{"id":"8aa35f68-87c2-4131-8abd-25836ca04db0","arxiv_id":"2608.02131","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"low","formal_verification":"none","parameter_count":4,"one_line_summary":"A single excitation on a finite biomolecular chain spreads asymmetrically unless it starts at the chain center, because the off-center starting point breaks the symmetry between left and right boundaries.","lead":"This paper analyzes how a single quantum excitation moves through a finite segment of a biomolecular chain, modeled as a chain of coupled sites with reflecting ends. It finds that the excitation's spreading pattern is asymmetric unless the excitation starts exactly at the segment's center, which matters for understanding energy transport in proteins.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Mean-field neglect of residual polaron–phonon interactions may invalidate the predicted asymmetry for the stated parameters.","rationale":"The paper's derivation is correct and the asymmetry is a generic property of finite tight-binding chains; I verified the partial-fraction step leading to Eq. (14) and the sign factors involving Chebyshev polynomials work out. The reader's weakest_assumption identifies the right soft spot: the mean-field truncation of H_rest. I add that for the specific parameters (S=0.3, B=0.1, θ=4), the small-polaron criterion S/B≫1 is marginal and the thermal narrowing is large, making the residual coupling potentially comparable to the effective hopping. This does not overturn the model's internal consistency, but it means the physical prediction of coherent asymmetric migration is not established for real biomolecular chains under the stated conditions; at least a quantitative estimate of the polaron scattering rate is needed. The paper's explicit caveat supports the reader's CONDITIONAL verdict, and I see no reason to change it. I also note that the 'ratchet-like' language is overstated, but that is a framing issue rather than a correctness issue.","tokens_in":14367,"tokens_out":16561,"duration_ms":366349,"concrete_test":"Perform a numerically converged simulation of the single-excitation Holstein model on a K=21 chain with S=0.3, B=0.1, θ=4 (e.g., using a trimmed phonon basis or ML-MCTDH), and compare the resulting p_n(τ) with Eq. (14). If including H_rest changes the asymmetry pattern or introduces decoherence on timescales ≲T_min≈700, the mean-field claim is not robust. A complementary check: compute the second-order polaron self-energy from H_rest and estimate Γ; if Γ ≳ B e^{-W}ω0, the coherent dynamics is overdamped.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is mathematically sound for the mean-field Hamiltonian (5), but its physical relevance hinges on the neglect of H_rest (Sec. II). For the parameters used in all figures (S=0.3, B=0.1, θ=4), this neglect is not quantitatively justified. The authors' stated small-polaron criterion S/B≫1 is only marginally met (S/B=3), and at θ=4 the narrowing factor is e^{-W}=e^{-S coth(1/2θ)}≈0.09, giving an effective hopping J_eff≈(B/2)e^{-W}ℏω0≈0.0045ℏω0. The residual couplings in H_rest scale as the bare J0 (≈(B/2)ℏω0) times the fluctuation of T±, which is O(1) at this thermal occupation; this is ~20 times larger than J_eff. Standard small-polaron theory predicts that at such high temperature the polaron mobility is incoherent and the coherent bandwidth is heavily damped. If H_rest is not negligible, the coherent superposition in Eq. (14) acquires a decoherence rate Γ comparable to or exceeding the mode spacings Ω_k−Ω_l, washing out the interference asymmetry and the fragmentation pattern that the paper reports. The paper's caveat that 'dissipative processes are not captured' is accurate but leaves the regime of validity unquantified, so the central claim is conditional on a parameter-safety check that is not supplied.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies single-excitation transport in a finite segment of a molecular chain modeled by the Holstein Hamiltonian with optical phonons. After a Lang-Firsov transformation and thermal mean-field averaging, the dynamics reduces to a K-site tight-binding chain with renormalized hopping J_eff = (B/2)e^{-S coth(1/2θ)} and reflecting boundaries (Eqs. (1)-(5)). The authors solve the polaron correlation function V_n(τ) via Laplace transform and Chebyshev polynomials, obtaining the closed-form superposition Eq. (14), and compute p_n(τ)=|V_n(τ)|^2. They report that for an off-center initial site, symmetrically placed sites have different temporal probability spectra, with exact symmetry only for a central initial site; the non-equidistant spectrum Ω_k causes dephasing and fragmentation of the probability peak. The model is connected to continuous-time quantum walks. Numerical results use S=0.3, B=0.1, θ=4.","tokens_in":14691,"tokens_out":22960,"duration_ms":162608,"significance":"The central formal result is a strength: Eq. (14) is an explicit, easily checkable exact solution of the effective tight-binding model, and the claimed symmetry properties follow directly from the weighting coefficients in Eq. (13) rather than from an assumed ansatz. The connection to CTQW is appropriate and gives the result a useful conceptual context. The paper is also explicit that dissipative processes are not captured. However, the physical claim that this describes coherent migration in real biomolecular segments at the stated biological parameters is not yet supported because the validity of the neglect of H_rest is not quantified. The paper's main value is therefore as an exact treatment of a clearly defined mean-field model; its applicability to the motivating biomolecular scenario remains conditional.","major_comments":[{"comment":"The central approximation is that the residual polaron-phonon coupling H_rest is weak and can be neglected, but no quantitative validity condition is given. For the parameter set used in all figures (S=0.3, B=0.1, θ=4), S/B=3 is only marginally above the stated S/B≫1 criterion. Moreover, W=S coth(1/(2θ))≈2.4, so e^{-W}≈0.09 and J_eff=(B/2)e^{-W}ℏω0≈0.0045ℏω0, while the residual couplings in H_rest scale as the bare J0=0.05ℏω0 times O(1) fluctuations of T± at the thermal occupation n_q≈3.5. A rough estimate gives H_rest/J_eff=O(e^W)≈10, suggesting that the polaron damping rate may be comparable to or larger than the mode spacings Ω_k−Ω_l that produce the interference asymmetry. The manuscript needs a quantitative estimate of the incoherent rate, or an explicit restricted regime, before the physical asymmetry claim for biomolecular segments can be accepted.","section":"Sec. II, Eqs. (5)-(6); Sec. III parameters"},{"comment":"The initial state and the observable are defined in the polaron representation: after the Lang-Firsov transformation, a†_n creates a dressed polaron, V_n(τ) is the polaron propagator, and p_n(τ) is the polaron occupation probability. The text, however, repeatedly refers to an 'injected excitation' and to 'the probability of finding the excitation'. A bare exciton injected at n0 would have a phonon coherent component in the polaron representation, so Eq. (9) would not describe it, and the bare-exciton occupation would differ from p_n(τ). Please state explicitly that the initial state is assumed to be a pre-formed polaron and justify the polaron-formation timescale, or compute the appropriate observable for the injection scenario.","section":"Sec. II, Eqs. (7)-(9)"}],"minor_comments":[{"comment":"The definition D_n(x)=U_n(2x) is inconsistent with the trigonometric representation D_n(x)=sin((n+1)φ)/sinφ, x=2cosφ, and with the zero locations x_k=2cos(kπ/(n+1)). The correct relation is D_n(x)=U_n(x/2). Please correct the definition or the substitution.","section":"Sec. II, Eqs. (11)-(12)"},{"comment":"The printed formula T_min∼2π/[B e^{S coth(1/2θ)}] is inconsistent with Ω_k=B e^{-S coth(1/2θ)}cosφ. The minimal period should be (2π/B)e^{S coth(1/2θ)}≈700, matching the numerical value given in the text; as printed the formula gives ≈5.6.","section":"Sec. III.B"},{"comment":"The derivation from Eq. (10) to Eq. (13) is sketched only by reference to Ref. 9. An appendix containing the partial-fraction identity and the relevant Chebyshev identities would make the paper self-contained.","section":"Sec. II, Eqs. (10)-(13)"},{"comment":"The caption contains typos ('ant the fifith SE') and 'Rectangled area' should be 'Rectangular area'. The definition of 'above/below' relative to the panel layout should also be clarified.","section":"Fig. 7 caption"}],"recommendation":"major_revision","confidential_remarks":"I concur with the conditional assessment. The mathematical core is sound, and the asymmetry result is an exact property of the effective tight-binding model. The main issue is the missing validity check for the neglect of H_rest: without a quantitative estimate of the polaron damping rate, the physical claims go beyond what the model supports. The initial-state/observable ambiguity should also be resolved. These are fixable within the manuscript's scope, so major revision is appropriate rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper gives a clean Chebyshev-polynomial solution for a mean-field Holstein polaron on a finite chain, and the derivation is internally consistent. The main advertised effect—left–right asymmetry from an off-center initial site in a homogeneous chain with reflecting boundaries—is real within the model, but it is not new: it is a generic property of any finite tight-binding chain with an arbitrary initial state, and the authors' own CTQW references cover it. The abstract and conclusion frame it as a discovery, which overstates the case.\n\nWhat the paper does well: the Laplace-transform route to the time-domain correlation functions is careful, the connection to CTQW is legitimate, and the treatment is self-contained. The authors also explicitly state the neglect of residual polaron–phonon scattering, which is not hidden.\n\nThe soft spots are in proportion to how much they matter. First, the novelty claim is inflated; the asymmetry is elementary, and the 'ratchet-like' and 'preferred direction' language risks misleading even with the caveat that there is no net current. Second, and more seriously, the parameter regime used in all figures may not support the mean-field truncation. For S=0.3, B=0.1, θ=4, the narrowing factor is e^{-S coth(1/2θ)}≈0.09, so J_eff≈0.0045 ℏω0. The residual terms in H_rest couple J0 (≈0.05 ℏω0) to fluctuations of T±−⟨T±⟩, which are order one at this thermal occupation. That puts the decoherence scale an order of magnitude above the effective hopping, exactly the regime where small-polaron theory predicts incoherent, damped motion. The authors' caveat that dissipative processes are not captured is accurate, but they never quantify when the neglect is justified. This is a real gap, not a quibble: the interference pattern and fragmentation the paper reports would be washed out if the residual interaction is included.\n\nAll that said, I would not desk-reject it. The mathematical solution is a useful technical contribution, and a serious referee could push for a validity condition on the mean-field averaging (e.g., a bound on the decoherence rate relative to J_eff) and for toned-down language about novelty and 'ratcheting.' If the authors can state clearly the regime where their model applies, the paper has value as an exact treatment of coherent dynamics in finite segments. I recommend sending it to peer review.","headline":"Solid math, oversold novelty; the coherent regime may not hold for the paper's own parameters.","tokens_in":15196,"tokens_out":4290,"would_cite":false,"duration_ms":35982,"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":"A single excitation injected off-center into a finite molecular segment propagates with a left-right asymmetric probability distribution, proving that initial-state geometry alone can break transport symmetry.","keywords":["single excitation migration","nonadiabatic polaron","finite molecular segment","asymmetric probability distribution","continuous-time quantum walk","Chebyshev polynomials","Holstein model","coherent dephasing"],"falsifier":"Numerically diagonalize the full Holstein Hamiltonian including H_rest for a 21-site segment (S=0.3, B=0.1, θ=4) with an off-center initial site, and compare the resulting probability distribution p_n(t) with Eqs. (14)-(15). If the left-right imbalance deviates appreciably at times shorter than the dephasing time, or if a centered initial site develops asymmetry, the mean-field neglect is falsified. Alternatively, in an experimental realization of a finite tight-binding chain with phonon-like coupling, measure p_{n0+d}(t)/p_{n0-d}(t): it should differ from 1 for off-center injection and equal","tokens_in":14235,"feed_emoji":"🧬","tokens_out":5998,"duration_ms":55604,"temperature":0.7,"pith_summary":"This paper studies the coherent migration of a single vibron excitation injected into a finite segment of a biomolecular chain, where the excitation couples to thermal vibrations and forms a self-trapped nonadiabatic polaron. The authors solve the mean-field Holstein model exactly, obtaining a closed-form expression for the time-dependent probability of finding the excitation at every site of the segment. Their central claim is that the probability distribution is generically asymmetric with respect to the initially excited site, even though the chain itself is homogeneous, and that this asymmetry comes solely from the off-center placement of the initial excitation. Only when the excitation starts at the exact center does the distribution become symmetric. They also show that non-equidistant mode frequencies prevent full revivals and cause the initially localized probability peak to fragment into a dominant maximum with secondary maxima.","feed_headline":"Off-center injection makes a molecular chain's transport asymmetric","feed_subtitle":"Exactly solved model shows a single polaron spreads unevenly left-right unless it starts at the center.","key_machinery":"The key object is the exact analytical solution for the correlation function V_n(τ), built from modified Chebyshev polynomials of the second kind. After a Lang-Firsov transformation, a mean-field average over renormalized phonons, and a Laplace transform in time, each correlation function becomes a coherent superposition of K discrete modes with frequencies Ω_k = B e^{-S coth(1/2θ)} cos(kπ/(K+1)), weighted by Chebyshev products Ψ_{n,0}^{{M,N}}(φ_k). These weights carry the entire dependence on the initial position: M and N count the sites to the left and right of the injection point, and the asymmetric product sin[(M+n+1)φ_k] sin[(M+1)φ_k] on the right side versus its left-side counterpart i","core_discovery":"The central discovery is a symmetry-breaking effect in a closed, undriven, homogeneous quantum chain. For a finite segment with reflecting boundaries and a single initial excitation, the probability of finding the excitation at nodes on opposite sides of the injection point is generally different. The asymmetry is not introduced by the Hamiltonian—the transfer integrals are identical—but by the initial condition: the injection site's position relative to the two boundaries. In the exact analytical solution, this enters through Chebyshev weighting factors Ψ_{n,0}^{{M,N}} that differ between the left and right branches of the solution. The exception is the centered initial site, where left and","pith_inferences":["Because the asymmetry arises purely from the initial condition relative to boundaries, the prediction should also hold for any coherent tight-binding simulator—for example, arrays of coupled waveguides or cold atoms in optical lattices—provided the effective Hamiltonian has reflecting boundaries and negligible dissipation; measuring the imbalance would directly test the mean-field approximation.","The model's neglect of H_rest means the long-time dephasing is an interference effect, not true environmental decoherence; in a real molecular chain, polaron-phonon scattering would likely wash out the fine interference pattern after a dissipative timescale, so the predicted fragmented maxima may only be observable at short to intermediate times.","The same Chebyshev decomposition could be extended to absorbing or semi-infinite boundary conditions to compute first-passage and transfer probabilities to an active site, turning the asymmetry into a design principle for directing excitation flow in finite molecular wires."],"forward_implications":["Off-center initial excitation in any finite, homogeneous, reflecting-boundary tight-binding chain produces a left-right asymmetric detection probability; only center injection stays symmetric.","Temperature enters the dynamics by renormalizing the hopping amplitude via the factor e^{-S coth(1/2θ)}, rather than by introducing decoherence, so the coherent quantum-walk description holds with a temperature-tuned hopping.","The non-equidistant mode spectrum means the system never fully revives; only partial rephasing occurs, so a localized excitation fragments into one dominant peak plus several smaller ones.","The residence time of the excitation near a given site is approximately T_min ∼ 2π/(B e^{S coth(1/2θ)}), which grows exponentially with coupling S and inverse temperature 1/θ.","The formal mapping to continuous-time quantum walks provides a direct route to use quantum-walk theory for polaron transport in biomolecular chains, with temperature-dependent hopping bridging idealized models and molecular environments."],"fun_headline_variants":["Injection site breaks left-right symmetry in molecular chain","Off-center start skews quantum transport in finite chain","Asymmetric spread traced to injection position in biomolecular chain","Finite molecular chain shows asymmetric spread from off-center excitation","Polaron spread asymmetry due to initial injection location"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The residual interaction between the dressed polaron and the renormalized phonons (H_rest) is neglected, so the excitation evolves coherently under the mean-field Hamiltonian; if that interaction is not weak, the predicted asymmetry and dephasing would be washed out by genuine decoherence.","fun_headline_variants_meta":{"raw":{"variants":["Injection site breaks left-right symmetry in molecular chain","Off-center start skews quantum transport in finite chain","Asymmetric spread traced to injection position in biomolecular chain","Finite molecular chain shows asymmetric spread from off-center excitation","Polaron spread asymmetry due to initial injection location"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00047,"raw_usage":{"total_tokens":2179,"prompt_tokens":748,"completion_tokens":1431,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":492,"completion_tokens_details":{"reasoning_tokens":1363}},"tokens_in":492,"tokens_out":1431,"duration_ms":78248,"temperature":1.0,"reasoning_tokens":1363,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T14:33:17.866289+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Numerically diagonalize the full Holstein Hamiltonian including H_rest for a 21-site segment (S=0.3, B=0.1, θ=4) with an off-center initial site, and compare the resulting probability distribution p_n(t) with Eqs. (14)-(15). If the left-right imbalance deviates appreciably at times shorter than the dephasing time, or if a centered initial site develops asymmetry, the mean-field neglect is falsified. Alternatively, in an experimental realization of a finite tight-binding chain with phonon-like coupling, measure p_{n0+d}(t)/p_{n0-d}(t): it should differ from 1 for off-center injection and equal","supporting_citations":[],"review_version":1}