{"id":"9a9aec19-de61-4b70-a90f-cf20dfea51c5","arxiv_id":"2607.19097","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Spatially increasing loss alone produces a weak boundary-localized loss peak (quasi-NHEB) in a non-Hermitian quantum walk even when the non-Hermitian skin effect is absent.","lead":"This paper studies quantum particles hopping on a lossy chain where losses are stronger deeper into the bulk, and finds that even without the usual skin effect that pushes particles to edges, an enhanced escape signal appears at the boundary. It names this effect the quasi-NHEB and shows it strengthens with the loss gradient.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"NHSE-free classification at φ=0 rests on an unspecified eigenstate subset and an L=80-specific MIPR threshold; the quasi-NHEB may be a hidden imaginary-Stark skin effect.","rationale":"The reader's weakest_assumption correctly identifies the undefined eigenstate subset and the L=80-specific MIPR threshold as the insecure basis for 'NHSE absent at φ=0'. My stress-test concurs and sharpens the concern: since the nonuniform loss breaks translational invariance, the standard PBC/OBC spectral criterion is ill-defined for this problem, and the paper itself shows that enclosing spectral loops (Fig. 4) do not imply skin localization for φ=π/2. Therefore the classification of the quasi-NHEB as NHSE-independent is underdetermined by the presented evidence. I do not dispute the numerical presence of a boundary-localized loss peak or its growth with γ — those are directly supported by Figs. 3, 5, and 6. The x0-independence in Fig. 6 is a useful discriminator and goes some way toward distinguishing the phenomenon from a conventional flux-induced NHSE. But the central scientific novelty is the claim that spatially nonuniform loss alone produces a boundary burst in the complete absence of any NHSE. Because Ref. [72] has already shown an 'imaginary-Stark NHSE' in a closely related nonuniform-loss setting, the burden is on the authors to rule out a generalized skin effect by a direct boundary-condition dependence test. The twisted-boundary spectrum and winding-number calculation I propose provides exactly such a test. The verdict should remain CONDITIONAL pending this check; no rejection is warranted because the phenomenon is plausible and internally consistent, but the headline classification should not be accepted without a non-threshold-based NHSE diagnostic.","tokens_in":14909,"tokens_out":14481,"duration_ms":149939,"concrete_test":"At φ=0, compute the complex spectrum E(θ) of the full 2L-site Hamiltonian under twisted boundary conditions: multiply all hopping amplitudes crossing the L–1 boundary (the relevant t1, t2, t3 periodic links) by e^{iθ}, keep the linear loss profile γ_x = γ x in the bulk, and let θ run from 0 to 2π for γ = 1, 2, 5, 10. For the near-real-axis eigenstates, compute the spectral winding number w(E_ref) = ∮ (dθ/2πi) ∂_θ log det[H(θ)-E_ref] and track the mean spatial position of the corresponding eigenstates as θ varies. If w ≠ 0 or eigenstate centers shift to the boundary for some θ, a boundary-condition-dependent skin mode exists and the 'NHSE-free' classification fails; if w = 0 and eigenstates remain extended for all θ, the quasi-NHEB is genuinely independent of the NHSE. This replaces the ad hoc MIPR threshold with a direct topological diagnostic.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the φ=0 edge burst is 'quasi' — boundary-localized loss without an NHSE. This requires a reliable diagnosis of NHSE absence. The paper's diagnosis is not reliable. In Sec. III, 'an MIPR value close to 0.018 is taken as a practical criterion for the absence of the NHSE throughout this work', with the caveat that it is 'specific to the system size L=80'. In Sec. IV, the MIPR is evaluated 'only for the subset of eigenstates associated with the NHSE', but the paper never defines how that subset is selected or why the excluded vertical-branch states cannot contribute to the long-time loss integral in Eq. (4). Moreover, the usual PBC/OBC spectral comparison is explicitly shown to be inconclusive: Sec. IV and Fig. 4 demonstrate that the PBC loop encloses the OBC spectrum for both φ=±π/2, yet at φ=π/2 the eigenstates are not skin-localized. Thus the quantitative support for 'NHSE absent at φ=0' reduces to an ad hoc threshold applied to an unspecified set of modes. Because Ref. [72] reports an 'imaginary-Stark NHSE' for the same nonuniform-loss setting, the quasi-NHEB could be a manifestation of that generalized skin effect rather than an NHSE-independent phenomenon. No generalized Brillouin zone or boundary-twist winding calculation is provided to settle this.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a one-dimensional non-Hermitian tight-binding model on a two-sublattice ladder with a magnetic flux and a position-dependent imaginary potential. It reports that a boundary-localized loss probability peak persists at zero flux, where the non-Hermitian skin effect (NHSE) is claimed to be absent, and terms this phenomenon a quasi–non-Hermitian edge burst (quasi-NHEB). The authors further classify edge bursts into conventional, hybrid, and quasi types, and use the dependence on the initial position x0 to argue for a distinct bulk–edge scaling relation.","tokens_in":15301,"tokens_out":4255,"duration_ms":40492,"significance":"If the central claim is correct, the paper would establish that spatially nonuniform loss alone can generate boundary-localized loss anomalies without the NHSE, thereby broadening the NHEB framework. The model is concrete and the dynamics are computed directly from the Schrödinger equation, with a check against the previously studied case in Ref. [66]. The proposed x0-dependence as a discriminator between the quasi-NHEB and the conventional NHEB is a useful diagnostic. However, the load-bearing diagnosis of NHSE absence is based on a hand-set MIPR threshold that is acknowledged to be L-specific, and the paper lacks convergence checks and a non-circular boundary-mode criterion. The contribution is potentially significant but currently under-validated.","major_comments":[{"comment":"The claim that the φ=0 edge burst is NHSE-independent rests on the MIPR≈0.018 threshold, which the paper itself states is 'specific to L=80' and which is applied only to an undefined 'subset of eigenstates associated with the NHSE' (Sec. IV). The PBC/OBC spectral comparison is acknowledged to be inconclusive in Fig. 4: the PBC loop encloses the OBC spectrum for both φ=±π/2, yet only φ=−π/2 shows skin-localized eigenstates. A reliable diagnosis of NHSE absence requires a non-circular criterion, e.g., finite-size scaling of the relevant eigenstate IPRs or a generalized Brillouin zone/winding-number calculation for the nonuniform loss profile. Without this, the distinction between quasi-NHEB and an imaginary-Stark-type NHSE (Ref. [72]) is not established.","section":"Sec. III, Sec. IV, Fig. 3(a)"},{"comment":"The central scaling statement—'P_edge remains nearly independent of x0' for the quasi-NHEB—requires a precise definition of P_edge, which is never given. If P_edge is simply P_x at x=1, it may miss the broad boundary region over which the quasi-NHEB extends; if it is a sum over several sites, the cutoff matters. Because the x0-independence is the key discriminator from the conventional NHEB, the authors should define P_edge explicitly and test the sensitivity of the conclusion to that definition.","section":"Eq. (4), Sec. V, Fig. 6"},{"comment":"The paper contains no error bars, convergence checks for the time integral in Eq. (4), or finite-size scaling. The claimed power-law decay of the conventional NHEB and the flatness of P_edge for the quasi-NHEB are asserted from visual inspection. A quantitative fit (with exponents and residuals) and at least one L-scaling test would substantially strengthen the classification.","section":"Sec. V, Fig. 6"}],"minor_comments":[{"comment":"Typo: 'These difference in the MIPR suggest' should be 'These differences in the MIPR suggest'.","section":"Sec. IV, after Fig. 3(a)"},{"comment":"The sentence 'an edge burst still emerges, we term this NHSE-independent edge burst a quasi–non-Hermitian edge burst' is a run-on; please rephrase for clarity.","section":"Sec. IV"},{"comment":"The text mentions 'an eigenstate that exhibits a relatively localized probability density near the left side of the chain.' Clarify whether this belongs to the near-real-axis subset or to the vertical imaginary branch, since the later discussion rules it out as the origin of the quasi-NHEB.","section":"Sec. IV, Fig. 3(d) inset"},{"comment":"The axes in the eigenstate density panels (a2) and (b2) are not labeled; adding 'site' and '|ψ|' labels would aid readability.","section":"Fig. 4"},{"comment":"The discussion of Ref. [72] would benefit from a one-sentence summary of the imaginary-Stark NHSE mechanism, so that the reader can appreciate why the present nonuniform-loss case might be related.","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":"The paper is clearly written and the central question—whether a boundary-localized loss peak can appear without the NHSE—is interesting. However, the current evidence is insufficient to rule out that the quasi-NHEB is a manifestation of the imaginary-Stark NHSE discussed in Ref. [72]. The MIPR threshold is explicitly L-specific and applied to an unspecified eigenstate subset, and the spectral-enclosure criterion is shown to be inconclusive. These are fixable with additional numerical diagnostics (e.g., finite-size IPR scaling, GBZ/winding-number computation, and a clear definition of P_edge). I therefore recommend major revision rather than rejection; the manuscript's scope can accommodate the required additions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper has a real observation — at zero flux, a boundary loss peak grows with the loss gradient even though the eigenstates look extended — but the way it rules out the NHSE is the weakest link, and the central term 'quasi-NHEB' is only as convincing as that criterion.\n\nWhat's actually new: the zero-flux case and the asymmetry between φ=-π/2 and φ=π/2 are absent from the earlier papers, which concentrated on φ=-π/2 or uniform loss. The authors reproduce the known φ=-π/2 result, so the numerics are at least consistent. The x0-dependence curves in Fig. 6 are a clean diagnostic: P_edge is flat in x0 for the quasi-NHEB, while the conventional NHEB decays as a power law. That separation is useful and likely to survive scrutiny.\n\nThe paper is also honest about the spectral criterion: it explicitly shows the PBC loop enclosing the OBC spectrum at both ±π/2, yet the eigenstate profiles at π/2 are extended. That is a good caution against relying on winding numbers alone.\n\nSoft spots: the NHSE-absence diagnosis rests on a MIPR threshold of 0.018, which the authors admit is specific to L=80, and on a 'subset of eigenstates associated with the NHSE' that is never defined. At φ=π/2 the MIPR is 0.017, essentially equal to the 'no NHSE' value, so the boundary between skin and no-skin is being decided by a number that no one can reproduce. The stress-test worry — that the quasi-NHEB is secretly an imaginary-Stark skin effect — does not land hard for φ=0, because the hopping there is symmetric and a linear loss gradient gives a perfectly natural, NHSE-free explanation. But a GBZ analysis or finite-size scaling of the MIPR would settle it, and the paper has neither.\n\nThere is no code, no data, no error bars, and the system sizes (L=80, 150) are modest. The final mechanism — an effective potential barrier from the loss gradient — is heuristic, not derived.\n\nBottom line: the observed effect is probably real, but the classification is under-supported. The paper deserves a serious referee, and a revision could make the quasi-NHEB a solid addition to the edge-burst literature.","headline":"Real numerical observation of a loss-gradient edge burst at zero flux, but the no-NHSE classification is too hand-wavy to take as established.","tokens_in":15724,"tokens_out":4931,"would_cite":true,"duration_ms":47124,"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":"Spatially nonuniform loss alone can create boundary-localized loss bursts even without the non-Hermitian skin effect, and these bursts grow with the loss gradient.","keywords":["non-Hermitian skin effect","non-Hermitian edge burst","nonuniform loss","quantum walk","magnetic flux","inverse participation ratio","boundary localization","dissipative lattice"],"falsifier":"A generalized Brillouin zone computation for the nonuniform-loss model at φ=0 showing that all eigenstates have localization lengths that scale with system size (i.e., a weak NHSE), or an experiment comparing the zero-flux nonuniform-loss case to a zero-flux uniform-loss control that exhibits an equally strong boundary peak, which would show the peak is not caused by the loss gradient.","tokens_in":14845,"feed_emoji":"⚛️","tokens_out":5117,"duration_ms":45990,"temperature":0.7,"pith_summary":"The paper tries to establish that boundary-localized loss anomalies in non-Hermitian quantum walks do not require the non-Hermitian skin effect (NHSE). In a lattice with magnetic-flux-tunable NHSE and a linearly increasing loss rate, the authors find that at zero flux—where they argue the NHSE is absent—a weak boundary peak in the loss probability still appears and strengthens as the loss gradient grows. They name this the quasi-NHEB and show it is nearly independent of the walker's initial position, unlike the conventional NHSE-driven edge burst. The authors also show that nonuniform loss can suppress the NHSE in the positive-flux regime even when spectral criteria would predict it, indicating that spectral structure and eigenstate localization can decouple under inhomogeneous dissipation. If correct, this separates two physical mechanisms for edge bursts and opens a route to controlling boundary loss through engineered dissipation alone.","feed_headline":"Loss gradients trigger edge bursts without the skin effect","feed_subtitle":"Spatially nonuniform loss alone localizes loss at a boundary and grows with the loss gradient.","key_machinery":"The model is a one-dimensional two-sublattice tight-binding chain with open boundaries, non-Hermiticity from a site-dependent imaginary on-site potential −iγx on the B sublattice, and magnetic flux φ introduced via Peierls phases that control the NHSE direction and strength. The key mechanism the authors invoke is the linearly increasing imaginary potential, which acts as an effective potential barrier that suppresses intercell hopping and biases the walker toward regions of smaller loss, thereby accumulating loss probability near the boundary even without skin-effect eigenstate localization. The inverse participation ratio (IPR) and its mean (MIPR) serve as the operational diagnostics for t","core_discovery":"The central claim is that a spatially nonuniform loss profile generates a boundary-localized accumulation of loss probability—termed the quasi-non-Hermitian edge burst (quasi-NHEB)—even in the absence of the non-Hermitian skin effect. At zero magnetic flux, where the authors' MIPR-based analysis indicates no NHSE, the loss probability shows a peak at the boundary whose magnitude increases monotonically with the loss gradient γ, while the peak near the initial position decreases. The quasi-NHEB is distinguished from the conventional NHEB by its broad spatial profile and its near-independence of the initial position x0. When flux is introduced, the interplay between nonuniform loss and the NHS","pith_inferences":["If the effective-barrier picture is right, other monotonic loss profiles (e.g., exponential or step-like) should produce quasi-NHEBs with strengths set by the local gradient; this is a direct, testable extension.","The near-independence of P_edge on x0 suggests the quasi-NHEB arises from a local escape process near the boundary rather than from global spectral properties, which could be modelled by a position-dependent decay-rate analysis.","Because the MIPR threshold is size-specific, the claim of NHSE absence at φ=0 should be revisited with a generalized Brillouin zone calculation for the nonuniform-loss model; if a weak NHSE is present at large L, the quasi-NHEB might be a finite-size effect.","The decoupling of spectral and localization properties under inhomogeneous loss may extend to disordered or random loss landscapes, where spectral winding may fail to predict boundary behavior."],"forward_implications":["Boundary-localized dissipation anomalies can be engineered purely by shaping the loss profile, without needing nonreciprocal hopping or magnetic flux.","The quasi-NHEB's insensitivity to the initial position provides an experimental fingerprint that separates loss-gradient-driven bursts from skin-effect-driven bursts; measuring P_edge vs x0 distinguishes them.","In systems with nonuniform loss, spectral encirclement criteria for the NHSE can be misleading; eigenstate-based measures such as the MIPR are needed to diagnose skin localization.","The hybrid NHEB regime offers a tunable platform where reversing the magnetic flux can completely switch off the skin effect and its associated edge burst, which could be probed in photonic waveguide arrays or electric circuits with engineered loss."],"fun_headline_variants":["Loss gradients alone spark edge loss bursts","Edge bursts without skin effect from nonuniform loss","Nonuniform loss yields boundary loss peaks","Quasi-NHEB emerges from loss gradients alone"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The claim that the quasi-NHEB occurs in the absence of the NHSE rests on a manually chosen MIPR threshold (≈0.018, specific to L=80) applied to an unspecified subset of eigenstates; if a different subset or threshold were used, the zero-flux case might host a weak skin effect, and the key distinction would dissolve.","fun_headline_variants_meta":{"raw":{"variants":["Loss gradients alone spark edge loss bursts","Edge bursts without skin effect from nonuniform loss","Nonuniform loss yields boundary loss peaks","Quasi-NHEB emerges from loss gradients alone"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000205,"raw_usage":{"total_tokens":1227,"prompt_tokens":740,"completion_tokens":487,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":484,"completion_tokens_details":{"reasoning_tokens":431}},"tokens_in":484,"tokens_out":487,"duration_ms":5588,"temperature":1.0,"reasoning_tokens":431,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T13:26:04.100237+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A generalized Brillouin zone computation for the nonuniform-loss model at φ=0 showing that all eigenstates have localization lengths that scale with system size (i.e., a weak NHSE), or an experiment comparing the zero-flux nonuniform-loss case to a zero-flux uniform-loss control that exhibits an equally strong boundary peak, which would show the peak is not caused by the loss gradient.","supporting_citations":[],"review_version":1}