{"id":"51fd4950-cc20-4bf3-80b2-bc38bc66572a","arxiv_id":"2608.10052","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A quenched fermionic superfluid shows coherent edge oscillations, and a quench across the topological transition produces density ripples that the authors tie to hybridization of two Majorana modes.","lead":"In computer simulations of a spin-orbit-coupled superfluid of fermions, the authors show that when the magnetic field is suddenly changed, the boundary-localized Majorana modes either keep oscillating at the edge or, if the field change crosses a topological transition, collapse inward and create ripple patterns in the density.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The ripple pattern is attributed to Majorana hybridization, but Appendix B credits it to low-energy bulk modes near the critical point; without a trivial-to-trivial near-critical control, the causal claim is unestablished.","rationale":"The paper's strongest claim is causal: ripples originate from coherent hybridization and interference of initially separated Majorana boundary states. For that to hold, the ripple must be absent or substantially weaker when the initial state has no Majorana components but the quench still passes near the topological critical point. The manuscript does not provide that control. Worse, Appendix B's description of the finite-time ramp explicitly assigns the ripples to low-energy bulk quasiparticle modes near the critical point, which is a different mechanism. This is an internal tension, not merely a disagreement with the literature. The reader's weakest_assumption about mean-field accuracy is a reasonable secondary concern, but the more direct vulnerability is the missing attribution control: even within the manuscript's own framework, the observable can be explained by bulk critical dynamics. I therefore recommend keeping the CONDITIONAL verdict, with the condition expanded to include a trivial-to-trivial near-critical control and a mode-decomposition of the ripple signal. An honest non-finding is not appropriate here because the paper's own Appendix B text undercuts the headline claim.","tokens_in":14192,"tokens_out":4317,"duration_ms":40183,"concrete_test":"Perform the same self-consistent TDBdG simulation for a quench entirely within the trivial phase but near the critical point, e.g., h_i=0.90E_F to h_f=0.50E_F (and a finite ramp crossing the same interval), with identical N=100, trap, and time step. If pronounced ripple structures with inward-moving wavefronts appear in n(x,t) and Delta(x,t), the ripple is a generic low-energy bulk response, not a Majorana-specific signature. Independently, decompose the post-quench density fluctuation delta n(x,t) into the contribution from the two initial Majorana wavefunctions evolved under the final BdG Hamiltonian versus all other quasiparticle modes; if the Majorana-projected weight carries only a small fraction of the ripple amplitude, the central attribution fails. Either result would settle whether the claim requires revision.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"In Sec. III-C and the Conclusion, the paper's central claim is that the post-quench density ripples arise from inward propagation, hybridization, and interference of the initially separated Majorana boundary states. However, Appendix B describes the same mechanism as a bulk effect: it states that the time-dependent variation of the Zeeman field excites low-energy bulk quasiparticle modes near the critical point, and that the propagation and interference of these excitations produce oscillatory spatial structures in the order parameter and density distributions. That attribution is generic, not Majorana-specific. The only trivial-side control (Appendix B, Fig. 6) uses h_i=0.70E_F and h_f=0.50E_F, which stays far from the critical field h_c=0.94E_F, so it never tests whether a trivial initial state brought near the critical region produces the same ripples. The Majorana fidelity F(t) defined in Eq. (5) is computed on the lowest-energy quasiparticle mode; in the trivial phase that mode is just a low-energy bulk mode, so a drop in F does not by itself prove Majorana hybridization. What is missing is a quantitative decomposition of the ripple signal into contributions from the initial Majorana-projected components versus bulk modes of the final Hamiltonian. The vague mention of a spatially tailored potential in Sec. III-A adds an unresolved inconsistency, but the central issue is that the causal claim is not distinguished from a generic critical response.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies quantum quench dynamics of a one-dimensional spin-orbit-coupled fermionic superfluid within a self-consistent time-dependent Bogoliubov-de Gennes framework. For quenches that remain inside the topological phase, it reports coherent boundary-localized oscillations of the density and pairing field, interpreted as nonadiabatic deformation of surviving Majorana modes. For quenches from the topological to the trivial phase, it reports pronounced spatiotemporal ripples in the density and order parameter, which the abstract and Sec. III-C attribute to inward propagation, hybridization, and interference of the initially separated Majorana boundary states. A particle-hole self-conjugacy fidelity is introduced to quantify the loss of Majorana character, and a boundary-sensitive dynamical phase diagram is constructed in the (h_i, h_f) plane. Appendices provide supplementary finite-time ramp results and trivial-side control quenches.","tokens_in":14376,"tokens_out":5302,"duration_ms":54052,"significance":"If the central attribution is correct, the paper would establish a time-resolved density observable that is directly sensitive to Majorana hybridization, complementary to equilibrium tunneling and interferometric probes, and relevant to ultracold-atom emulations of topological superconductors. The work has several genuine strengths: the TDBdG simulation self-consistently updates the pairing field; multiple control protocols are shown (intra-topological, trivial-to-trivial, trivial-to-topological); finite-time annealing is used to separate adiabatic from nonadiabatic behavior; and the Majorana fidelity in Eq. (5) provides a quantitative, if one-dimensional, diagnostic. However, the central causal claim is not yet distinguished from a generic low-energy critical response, and the Appendix B attribution partially contradicts the main-text narrative. The needed additional analysis—a quantitative decomposition of the ripple signal and a near-critical trivial-side control—is well within the scope of the manuscript, so the result is potentially significant but not yet established.","major_comments":[{"comment":"The main text, abstract, and conclusion attribute the ripple pattern specifically to the coherent hybridization and interference of initially separated Majorana boundary states, but Appendix B states that, in the same cross-critical protocols, the time-dependent Zeeman field excites low-energy bulk quasiparticle modes near the critical point and that propagation and interference of these excitations produce the oscillatory spatial structures. These are two different causal explanations. The manuscript needs a quantitative decomposition of the post-quench density response into (i) contributions from the projection of the initial Majorana wavefunctions onto final eigenstates and (ii) contributions from generic bulk modes of the final Hamiltonian. Without such a decomposition, the central claim that the ripples are a Majorana signature rather than a generic critical response is unestablished.","section":"Sec. III-C and Appendix B (text near Fig. 5)"},{"comment":"The only trivial-to-trivial control uses h_i = 0.70 E_F and h_f = 0.50 E_F, which are far from the critical field h_c = 0.94 E_F. This control therefore does not test whether a trivial initial state brought close to the critical point produces the same ripple structures as the topological-to-trivial quench. I request a trivial-to-trivial quench with both fields near h_c (for example h_i = 0.92 E_F and h_f = 0.80 E_F) and a quantitative comparison of the density ripple amplitude, spatial structure, and fidelity dynamics with the results in Fig. 4. Similarly, the claim in Sec. III-A that the ripple mechanism is absent for reverse trivial-to-topological quenches needs to be supported by a comparison of the reverse quench with the same closeness to the critical point; Fig. 7 alone does not establish the claimed asymmetry.","section":"Appendix B, Fig. 6 and Sec. III-A"},{"comment":"The Majorana fidelity F(t) is computed on the lowest-energy quasiparticle mode. In the trivial phase after the quench, the lowest-energy mode is generally a finite-energy bulk mode, so a drop in F(t) does not by itself prove that the initial Majorana components hybridize; it may only indicate that the mode tracked is no longer the zero-energy boundary mode. The manuscript should demonstrate that the tracked mode is continuously connected to the initial Majorana mode, for example by monitoring the overlap between the time-evolved wavefunction and the initial Majorana components, or by checking for level crossings or identity swaps in the low-energy spectrum. Without this, the fidelity collapse is not a self-contained proof of Majorana hybridization.","section":"Sec. III-C, Eq. (5)"},{"comment":"The simulations use a self-consistent time-dependent BdG approximation for a small trapped system (N = 100) with a sudden, large-amplitude quench, but the accuracy of this mean-field treatment is not benchmarked for the parameter regime considered. For a one-dimensional system with attractive interactions, beyond-mean-field fluctuations can be significant, and the quench injects considerable energy. I request either a benchmark against time-dependent DMRG or exact diagonalization for a reduced system size, or at minimum a discussion of the expected validity of the TDBdG approximation for the qualitative mechanism claimed, including how the results depend on the chosen interaction strength gamma and on the system size.","section":"Sec. II, Eqs. (2)-(4)"}],"minor_comments":[{"comment":"The sentence 'these ripple structures originates from' should be 'originate from'.","section":"Abstract"},{"comment":"The sentence 'we introduce a spatially potential that allows boundary states to be engineered within a prescribed region of the system' is vague and not followed by any equation, figure, or quantitative description; it should be clarified or removed.","section":"Sec. III-A"},{"comment":"The phrase 'We next adobe finite-time annealing' contains a typo: it should be 'adopt'.","section":"Sec. III-B"},{"comment":"The phrase 'a nonadiabatic deformation fo surviving Majorana modes' contains a typo: it should be 'of'.","section":"Sec. III-A"},{"comment":"The notation in Eq. (5) is not fully defined: the inner products and norms should be written explicitly with integrals, and the mode index (lowest-energy mode) should be stated in the equation itself rather than only in the surrounding text.","section":"Eq. (5)"},{"comment":"The dimensionless interaction strength gamma and the spin-orbit coupling strength alpha used in the simulations are not listed; the results in Figs. 2-7 cannot be reproduced without this information.","section":"Sec. II and Appendix A"},{"comment":"The phase boundaries in Fig. 1 are described only qualitatively ('dashed lines', 'white gradient area'). A quantitative criterion, such as a threshold on the amplitude or spatial width of density oscillations, should be given so that the phase diagram is reproducible.","section":"Sec. III-A and Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal and the TDBdG machinery is appropriate, but the central claim of Majorana-induced ripples is currently undercut by the generic critical-response attribution in Appendix B and by the lack of a near-critical trivial control. The needed controls and decomposition analysis are feasible and would strengthen the paper considerably; I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"One thing to know: the paper reports a new numerical observation — after a sudden Zeeman quench from the topological to the trivial phase in a 1D spin-orbit-coupled Fermi superfluid, the density and pairing field develop ripple patterns. The authors attribute the ripples to inward propagation, hybridization, and interference of the two initial Majorana boundary states. That is an interesting idea, and the authors do solid work with self-consistent TDBdG and control runs. But the causal claim is not solid: the paper's own Appendix B describes the same ripples as a generic response of low-energy bulk modes near the critical point.\n\nWhat's new and good: previous quench studies in this model focused on the bulk order parameter. This paper adds a boundary-resolved phase diagram, with an oscillation phase for intra-topological quenches and a ripple phase for topology-crossing quenches. The annealing comparison is a nice touch, showing that boundary oscillations vanish under slow ramps and are thus nonadiabatic deformations of surviving Majorana modes, not equilibrium features. The trivial-to-trivial and trivial-to-topological controls are useful.\n\nSoft spots. The main issue is the contradiction between Sec. III-C and Appendix B. In the main text, the ripples are attributed to Majorana hybridization; Appendix B says the time-dependent Zeeman field excites low-energy bulk quasiparticle modes near the critical point, and their propagation and interference produce the oscillatory structures. That is not a Majorana-specific explanation. The trivial-to-trivial control (h_i=0.70, h_f=0.50) stays far from h_c=0.94, so it never tests a trivial initial state near the critical region. Without that control, or a quantitative decomposition of the ripple into Majorana-projected versus bulk contributions, the 'Majorana hybridization' claim remains unproven. The Majorana fidelity F(t) is computed on the lowest-energy quasiparticle mode; in the trivial phase that mode is just a low-energy bulk state, so its drop in F is generic, making the diagnostic partly circular.\n\nMinor issues: the paper mentions a 'spatially tailored potential' in Sec. III-A that never appears in the model; key numerical parameters (alpha, gamma, omega) are not stated, and no code or data is deposited. These are fixable. The mean-field TDBdG approximation for N=100 is a standard caveat, not a fatal flaw.\n\nWho it's for: specialists in quench dynamics or Majorana physics in cold atoms will find the phase diagram and the ripple observation worth discussing. I would not cite the paper for the causal claim until the authors either quantify the Majorana contribution or soften their conclusion.\n\nRecommendation: send to peer review. The observation is worth publishing, but a serious referee should ask for the control near the critical point or a rewording of the attribution.","headline":"The ripple observation is intriguing, but the paper's causal claim that the ripples come from hybridizing Majorana components is undercut by its own appendix describing the same pattern as a bulk critical response.","tokens_in":15059,"tokens_out":4819,"would_cite":false,"duration_ms":43380,"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":"After a topology-changing quench, two initially separated Majorana boundary modes propagate inward, hybridize, and interfere, producing density ripples that directly signal the loss of Majorana character.","keywords":["Majorana zero modes","quantum quench dynamics","spin-orbit-coupled Fermi gas","time-dependent Bogoliubov-de Gennes theory","topological phase transition","density ripple patterns","Majorana fidelity","nonequilibrium superfluid dynamics"],"falsifier":"Run a numerically exact many-body simulation of the same Zeeman-field quench for a smaller trapped system, or perform time-resolved density imaging on a spin-orbit-coupled Fermi gas after the quench: the central claim is falsified if no inward-colliding ripple pattern with a central density peak appears for topological-to-trivial quenches, or if a comparable ripple pattern appears for trivial-to-topological quenches, because the proposed mechanism is specifically direction-dependent and tied to the initial Majorana content.","tokens_in":13884,"feed_emoji":"🌊","tokens_out":10082,"duration_ms":90409,"temperature":0.7,"pith_summary":"This paper tries to establish that the real-time dynamics of Majorana boundary modes can be read directly from a quenched superfluid's density and pairing field. Using self-consistent time-dependent Bogoliubov–de Gennes simulations of a one-dimensional spin-orbit-coupled Fermi gas, it claims that quenches staying inside the topological phase leave the Majorana sector intact, producing coherent boundary-localized oscillations, while quenches crossing into the trivial phase project the two separated Majorana components onto finite-energy states that propagate inward, hybridize, and interfere. The resulting ripple pattern in the density distribution is identified as a direct dynamical signature of the loss of Majorana character. A sympathetic reader would care because this gives a time-resolved, equilibrium-independent way to probe Majorana physics in cold-atom experiments, and it shows that static topological protection does not by itself determine how boundary modes behave under rapid driving.","feed_headline":"Ripples in a quenched superfluid expose dying Majorana modes","feed_subtitle":"Ripples appear only when a topological quench destroys boundary modes, so density movies can probe Majorana physics.","key_machinery":"The load-bearing machinery is the self-consistent time-dependent Bogoliubov–de Gennes (TDBdG) framework: the quasiparticle spinor $\\Psi_\\eta(x,t)$ evolves under a time-dependent BdG Hamiltonian while the pairing order parameter $\\Delta(x,t)$ is updated from the evolving quasiparticle wave functions, so the condensate and the quasiparticles respond to each other throughout the quench. Around this framework, the paper builds a boundary-sensitive dynamical phase diagram in the space of initial and final Zeeman fields, and introduces the Majorana fidelity $F(t)=|\\langle v|u\\rangle|/(|u||v|)$, a normalized particle-hole self-conjugacy overlap that distinguishes a well-defined Majorana state ($F\\approx 1$) from a hybridized finite-energy quasiparticle ($F\\to 0$). The combination of spatially resolved wave-function dynamics and fidelity evolution carries the argument: it traces the survival, oscillation, hybridization, and eventual loss of Majorana character that the density ripples report.","core_discovery":"On the paper's own terms, the central discovery is that a sudden Zeeman-field quench from the topological into the trivial phase converts Majorana boundary modes into a detectable interference pattern. The initially separate Majorana components retain boundary localization only transiently, then propagate toward the trap center, hybridize with each other and with finite-energy Bogoliubov quasiparticles, and generate pronounced ripples in the pairing order parameter $\\Delta(x,t)$ and the spin-resolved density $n_\\sigma(x,t)$; the same mechanism appears in finite-time ramps across the transition. The paper introduces a normalized particle-hole self-conjugacy fidelity $F(t)$ that stays near unity for intratopological quenches and collapses to zero when the two Majorana components overlap after a topology-changing quench, quantifying the dynamical loss of Majorana character. Because trivial-to-topological quenches and quenches confined entirely to the trivial phase do not produce the same boundary-driven ripple response, the paper attributes the ripples specifically to the coherent hybridization of the initially separated Majorana states.","pith_inferences":["One testable extension is to measure the time at which the two inward-propagating wave packets collide at the trap center and check that this collision time scales with the inverse hybridization energy splitting as the final Zeeman field approaches the critical value.","If the ripple attribution is correct, time-resolved density imaging alone could act as a Majorana detector, without requiring tunneling contacts or equilibrium spectroscopy, and the same boundary-sensitive diagnostic could be applied to other symmetry-protected edge modes in one-dimensional topological phases.","Because the claim is made within a self-consistent mean-field approximation, the strongest check would be an exact many-body simulation of a smaller trapped system with the same quench protocol; if ripples survive with the same direction dependence and collision dynamics, the mechanism is likely robust beyond mean field."],"forward_implications":["Intratopological quenches leave Majorana zero modes dynamically robust, but with boundary-localized oscillations whose amplitude grows with quench strength and shrinks as the ramp becomes slower.","Topology-changing quenches produce a ripple pattern in the density and pairing field that is a direct, time-resolved signature of Majorana hybridization and loss of self-conjugacy.","The Majorana fidelity provides a quantitative measure for the dynamical phase diagram, separating persistent Majorana dynamics from boundary-bulk hybridization and complete loss of Majorana character.","Near the critical field, the small excitation gap creates an intermediate hybrid regime with gradual fidelity decay, so the classification is not binary.","Finite-time ramps across the transition reproduce the ripple mechanism, meaning the signature is not an artifact of the sharp sudden-quench protocol."],"supporting_citations":[{"why":"It supplies the bulk three-regime classification of quenched spin-orbit-coupled Fermi gas dynamics that the paper's boundary-sensitive phase diagram extends.","marker":"[7]"},{"why":"It establishes that quenched Majorana modes project onto post-quench eigenstates and leave a memory, the projection picture used throughout the paper.","marker":"[9]"},{"why":"It provides the framework for persistent order-parameter oscillations in fermionic condensates that underlies the oscillatory post-quench response.","marker":"[19]"},{"why":"It shows how quench dynamics can signal the topological phase transition in the same one-dimensional Fermi gas platform.","marker":"[29]"},{"why":"It gives the foundational model of Majorana zero modes as boundary states of topological wires, whose localization the paper tracks in time.","marker":"[33]"},{"why":"It underpins the self-consistent time-dependent Bogoliubov–de Gennes method through the collective Rabi-oscillation treatment of time-dependent BCS pairing.","marker":"[36]"},{"why":"It provides the contrasting case of quenched topological boundary modes persisting in a trivial system, against which the paper's loss-and-hybridization mechanism is defined.","marker":"[56]"}],"fun_headline_variants":["Quenched superfluid ripples reveal Majorana hybridization","Ripples expose dying Majorana modes after topological quench","Majorana hybrid waves in quenched superfluid density","Quench-induced ripples fingerprint Majorana modes","Density ripples mark Majorana collapse across quench"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the self-consistent time-dependent Bogoliubov–de Gennes mean-field treatment faithfully captures the strongly quenched dynamics of the trapped $N=100$ gas; the paper does not benchmark this approximation against an exact many-body calculation, so if beyond-mean-field fluctuations or trap details change how the boundary quasiparticles move and mix, the ripple pattern could have a different origin.","fun_headline_variants_meta":{"raw":{"variants":["Quenched superfluid ripples reveal Majorana hybridization","Ripples expose dying Majorana modes after topological quench","Majorana hybrid waves in quenched superfluid density","Quench-induced ripples fingerprint Majorana modes","Density ripples mark Majorana collapse across quench"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000979,"raw_usage":{"total_tokens":4150,"prompt_tokens":932,"completion_tokens":3218,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":548,"completion_tokens_details":{"reasoning_tokens":3140}},"tokens_in":548,"tokens_out":3218,"duration_ms":20139,"temperature":1.0,"reasoning_tokens":3140,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:14:15.302547+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a numerically exact many-body simulation of the same Zeeman-field quench for a smaller trapped system, or perform time-resolved density imaging on a spin-orbit-coupled Fermi gas after the quench: the central claim is falsified if no inward-colliding ripple pattern with a central density peak appears for topological-to-trivial quenches, or if a comparable ripple pattern appears for trivial-to-topological quenches, because the proposed mechanism is specifically direction-dependent and tied to the initial Majorana content.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the bulk three-regime classification of quenched spin-orbit-coupled Fermi gas dynamics that the paper's boundary-sensitive phase diagram extends."},{"cited_title":"Chung, Y.-H","cited_arxiv_id":null,"evidence_quote":"It establishes that quenched Majorana modes project onto post-quench eigenstates and leave a memory, the projection picture used throughout the paper."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It shows how quench dynamics can signal the topological phase transition in the same one-dimensional Fermi gas platform."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It provides the contrasting case of quenched topological boundary modes persisting in a trivial system, against which the paper's loss-and-hybridization mechanism is defined."}],"review_version":1}