{"id":"a1fa4076-fa56-4e54-a44a-49639c0e066b","arxiv_id":"2608.08080","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A biorthogonal response participation number separates coherent interference from spectral mixing in a dissipative Hatano-Nelson photonic chain and reveals a finite-size disorder crossover before the skin center shifts.","lead":"This paper develops a way to analyze light transmission through a small dissipative photonic chain with directionally biased hopping, separating coherent interference from the simple sum of modal weights. The proposed participation measure could help experiments tell apart ordinary line broadening from skin-effect localization using only a few input-output ports.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed ordering that N_eff responds to disorder before the response-weighted center moves is under-specified: Eq. (36) leaves the averaging window and broadening eta undefined, and Fig. 5 uses only five disorder realizations at L=26, so the crossover may be an artifact.","rationale":"The paper's core formalism, based on the biorthogonal Green function, coherent versus modal-weight decomposition, and the participation entropy, is standard and internally consistent. The analytic checks that are present, such as Eqs. (5)-(10) and the continuum estimate in Eq. (39), are correct, and the authors are suitably cautious that Fig. 4 curves are representative realizations and that W_cross is not a thermodynamic boundary. The load-bearing step is instead the finite-size crossover comparison in Fig. 5. That comparison is not reproducible from the text because <N_eff> in Eq. (36) depends on an unspecified frequency window and broadening eta, and the (g,W) map is built from five disorder realizations at L=26. The proposed diagnostic, that N_eff responds before the spatial center moves, is precisely a comparison of two functionals of the same p_nu(omega) distribution; unless the averaging convention is fixed, the ordering is convention-dependent. A systematic eta/window/realization sweep can settle whether the claim is robust. Because the concern is about numerical representativeness rather than an algebraic error, the appropriate verdict remains conditional: the claim is plausible and worth stating as a conjecture, but it should be accompanied by the missing numerical parameters and ensemble statistics.","tokens_in":10641,"tokens_out":7386,"duration_ms":79728,"concrete_test":"Recompute Fig. 5(a,b) at L=26, t=1 with the same boundary-to-boundary kernels, for eta/t in {0.005, 0.02, 0.05, 0.1} and for a window chosen as [min_nu Re Omega_nu - 0.5, max_nu Re Omega_nu + 0.5] and a second window of width equal to 20 times the mean level spacing, averaging over at least 100 disorder realizations per (g,W) point. Define W_N(g) as the smallest W at which <N_eff> drops by 10% from its W=0 value at fixed g, and W_X(g) as the smallest W at which <X_R_resp>/L drops by 10% from its clean boundary value. The central claim survives only if W_N(g) < W_X(g) for all eta and both windows; if any window or broadening reverses the ordering, the crossover is an artifact of the averaging convention.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that frequency-averaged N_eff drops with disorder before the response-weighted skin center X_R_resp departs from the boundary. That claim is a statement about a specific frequency average, but the average is never fully defined. Eq. (36) defines <N_eff> as an integral over [omega_1, omega_2], yet the text never gives omega_1, omega_2, or the numerical broadening eta used in Eq. (19); Fig. 5 refers only to a \"fixed finite frequency window\". This is not a cosmetic omission: N_eff(omega) is controlled by the Lorentzian tails in Eq. (19). For small eta, p_nu(omega) collapses onto the nearest pole and N_eff(omega) approaches 1 over most of the window; for large eta, all modes mix and N_eff is inflated. A fixed window also excludes modes whose resonance frequencies disorder shifts outside the window, so the observed decrease in <N_eff> can reflect spectral escape rather than modal dephasing. The comparison with <X_R_resp> is equally window-dependent, because Eq. (27) uses the same p_nu(omega). The empirical line W_cross about 1.35 in Fig. 5(a) is drawn from a (g,W) map with only five disorder realizations per point and no error bars; only Fig. 5(d) quantifies fluctuations, and there only for one g value with fifteen realizations. Thus the claimed ordering is not yet established as a robust diagnostic property; it is a numerical observation tied to unstated averaging choices.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies the linear response of a finite dissipative Hatano–Nelson photonic chain. It resolves the port-to-port response into a phase-coherent intensity R_coh (Eq. 20) and an incoherent modal-weight contribution R_mix (Eq. 21), and defines a mode-participation entropy S_resp and N_eff from the normalized modal weights (Eqs. 23–25). It also defines a response-weighted skin center X_R_resp (Eq. 27) and compares the frequency-domain diagnostics with a continuous-time quantum walk. Numerical results show that loss increases, periodic-boundary spectral winding increases, and disorder decreases the frequency-averaged participation number; the (g,W) map with disorder-ensemble averages is used to claim a finite-size crossover in which N_eff responds to disorder before the response-weighted center moves away from the skin boundary. The algebraic derivation is mostly straightforward, and the paper is explicit that the crossover is a finite-size diagnostic rather than a thermodynamic transition.","tokens_in":10979,"tokens_out":4913,"duration_ms":53532,"significance":"If the claimed ordering is robust, the participation number is a genuinely useful few-port diagnostic that complements spatial skin measures. The paper's strengths are the clean algebraic separation of coherent and modal-weight channels, the use of analytic length scales (Eqs. 8 and 28) as interpretive references, the independent time-domain check in Fig. 3, and the consistent caveats that the results are finite-size diagnostics. The central numerical claim, however, is currently tied to unstated frequency-window and broadening parameters and to very small disorder ensembles, so the crossover ordering is not yet quantitatively established as a robust diagnostic property.","major_comments":[{"comment":"The central crossover claim is stated in terms of the frequency-averaged participation number \\langle N_eff\\rangle defined in Eq. (36) over a window [\\omega_1,\\omega_2], and the modal weights in Eq. (19) depend on a numerical broadening \\eta, but the paper never specifies \\omega_1, \\omega_2, or \\eta. The text and figure captions only refer to a \"fixed finite frequency window.\" This is load-bearing because N_eff(\\omega) is controlled by the Lorentzian weights p_\\nu(\\omega): for small \\eta the response collapses onto the nearest pole, while for large \\eta all modes mix, and a window that excludes disorder-shifted resonances records spectral escape rather than modal dephasing. The authors should state the exact window, broadening, and frequency-grid parameters, and demonstrate that the crossover ordering in Fig. 5(a,b) is robust to reasonable variations of these parameters.","section":"Sec. VI, Eq. (36) and Fig. 5"},{"comment":"The empirical crossover scale W_cross \\simeq 1.35 and the claimed ordering that N_eff responds before X_R_resp is displaced are based on a (g,W) heat map computed with only five disorder realizations per grid point and no error bars. Fig. 5(d) shows that the disorder-averaged N_eff carries nontrivial standard errors even with fifteen realizations, and that check is performed at only one value of g. With five realizations, the horizontal bands and the position of W_cross in Fig. 5(a) cannot be regarded as established. The authors should provide ensemble-averaged maps or at least ensemble-averaged W sweeps with standard errors at several g values, including points near the claimed crossover, before concluding that the ordering is a robust finite-size property.","section":"Fig. 5(a,b,d)"}],"minor_comments":[{"comment":"The word \"enhances\" is misspelled as \"genhances\" in the caption of Fig. 4(b).","section":"Fig. 4 caption"},{"comment":"The window operators D_L, D_C, and D_R introduced in Eq. (29) are not used in any of the figures; the authors should either use them in the numerical analysis or remove them to avoid an unused definition.","section":"Eq. (29) and Sec. VI"},{"comment":"The time unit in Fig. 3 is stated as J^{-1}, whereas the Hamiltonian in Eq. (3) is parametrized by the hopping amplitude t and the text says all frequencies are measured in units of t; the notation should be unified.","section":"Fig. 3 caption"},{"comment":"The numerical sections should specify the chain lengths, probe profiles |a\\rangle and |b\\rangle, and window sizes used for Figs. 2, 4, and 5; the current text gives L=28 for sweeps and L=44 for frequency-resolved response, but not the corresponding probe and window details.","section":"Sec. VI numerical parameters"},{"comment":"The Kubo-type expression in Eq. (40) introduces occupation weights p_i, but these weights play no role in the rest of the paper; the passage could be shortened or clarified to avoid suggesting a thermodynamic interpretation that is explicitly disavowed elsewhere.","section":"Eq. (40)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is honest about its limitations and the algebraic framework is sound, but the missing numerical parameters and the very small disorder ensembles are exactly the points needed to support the central crossover claim. These are fixable within the scope of a revision, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper's real contribution is turning the biorthogonal Green function of a finite dissipative Hatano-Nelson chain into a response-weighted participation number N_eff, and then arguing that N_eff is a more sensitive finite-size probe of disorder than the spatial skin center. The decomposition into coherent and modal-weight channels is standard algebra, yes, but the packaging - modal residues with biorthogonal skin bias, entropy-based mode counting, and a (g,W) crossover map - is a reasonable and potentially useful diagnostic for few-port photonic experiments. The authors are also honest: they repeatedly label the crossover as finite-size, not thermodynamic, and they distinguish the asymptotic localization length from what their small chains actually show. The time-domain quantum walk is a nice independent check that non-reciprocity produces edge accumulation. The soft spots are real and mostly numerical. Eq. (36) defines the frequency-averaged N_eff but never gives the window [omega1, omega2] or the broadening eta used in Eq. (19). That matters because N_eff(omega) is controlled by Lorentzian tails; different eta or a window that excludes disorder-shifted resonances can change whether N_eff drops at all. The heat map in Fig. 5(a) uses only five realizations per grid point, and Fig. 4 uses single realizations for the sweeps. No code or data are provided. The stress-test note is correct: without these details, the claimed ordering - N_eff responds before the spatial center moves - is an observation tied to unstated choices, not a robust diagnostic property. That said, the concern is about reproducibility, not the underlying logic. The math is internally consistent, and the one ensemble-averaged panel (Fig. 5(d)) does show the monotonic decrease with disorder at g=0.22. This is an addressable paper, not a broken one. Who gets value from it: experimentalists working with non-Hermitian photonic lattices and few port measurements could use N_eff as a simple indicator; theorists may find the response-weighted center a clean way to talk about skin persistence. It is not a landmark, but it deserves serious referee time - precisely because a referee can demand the missing parameters, more disorder realizations, and open code. My recommendation: send it to peer review with a clear request for major revision on the numerical reproducibility, not a desk rejection.","headline":"A clean but conventional response-participation diagnostic for non-Hermitian lattices, undermined by under-specified numerics and tiny disorder ensembles; the core idea is worth refereeing, not rejecting.","tokens_in":743,"tokens_out":796,"would_cite":false,"duration_ms":31568,"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":"In a dissipative photonic lattice, the response participation number drops with disorder before the spatial skin center moves.","keywords":["non-Hermitian photonics","Hatano–Nelson model","non-Hermitian skin effect","biorthogonal Green function","response participation number","spectral mixing","disorder localization","photonic quantum walk"],"falsifier":"Recompute the $(g,W)$ map at a chain length well beyond the localization length (for example $L=200$) with many disorder realizations and with the frequency window and $\\eta$ in Eq. (36) varied over a decade; if the disorder strength at which $\\langle N_{\\mathrm{eff}}\\rangle$ begins to drop no longer lies below the disorder strength at which $\\langle X^R_{\\mathrm{resp}}\\rangle/L$ leaves the skin boundary, the claimed ordering is a finite-size artifact rather than a diagnostic property.","tokens_in":10411,"feed_emoji":"🔦","tokens_out":12563,"duration_ms":121279,"temperature":0.7,"pith_summary":"At stake is whether a small set of port-to-port optical response measurements can distinguish two effects that both accompany non-Hermitian transport in a finite photonic lattice: dissipative spectral mixing, which spreads the signal over many modes, and skin localization, which pins it to one boundary. The paper argues yes, using the biorthogonal Green function to split the response into a phase-coherent intensity and an incoherent modal-weight sum, and defining a participation number $N_{\\mathrm{eff}}$ that counts how many complex modes actually carry the measured signal. Numerically, loss increases $N_{\\mathrm{eff}}$, periodic-boundary non-reciprocal winding increases it, and onsite disorder decreases it. In a $(g,W)$ parameter map averaged over disorder, $N_{\\mathrm{eff}}$ drops with disorder while the response-weighted spatial center stays near the skin boundary, a finite-size crossover the paper proposes as a diagnostic ordering. If correct, this gives a practical spectral probe for disorder-induced dephasing in photonic experiments before the spatial mode profile visibly shifts.","feed_headline":"Participation number senses disorder before skin center moves","feed_subtitle":"A port-to-port response statistic drops with disorder while the skin center stays pinned, a finite-size crossover.","key_machinery":"The motor of the argument is the biorthogonal Green function spectral decomposition $G^R(\\omega)=\\sum_\\nu |R_\\nu\\rangle\\langle L_\\nu|/(\\omega-\\Omega_\\nu)$. Each modal amplitude $A_\\nu^{ab}(\\omega)=\\langle a|R_\\nu\\rangle\\langle L_\\nu|b\\rangle/(\\omega+i\\eta-\\Omega_\\nu)$ carries the skin bias through the boundary overlaps, and the paper compares the coherent response $R_{\\mathrm{coh}}=|\\sum_\\nu A_\\nu|^2$ with the modal-weight response $R_{\\mathrm{mix}}=\\sum_\\nu |A_\\nu|^2$. From $R_{\\mathrm{mix}}$ it defines the probability $p_\\nu$ over modes, the Shannon entropy $S_{\\mathrm{resp}}=-\\sum p_\\nu \\ln p_\\nu$, and the participation number $N_{\\mathrm{eff}}=\\exp(S_{\\mathrm{resp}})$, whose frequency average over a window is the diagnostic $\\langle N_{\\mathrm{eff}}\\rangle$. The spatial counterpart is the response-weighted center $\\langle X^R_{\\mathrm{resp}}\\rangle=\\sum p_\\nu X^R_\\nu$, where $X^R_\\nu$ is the right-eigenmode center of mass. The separation of $R_{\\mathrm{coh}}$ and $R_{\\mathrm{mix}}$ is what isolates interference among non-Hermitian modal residues, and the pair $(\\langle N_{\\mathrm{eff}}\\rangle, \\langle X^R_{\\mathrm{resp}}\\rangle)$ is what makes the disorder-before-skin-shift ordering visible.","core_discovery":"The paper's central claim is that in a finite dissipative Hatano–Nelson photonic chain, the response participation number $N_{\\mathrm{eff}}(\\omega)=\\exp[S_{\\mathrm{resp}}(\\omega)]$, built from the biorthogonal modal weights $p_\\nu(\\omega)\\propto |\\langle a|R_\\nu\\rangle\\langle L_\\nu|b\\rangle/(\\omega+i\\eta-\\Omega_\\nu)|^2$, is a more sensitive finite-size probe of disorder-induced modal dephasing than the response-weighted skin center $\\langle X^R_{\\mathrm{resp}}\\rangle/L$. Loss broadens resonances and increases $N_{\\mathrm{eff}}$; periodic boundary conditions expose the complex spectral loop and increase modal participation; onsite disorder localizes the modes and suppresses $N_{\\mathrm{eff}}$. In the $(g,W)$ map at $L=26$, the suppression of $N_{\\mathrm{eff}}$ begins before the spatial center leaves the skin boundary, with an empirical crossover scale $W_{\\mathrm{cross}}\\simeq 1.35$ that the paper identifies as a finite-size effect rather than a thermodynamic transition. The time-domain quantum walk independently shows drift and right-edge accumulation of a localized excitation, consistent with the skin profile of the right eigenvectors.","pith_inferences":["Inference: In longer chains the crossover scale should move to smaller $W$, because the one-dimensional localization estimate $\\xi_A\\sim 96t^2/W^2$ makes the comparison with $L$ length-dependent; this is a testable scaling prediction the paper does not make.","Inference: The $R_{\\mathrm{coh}}$–$R_{\\mathrm{mix}}$ separation suggests a two-measurement experimental protocol: a total transmitted intensity carries the coherent part, while a mode-resolved spectrum carries the modal weights, and comparing them would directly test whether interference among biorthogonal residues is observable.","Inference: If the ordering is generic, $N_{\\mathrm{eff}}$ could serve as an early-warning diagnostic for decoherence in non-reciprocal photonic devices, detecting disorder-induced dephasing before the output mode profile moves; the five-realization ensemble at $L=26$ is only a first step toward that claim."],"forward_implications":["If the ordering holds, $N_{\\mathrm{eff}}$ can be extracted from a small number of port-to-port spectra and used as a disorder sensor in finite non-Hermitian photonic lattices, without needing full eigenvector tomography.","Loss and non-reciprocity produce opposite tendencies in the same diagnostic: adding linewidth raises $\\langle N_{\\mathrm{eff}}\\rangle$, while adding onsite disorder lowers it.","Periodic-boundary non-reciprocity increases modal participation through the complex spectral winding, so $N_{\\mathrm{eff}}$ is sensitive to boundary conditions as well as to disorder.","The time-domain result gives an independent, experimentally accessible signature: an edge-accumulated wave packet with $P_{\\mathrm{skin}}(\\tau)$ approaching unity is direct evidence of the skin effect.","The crossover at $W_{\\mathrm{cross}}\\simeq 1.35$ is not a phase transition; the paper claims only that response participation changes before the spatial center changes at these finite sizes."],"supporting_citations":[{"why":"Defines the Hatano–Nelson model with asymmetric hopping that the paper's photonic chain is built on.","marker":"[1]"},{"why":"Establishes the non-Hermitian skin effect under open boundaries and the point-gap spectral winding under periodic boundaries.","marker":"[9]"},{"why":"Provides non-Bloch band theory, used to relate the periodic spectral loop to open-boundary skin accumulation.","marker":"[12]"},{"why":"Supplies the standard coherent-versus-incoherent response decomposition on which $R_{\\mathrm{coh}}$ and $R_{\\mathrm{mix}}$ are modeled.","marker":"[14]"},{"why":"Supports reading the $R_{\\mathrm{coh}}$–$R_{\\mathrm{mix}}$ difference as interference among modal amplitudes, as in mesoscopic speckle and coherent backscattering.","marker":"[15]"},{"why":"Cautions that non-Hermitian critical scaling can involve a skin-depth scale, which the paper cites to avoid claiming a thermodynamic transition.","marker":"[17]"},{"why":"Shows biased dissipative couplings can generate directional motion and boundary accumulation in a many-body lattice, motivating the effective non-reciprocity parameter $g$.","marker":"[18]"},{"why":"Shows correlated gain and loss channels can produce effective non-reciprocal transport, the dissipative route to $g$.","marker":"[19]"}],"fun_headline_variants":["Participation number feels disorder before skin center moves","Loss broadens modes, disorder shrinks: crossover in N_eff first","Modal spread drops while skin edge stays pinned in finite lattices","N_eff senses disorder earlier than the skin center shift","Finite-size probe: disorder dephases modes before skin drift"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The crossover ordering rests on the unstated frequency window and numerical broadening $\\eta$ used to average $N_{\\mathrm{eff}}$, together with only five disorder realizations per $(g,W)$ point at $L=26$; if those choices are unrepresentative, the finding that $N_{\\mathrm{eff}}$ drops before the spatial center moves could be a numerical artifact rather than a stable diagnostic property.","fun_headline_variants_meta":{"raw":{"variants":["Participation number feels disorder before skin center moves","Loss broadens modes, disorder shrinks: crossover in N_eff first","Modal spread drops while skin edge stays pinned in finite lattices","N_eff senses disorder earlier than the skin center shift","Finite-size probe: disorder dephases modes before skin drift"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000231,"raw_usage":{"total_tokens":1514,"prompt_tokens":1000,"completion_tokens":514,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":616,"completion_tokens_details":{"reasoning_tokens":428}},"tokens_in":616,"tokens_out":514,"duration_ms":6174,"temperature":1.0,"reasoning_tokens":428,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T00:27:05.257329+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the $(g,W)$ map at a chain length well beyond the localization length (for example $L=200$) with many disorder realizations and with the frequency window and $\\eta$ in Eq. (36) varied over a decade; if the disorder strength at which $\\langle N_{\\mathrm{eff}}\\rangle$ begins to drop no longer lies below the disorder strength at which $\\langle X^R_{\\mathrm{resp}}\\rangle/L$ leaves the skin boundary, the claimed ordering is a finite-size artifact rather than a diagnostic property.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Hatano–Nelson model with asymmetric hopping that the paper's photonic chain is built on."},{"cited_title":"”Edge states and topological invariants of non-Hermitian systems.” Physical review letters 121.8 (2018): 086803","cited_arxiv_id":null,"evidence_quote":"Establishes the non-Hermitian skin effect under open boundaries and the point-gap spectral winding under periodic boundaries."},{"cited_title":"”Non-Bloch band theory of non-Hermitian sys- tems.” Physical review letters 123.6 (2019): 066404","cited_arxiv_id":null,"evidence_quote":"Provides non-Bloch band theory, used to relate the periodic spectral loop to open-boundary skin accumulation."},{"cited_title":"”Random-matrix theory of quantum transport.” Reviews of modern physics 69.3 (1997): 731","cited_arxiv_id":null,"evidence_quote":"Supplies the standard coherent-versus-incoherent response decomposition on which $R_{\\mathrm{coh}}$ and $R_{\\mathrm{mix}}$ are modeled."},{"cited_title":"Mesoscopic physics of electrons and photons","cited_arxiv_id":null,"evidence_quote":"Supports reading the $R_{\\mathrm{coh}}$–$R_{\\mathrm{mix}}$ difference as interference among modal amplitudes, as in mesoscopic speckle and coherent backscattering."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows biased dissipative couplings can generate directional motion and boundary accumulation in a many-body lattice, motivating the effective non-reciprocity parameter $g$."},{"cited_title":"”Many-body non-Hermitian skin effect with exact steady states in the dissipative quantum link model.” Physical review letters 135.26 (2025): 260401","cited_arxiv_id":null,"evidence_quote":"Shows correlated gain and loss channels can produce effective non-reciprocal transport, the dissipative route to $g$."}],"review_version":1}