{"id":"40e97884-6ef6-498e-8d7f-91c52e403d2d","arxiv_id":"2501.04502","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A complex phase in the quasiperiodic potential of a non-Hermitian Aubry-André chain controls whether eigenstates sit at an interface (skin effect) or near the excitation site (Anderson localization), and a topolectrical circuit reproduces this tuning in its voltage profile.","lead":"This paper studies a one-dimensional chain where disorder tries to trap waves and directional hopping tries to push them to an interface, and shows that a single complex phase in the disorder decides which effect wins. The authors then design an electrical circuit whose simulated voltage patterns mimic both effects, offering a tunable laboratory platform.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quantitative control claim rests on Eq. (2), which is neither rederived for the two-domain interface geometry nor applied consistently with the stated parameters; a direct numerical check is needed before the α_c threshold is accepted.","rationale":"The paper has genuine merits: the circuit mapping in Appendix A is a careful construction, the qualitative trend (tuning α moves the response from the interface to the excitation site) is consistent across the TB eigenstate plots and the LTspice voltage profiles, and the idea of a classical circuit analog of the AL–NHSE competition is useful. The concern is not that the effect is absent, but that the quantitative control claim is pinned to Eq. (2), which is imported from a uniform-chain analysis and then used with parameter values that do not reproduce the formula. This is the load-bearing point because the abstract and conclusion promise 'precise control' via α_c; if Eq. (2) is not the correct threshold for the two-domain geometry, the central claim is only qualitative. The reader's weakest assumption also targeted this transfer of Eq. (2); I agree. My proposed numerical scan is a minimal, self-contained check: it directly tests whether Eq. (2) is the actual transition point for Eq. (1) and whether the circuit Laplacian shows the same threshold. Separately, the time-evolution derivation assumes an orthonormal eigenbasis for a non-Hermitian Hamiltonian, which is invalid and should be corrected, but the quantitative control claim is already exposed by the Eq. (2) issue. Until that is done, the paper should remain conditional, not accepted as a quantitative demonstration.","tokens_in":17719,"tokens_out":8870,"duration_ms":87773,"concrete_test":"Fix the interface Hamiltonian (1) with L0=L and 2L+1 a Fibonacci number (e.g., 233). For t=0.65, γ=0.35 and at least λ=0.5, 0.9, 1.0, diagonalize H and compute, as functions of α, the mean inverse participation ratio and the center of mass of all eigenstates. Extract the crossing value α* where the eigenstates switch from interface-concentrated skin modes to bulk Anderson-localized modes, and compare it with Eq. (2). Repeat the same scan for a uniform chain without the interface. If α* differs between the two geometries, or if Eq. (2) does not reproduce the quoted 0.425 for any consistent parameter set, the quantitative control claim should be revised. As a secondary check, perform the same scan on the 21-node circuit Laplacian (A4) and locate where the driven voltage profile moves from node 11 to the excitation node; this directly tests the circuit-level control threshold.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim is the threshold α_c = ln|max(t+γ,t−γ)/λ| (Eq. 2), advertised as the single knob that switches between interface-localized skin states and Anderson-localized states. That formula is quoted from Ref. [40], whose transfer-matrix/Lyapunov analysis applies to a uniform nonreciprocal quasiperiodic chain. Hamiltonian (1) instead has a domain wall at L0+1 with opposite nonreciprocity on the two sides; the non-Bloch boundary-condition treatment that would justify Eq. (2) in this geometry is not performed. Because skin states at the interface are themselves a boundary-condition effect, the threshold can shift with L0 and with the interface terms, so transferring Eq. (2) is a substantive assumption, not a harmless one. In addition, the paper's own numbers are not consistent with Eq. (2): for the stated TB parameters t=0.65, γ=0.35 and λ=1, Eq. (2) gives α_c=0, not α_c≈0.425 as quoted for Fig. 2; if the circuit-mapping values t≈1.53, γ≈1.04 are used instead, Eq. (2) gives α_c≈0.944 for λ=1. Thus the threshold underpinning the 'precisely controlled' claim is not currently derived for the interface problem and is not applied consistently.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a non-Hermitian Aubry-André model with an interface separating two chains of opposite nonreciprocity, and proposes a topolectrical circuit realization. The main claims are: (i) the complex phase α of the quasiperiodic potential controls the competition between Anderson localization and the non-Hermitian skin effect, with a transition at α_c = ln|max(t+γ, t−γ)/λ| (Eq. 2); (ii) time evolution under a single-site excitation exhibits non-Hermitian jumps between skin states and Anderson-localized states; and (iii) an LTspice topolectrical circuit reproduces interface localization of the voltage profile for α < α_c and localization near the excitation node for α > α_c, with a tunable intermediate channel. The paper includes open data and code.","tokens_in":18025,"tokens_out":6690,"duration_ms":69571,"significance":"If the central claims were established, the work would provide a useful and experimentally accessible classical analog of the AL–NHSE competition, with a plausible control knob (the phase α) and a concrete circuit design with explicit component values. The paper is commendable for shipping the simulation data and code (Ref. [69]) and for making falsifiable predictions about the voltage profile. However, the quantitative control claim rests on an imported critical-value formula that is neither rederived for the interface geometry nor applied with consistent parameters, and the time-evolution analysis is built on an invalid orthonormality assumption for non-Hermitian eigenstates. The significance is therefore contingent on fixing these load-bearing issues.","major_comments":[{"comment":"Equation (4) assumes that the right eigenstates ψ_q of the non-Hermitian Hamiltonian H form a complete orthonormal basis and sets a_q(0)=⟨ψ_q|Ψ(0)⟩. For a non-Hermitian operator this is not valid: the correct expansion coefficients require the left eigenstates ψ̃_q, namely a_q(0)=⟨ψ̃_q|Ψ(0)⟩/⟨ψ̃_q|ψ_q⟩. Equation (6), the subsequent time evolution in Fig. 2, and the central claim of non-Hermitian jumps all rest on this invalid expansion. The authors should redo the time evolution with a biorthogonal basis or, more robustly, by direct numerical integration of the Schrödinger equation with the norm renormalization in Eqs. (7)–(8), and check whether the reported jumps survive.","section":"Section III, Eq. (4)"},{"comment":"The critical value α_c = ln|max(t+γ, t−γ)/λ| is taken from Ref. [40], which analyzes a uniform nonreciprocal quasiperiodic chain. The Hamiltonian in Eq. (1) instead has two domains with opposite signs of γ and an interface; no derivation or numerical verification is given that the same Lyapunov exponent controls the localization transition in this geometry. The paper's own numbers are also inconsistent with Eq. (2): with the stated TB parameters t=0.65, γ=0.35 and λ=1, Eq. (2) gives α_c=0, not the quoted α_c≈0.425 in Fig. 2; with γ=0, t=0.65 and λ=1 it gives α_c=ln(0.65)<0, not 0.425 in Fig. 5; and for λ=1.5 in Fig. 6, even using the circuit-mapped max(t+γ,t−γ)≈1.53, Eq. (2) gives α_c≈0.02, not 0.54. A definitive numerical determination of the transition for the interface Hamiltonian, for example via the inverse participation ratio or the OBC Lyapunov exponent as a function of α, is needed before the quantitative control claim can be accepted.","section":"Section II, Eq. (2); Figs. 2, 5, 6"},{"comment":"The same orthonormality assumption is applied to the circuit Laplacian: Eq. (B2) assumes V_a^† V_b = δ_ab and projects with V_k^† I(t). However, the Laplacians in Eqs. (A3) and (A4) are non-Hermitian because of the asymmetric off-diagonal couplings (C+C′) vs (C−C′), so their eigenvectors are not generally orthogonal and the projection formula is incorrect. This undermines the claimed correspondence between the circuit voltage response and the time-evolved wavefunction of the tight-binding model. The authors should either use left eigenvectors of the Laplacian or solve the circuit equations directly for the single-source excitation.","section":"Appendix B, Eq. (B2)"},{"comment":"The identification of the measured voltage profile with eigenstate localization is not quantitatively established. With a single-node current source at the resonant frequency, the steady-state response is governed by the Green's function L(ω_R)^{-1} (with appropriate losses), not directly by the eigenvectors of L. The manuscript relies on RMS values over manually chosen time windows and linear interpolation (Section IV B) and does not provide a direct comparison of the simulated voltage response with the eigenvector profile of the corresponding Laplacian. A calculation or simulation showing that the spatial decay of the voltage response matches the eigenstate localization length is needed to justify the central 'classical analog' claim.","section":"Section IV B and IV D"}],"minor_comments":[{"comment":"The text states that 'all parameters in this TB model are in the unit of t', but then quotes t=0.65, γ=0.35 in the figures; please clarify the actual parametrization and consistently state the energy scale for each figure.","section":"Section II"},{"comment":"The phrase 'reciprocal NH AA model' is an oxymoron; if S1 is open and the nonreciprocity is removed, the model is the Hermitian (or reciprocal) AA model. Please correct the terminology.","section":"Section IV C"},{"comment":"The statement that Eq. (6) applies only to systems without boundaries is confusing: the finite chain with open boundaries has well-defined eigenstates that encode the boundaries, and the earlier expansion is in that basis. Please rewrite this passage to state what boundary conditions are actually being imposed.","section":"Section III, after Eq. (6)"},{"comment":"There are several typographical and formatting issues, including inconsistent spacing in 'Aubry-Andr ´e', 'non-equivalent' (likely 'inequivalent') in the Introduction, and the table formatting in Table I. A careful proofread would improve readability.","section":"Throughout"},{"comment":"The open data and code repository is a strength, but the availability statement should specify whether the LTspice netlists and raw simulation outputs are included alongside the Python codes.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The parameter inconsistencies across Figs. 2, 5, and 6 are substantial enough that the authors should be asked to provide a full table of the parameters used in each panel and to recompute all quoted critical values from a single, clearly stated convention. The biorthogonal-basis issue in Section III and Appendix B is a technical error that affects the main dynamical claims and must be corrected before the paper can be considered for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about this paper. First, the genuinely useful piece is the circuit proposal: a topolectrical network with an interface and a complex-phase quasiperiodic potential, where the voltage profile can be steered between interface-localized skin states and excitation-node-localized Anderson states by tuning α. That is a concrete, potentially realizable design, and the LTspice simulations back the qualitative picture. Second, the paper's central quantitative claim—the precise threshold α_c = ln|max(t+γ,t−γ)/λ|—is quoted from a uniform-chain result and applied to a two-domain interface geometry without rederivation, and the paper's own figures don't apply it consistently. That is a load-bearing soft spot, not a cosmetic one.\n\nWhat the paper does well: the circuit Laplacian derivation in Appendix A is careful, the component values are tied to resonance conditions rather than fitted to localization data, and the authors are honest that only LTspice simulations are shown, not physical measurements. The qualitative competition between NHSE and AL, including the partial delocalization channel between the interface and the excitation node, is a reasonable extension of known work and is clearly presented. The citation pattern is fine; the key prior results (Longhi, Jiang et al., Li et al.) are properly credited.\n\nThe soft spots, in proportion: (1) The time-evolution expansion in Eq. (4) assumes the right eigenstates of a non-Hermitian operator form an orthonormal basis, which is not generally true; the paper never introduces left eigenvectors. This is a real technical flaw, but the main qualitative conclusions about NH jumps are standard and probably survive a corrected biorthogonal treatment. (2) The stress-test note is right: for the stated t=0.65, γ=0.35, λ=1 parameters, Eq. (2) gives α_c = ln(1/1) = 0, not the quoted 0.425 for Fig. 2. The paper also quotes 0.54 in Fig. 6 for λ=1.5, and 0.105 in Fig. 1(d) for λ=0.9. These numbers are mutually inconsistent. Either the figures use different implicit parameters or the formula is being misapplied; either way the 'precisely controlled' claim needs a direct numerical check against Eq. (2) for the interface geometry. (3) The all-important transfer of Eq. (2) from a uniform chain to an interface geometry is not justified by any non-Bloch boundary-condition calculation; since the skin states are themselves a boundary-condition effect, the threshold could shift with L0 and interface terms. This is a minor-to-moderate flaw for the qualitative story but a serious one for the quantitative control claim.\n\nWho is this for: condensed-matter experimentalists working on topolectrical circuits, and theorists who want a concrete classical analog of AL-NHSE competition. The paper deserves a serious referee, but the referee should push hard for a consistent parameter set and a derivation or numerical verification of α_c in the interface geometry. I would not cite it for the threshold formula; I would cite it for the circuit design if the numbers get fixed.","headline":"A plausible circuit-design paper whose central quantitative claim (the α_c threshold) is quoted from a different geometry and applied inconsistently; the qualitative story likely survives, the numbers need a check.","tokens_in":18536,"tokens_out":776,"would_cite":false,"duration_ms":9605,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The imaginary phase of a quasiperiodic potential is a single control knob that switches a non-Hermitian chain between skin-localized and Anderson-localized states, and the paper shows this switch as a tunable voltage profile in a…","keywords":["non-Hermitian Aubry-André model","Anderson localization","non-Hermitian skin effect","topolectrical circuits","quasiperiodic disorder","complex phase potential","non-reciprocal hopping","localization transition"],"falsifier":"Compute the inverse participation ratio of the eigenstates of Eq. (1) as a function of α and check whether the skin-to-Anderson transition occurs precisely at α_c = ln|max(t+γ,t−γ)/λ|; if the crossing shifts or broadens, the quantitative control claim fails. In the circuit, sweep α across this value in a 21-node realization and look for the voltage profile to jump from the interface node to the excitation node at the predicted α.","tokens_in":17493,"feed_emoji":"⚡","tokens_out":9604,"duration_ms":85208,"temperature":0.7,"pith_summary":"This paper is about a single knob that chooses between two ways a wavefunction can be trapped in one dimension: the skin effect, which drives states to a boundary or interface because hopping is non-reciprocal, and Anderson localization, which pins states to disorder-selected sites because of the quasiperiodic potential. The knob is the imaginary phase α of the Aubry-André potential, and the paper claims that crossing α_c = ln|max(t+γ,t−γ)/λ| switches the eigenstates from interface-localized skin states to Anderson-localized states. The same switch is then shown in a topolectrical circuit, a classical network whose Laplacian maps onto the tight-binding Hamiltonian, where the measured voltage profile localizes at the interface below α_c and near the excited node above it. If the claim holds, a classical room-temperature circuit can probe and control the competition between two quantum localization phenomena, and the same parameter also tunes the output amplitude and creates a movable spatial channel for a signal.","feed_headline":"One phase angle turns skin states into Anderson-localized states","feed_subtitle":"In a topolectrical circuit the same knob moves the voltage profile from the interface to the excitation node.","key_machinery":"The central object is the complex phase α inside the on-site quasiperiodic potential λ_k = 2λ cos(2πβk + iα), which acts as a tunable imaginary gauge field. It competes with the non-reciprocity γ through the critical line α_c = ln|max(t+γ,t−γ)/λ|, which the paper takes from a Lyapunov-exponent analysis of nonreciprocal quasiperiodic chains: below this value the skin-effect decay length beats the disorder, and above it disorder wins. In the circuit, α is encoded in node-dependent grounded capacitors and resistors, C[k] = −Re(λ_k)/ω_R and R[k] = [Im(λ_k)]^{-1}, and the Laplacian at the resonant frequency ω_R reproduces the tight-binding Hamiltonian; switches S, S1, and S2 select whether non-reciprocity, quasiperiodic disorder, or both are active, which is what makes the voltage profile switch from interface to excitation node.","core_discovery":"The paper's central claim is that the complex phase α of the quasiperiodic potential λ_k = 2λ cos(2πβk + iα) is a control parameter that decides the winner in a non-Hermitian Aubry-André chain with an interface. For α below the critical value α_c = ln|max(t+γ,t−γ)/λ|, the non-reciprocity γ dominates: the eigenstates and the time-evolved density accumulate at the interface, which is the skin effect. For α above α_c, Anderson localization dominates and the states become pinned near disorder-determined sites instead. The authors argue that the same competition appears in a topolectrical circuit whose Laplacian reproduces the Hamiltonian at resonance; the voltage profile is localized at the interface for α < α_c and shifts to the excitation node for α > α_c, with a partially delocalized channel between the two nodes in the crossover. They also report that the tight-binding time evolution under a delta excitation exhibits non-Hermitian jumps between Anderson-localized states for α > α_c, while the circuit driven by a steady sinusoidal current settles into stable localization near the excitation node rather than jumping.","pith_inferences":["An implication the authors leave implicit is that the same α-control should transfer to other classical wave platforms with imaginary gauge fields, such as photonic mesh lattices or acoustic lattices, where complex on-site potentials are available.","A direct transfer-matrix derivation of Eq. (2) for the two-domain interface geometry would confirm or correct the quantitative α_c used here; until such a derivation appears, the sharp switching point is an assumption carried over from uniform chains.","A testable extension is to drive the same circuit with a short current pulse instead of a steady sinusoid; if the classical analog remains faithful, the voltage profile should mimic the model's non-Hermitian jumps rather than settling smoothly.","The partially delocalized channel could be characterized quantitatively by measuring two-terminal impedance or transmitted power between the excitation and interface nodes, which would turn the proposed sensing and routing application into a concrete device metric."],"forward_implications":["Tuning α from below to above α_c switches eigenstate localization in the tight-binding model from the interface to Anderson-localized sites while keeping λ and γ fixed.","In the topolectrical circuit, the same tuning moves the measured voltage profile from the interface node to the excitation node, giving a classical observable for the quantum transition.","In the crossover region the voltage profile is partially delocalized between the excitation node and the interface, forming a spatial channel whose endpoints can be chosen by design.","Increasing α also reduces the output amplitude, so one parameter controls both where the voltage sits and how large it is.","The tight-binding time evolution shows non-Hermitian jumps between Anderson-localized states, whereas the sinusoidally driven circuit does not, so the circuit's dynamics are smoother than the model's."],"supporting_citations":[{"why":"Supplies the non-reciprocal Aubry-André model with a complex quasiperiodic potential and its α_c = ln|t/λ| transition in the γ = 0 case.","marker":"[33]"},{"why":"Provides the asymmetric transfer-matrix computation from which the paper takes the general critical value α_c = ln|max(t+γ,t−γ)/λ|.","marker":"[40]"},{"why":"Establishes the λ_c = max(t+γ,t−γ) condition for non-reciprocal quasiperiodic lattices that fixes the α = 0 endpoint of the criterion.","marker":"[53]"},{"why":"Supplies the analytic framework for one-frequency Schrödinger operators used to locate the localization transition behind Eq. (2).","marker":"[63]"},{"why":"Supplies the negative-impedance-converter construction used to realize non-reciprocal hopping in the topolectrical circuit.","marker":"[47]"},{"why":"Demonstrates interface skin states in topolectrical circuits, the experimental analogue the paper's voltage-profile measurements build on.","marker":"[48]"},{"why":"Introduces the general mapping from tight-binding Hamiltonians to circuit Laplacians that underlies constructing the topolectrical circuit.","marker":"[42]"}],"fun_headline_variants":["One phase angle toggles skin effect vs Anderson localization","Phase knob in non-Hermitian circuit swaps localization mechanism","Single phase parameter flips between two confinement regimes","Controlled phase shifts electron delocalization in Aubry-André circuit","Circuit experiment reveals phase-tuned localization transition"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The control claim rests on the assumption that the transition criterion α_c = ln|max(t+γ,t−γ)/λ|, derived for a uniform non-reciprocal quasiperiodic chain, remains exactly valid for the interface-terminated chain of Eq. (1), a step the paper does not rederive.","fun_headline_variants_meta":{"raw":{"variants":["One phase angle toggles skin effect vs Anderson localization","Phase knob in non-Hermitian circuit swaps localization mechanism","Single phase parameter flips between two confinement regimes","Controlled phase shifts electron delocalization in Aubry-André circuit","Circuit experiment reveals phase-tuned localization transition"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000242,"raw_usage":{"total_tokens":1603,"prompt_tokens":1099,"completion_tokens":504,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":715,"completion_tokens_details":{"reasoning_tokens":424}},"tokens_in":715,"tokens_out":504,"duration_ms":5582,"temperature":1.0,"reasoning_tokens":424,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:31:21.281233+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the inverse participation ratio of the eigenstates of Eq. (1) as a function of α and check whether the skin-to-Anderson transition occurs precisely at α_c = ln|max(t+γ,t−γ)/λ|; if the crossing shifts or broadens, the quantitative control claim fails. In the circuit, sweep α across this value in a 21-node realization and look for the voltage profile to jump from the interface node to the excitation node at the predicted α.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the asymmetric transfer-matrix computation from which the paper takes the general critical value α_c = ln|max(t+γ,t−γ)/λ|."},{"cited_title":"Jiang, L.-J","cited_arxiv_id":null,"evidence_quote":"Establishes the λ_c = max(t+γ,t−γ) condition for non-reciprocal quasiperiodic lattices that fixes the α = 0 endpoint of the criterion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrates interface skin states in topolectrical circuits, the experimental analogue the paper's voltage-profile measurements build on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the general mapping from tight-binding Hamiltonians to circuit Laplacians that underlies constructing the topolectrical circuit."}],"review_version":1}