoji":"🌀","tokens_out":12282,"duration_ms":115900,"temperature":0.7,"texified_at":"2026-08-05T21:34:53.834866+00:00","pith_summary":"This paper sets out to show that a density-dependent gauge potential—an artificial gauge field whose effective rotation rate grows with the condensate's own density—can act as a continuously tunable 'nonlinear rotation' control in a toroidally trapped Bose–Einstein condensate. The central result is structural: as the nonlinear rotation strength is increased, the usual ring-shaped vortex lattice reorganizes into a single giant vortex with much higher quantum circulation, with the paper reporting circulation rising from 6 to 15 quanta across the range it displays. The giant vortex appears in the negative chemical-potential regime, so the ring trap—rather than repulsive interactions—provides the stabilization. The paper also maps the region where the Thomas–Fermi density profile is admissible, finds that the dipole collective mode softens (a violation of the Kohn theorem) while breathing modes stiffen, and argues that nonlinear rotation can make multiply quantized vortices globally but not locally stable. If correct, this would give experimentalists a new in-situ knob for engineering high-circulation vortex states in annular superfluids, relevant to persistent-current and atomtronic devices.","texify_model":"deepseek-v4-flash","texify_usage":{"total_tokens":7707,"prompt_tokens":864,"completion_tokens":6843,"prompt_tokens_details":{"cached_tokens":0},"prompt_cache_hit_tokens":0,"prompt_cache_miss_tokens":864,"completion_tokens_details":{"reasoning_tokens":6044}},"feed_headline":"Nonlinear rotation turns a vortex ring into a giant vortex","feed_subtitle":"A density-dependent gauge field in a ring trap funnels vortices into one core and lifts circulation from 6 to 15 quanta.","key_machinery":"The engine of the paper is the density-dependent gauge potential, which enters the two-dimensional Gross–Pitaevskii equation as a rotation rate $\\Omega_n = \\Omega + \\tilde{C} |\\psi|^2$ multiplying the angular-momentum operator $L_z$. This term couples the local density to the effective rotation, so denser regions of the condensate rotate faster. The toroidal trap $V(r)=\\frac{1}{2}(r-r_0)^2$ supplies the multiply connected geometry that quantizes circulation around a central hole. Three tools carry the analysis: a Thomas–Fermi density profile whose turning points come from a quartic equation and delimit the admissible parameter space; linearized quasiparticle equations that yield collective mode frequencies; and a phase–","core_discovery":"At fixed rigid-body rotation $\\Omega=0.45$, interaction strength $g=250$, and toroidal radius $r_0=4$, the paper finds that the ground state of the generalized Gross–Pitaevskii equation changes from a ring-shaped vortex lattice of total circulation six at zero nonlinear rotation to a giant vortex of circulation fifteen at $\\tilde{C}=12$. Positive nonlinear rotation drives annular vortices inward, enlarging the central hole; negative values push vortices outward and lower the circulation. The same trend appears when giant vortices are prepared either by atom removal or by a repulsive Gaussian potential, with the core area largest for positive $\\tilde{C}$. The paper derives a Thomas–Fermi density profile and sh","pith_inferences":["If the circulation is as tunable as the numerics suggest, the same gauge-field scheme could act as an in-situ control for persistent currents in atomtronic circuits, writing quantized flows without stirring lasers or phase imprinting.","The appearance of the giant vortex at negative chemical potential suggests that effectively attractive systems—dipolar condensates or quantum mixtures—might support giant vortices at lower rotation rates than ordinary repulsive condensates; a scattering-length ramp could test this.","The hydrodynamic equations derived here predict \\tilde C-dependent collective-mode shifts that could be probed by Bragg spectroscopy, making the predicted Kohn-theorem violation an experimentally clean signature.","Because local stability of multiply quantized vortices is not achieved, combining nonlinear rotation with a pinning potential or weak dissipation is a natural next step; closing the anomalous-mode gap could make high-circulation states long-lived and practically useful."],"forward_implications":["Positive nonlinear rotation shrinks the annulus and funnels vortices into the central hole; negative rotation widens the annulus and pushes vortices toward the periphery.","The giant vortex state sits in the negative chemical-potential regime, where the ring trap pins it against collapse, offering a route to stable high-circulation states without rapid external stirring.","The Thomas–Fermi parameter map shows that the allowable nonlinear rotation strength shrinks as ring radius or rigid-body rotation grows, placing practical bounds on the giant-vortex transition.","Dipole-mode softening with increasing nonlinear rotation is a direct signature of Kohn-theorem violation in this geometry, while the breathing-mode upturn marks radial compression accompanying the transition.","Multiply quantized vortices can be made globally stable by positive nonlinear rotation, but the persistent negative-energy splitting mode means they will still dissociate locally unless an additional pinning mechanism is added."],"fun_headline_variants":["Vortex ring morphs into giant vortex under nonlinear rotation","Giant vortex from six to fifteen quanta in rotating toroidal BEC","Nonlinear rotation switches vortex lattice to giant vortex state","Ring trap vortices converge into a single giant vortex","Toroidal BEC: nonlinear rotation triggers giant vortex emergence"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The central transition claim rests on the unstated assumption that the imaginary-time and real-time simulations behind the density and phase plots are properly converged solutions of the two-dimensional Gross–Pitaevskii equation—no grid size, time step, or convergence criterion is given—and the stability conclusion relies on a second implicit transfer of harmonic-trap results to the toroidal geometry.","fun_headline_variants_meta":{"raw":{"variants":["Vortex ring morphs into giant vortex under nonlinear rotation","Giant vortex from six to fifteen quanta in rotating toroidal BEC","Nonlinear rotation switches vortex lattice to giant vortex state","Ring trap vortices converge into a single giant vortex","Toroidal BEC: nonlinear rotation triggers giant vortex emergence"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001129,"raw_usage":{"total_tokens":4537,"prompt_tokens":760,"completion_tokens":3777,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":504,"completion_tokens_details":{"reasoning_tokens":3694}},"tokens_in":504,"tokens_out":3777,"duration_ms":27824,"temperature":1.0,"reasoning_tokens":3694,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T11:33:05.367365+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run an independent imaginary-time simulation of the two-dimensional Gross–Pitaevskii equation with fixed numerical parameters (grid spacing $\\leq 0.05$, time step $\\leq 10^{-5}$, and explicit boundary conditions) at $\\Omega=0.45$, $g=250$, $r_0=4$, and check whether the ground-state circulation rises from 6 at $\\tilde{C}=0$ to 15 at $\\tilde{C}=12$, with the phase accumulating $15 \\times 2\\pi$ around a single central core; failure to reproduce that jump would falsify the claimed transition.","supporting_citations":[],"review_version":1}