{"id":"20dd90c0-b829-4d7a-8fe8-5efc4ea4c8b6","arxiv_id":"2607.25508","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In a 1D driven-dissipative Bose-Hubbard model, spectral linewidths show KPZ z=3/2 scaling in the semiclassical regime, while tensor-network simulations reveal a change in the slowest Liouvillian excitation near the mean-field threshold.","lead":"This paper studies a one-dimensional chain of driven, lossy bosons. It shows that the spectral line width reveals universal Kardar-Parisi-Zhang scaling in the weakly interacting regime, and that the slowest relaxation mode changes character in the strongly interacting regime.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The spectral-function collapse in Fig. 6 uses a fitted amplitude exponent α≈1.89 instead of the KPZ prediction 7/2, so the evidence for z=3/2 may depend on an unconstrained rescaling.","rationale":"The reader's verdict is CONDITIONAL, with the weakest assumption identified as the narrow parameter window for KPZ scaling. That is a valid concern, but the prefactor mismatch in the spectral collapse is arguably more directly load-bearing: it affects the central evidence for the z=3/2 linewidth claim itself. The reader did mention the fitted amplitude exponent as a weakness, but not as the primary weakest assumption. My stress test identifies this as the single most important issue because it undermines the quantitative link between the numerical spectral function and the KPZ universality class. If the amplitude exponent is not fixed by theory, the collapse in Fig. 6 could be an artifact of overfitting, and the paper's central new assertion would be substantially weakened. The proposed test—using the predicted amplitude exponent or a joint fit with error analysis—would settle whether the mismatch is a benign finite-size correction or a breakdown of the KPZ mapping. Since the reader already recommended CONDITIONAL and this concern can be addressed by additional analysis, the verdict remains CONDITIONAL/UNCHANGED rather than moving to ACCEPT or REJECT.","tokens_in":17891,"tokens_out":6140,"duration_ms":63786,"concrete_test":"Re-analyze the semi-classical spectral data behind Fig. 6 by fixing the amplitude rescaling to the KPZ prediction: multiply A(k, ω−ω_k) by k^{(2χ+d+z)} = k^{7/2} and evaluate the collapse quality across k (e.g., the variance of the rescaled curves in the scaling variable) for z=3/2. If the collapse fails, perform a joint fit of (z, α) with bootstrap error bars over noise realizations and test whether α is consistent with 7/2. Alternatively, compute the spectral function from the phase-only KPZ approximation using the known Prähofer–Spohn scaling function and compare both the linewidth exponent and the amplitude prefactor with the GPE results.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the spectral linewidth exhibits KPZ scaling Γ(k) ~ k^z with z=3/2 is primarily supported by the collapse in Fig. 6 and the width fits in Fig. 5. The collapse, however, uses a fitted amplitude exponent α≈1.89, whereas the KPZ scaling form quoted in Eq. (26) predicts the amplitude prefactor |k|^{-(2χ+d+z)} = |k|^{-7/2} in d=1. The paper's own footnote acknowledges this mismatch and attributes it to a finite scaling window. This is load-bearing: if the amplitude does not scale as predicted, the collapse may be achieved simply because α is a free parameter that compensates the missing scaling, making the collapse in (ω−ω_k)/k^z a weaker test of KPZ universality than claimed. The linewidth exponent in Fig. 5 is also extracted from Lorentzian fits without error bars or a demonstrated collapse with the theoretically required amplitude, so the central claim that the spectral function directly reveals z=3/2 is not yet conclusive. A quantitative demonstration that the data are consistent with the full KPZ scaling form—including amplitude—is needed before accepting the z=3/2 identification.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the one-dimensional driven-dissipative Bose-Hubbard model with incoherent pump, one- and two-body losses, and a nonlocal loss term. It combines stochastic semiclassical simulations of the driven-dissipative Gross-Pitaevskii equation, tensor-network calculations of the quantum NESS and real-time dynamics, and one-loop Keldysh perturbation theory. The main claims are: (i) in the weakly interacting, large-filling semiclassical regime, the spectral-function linewidth shows KPZ scaling, Γ(k) ~ k^z with z = 3/2, instead of the Bogoliubov prediction z = 2; (ii) in the strongly interacting, low-filling quantum regime, the Liouvillian gap does not close at the mean-field transition, but the slowest relaxation mode changes identity at a level crossing; and (iii) a one-loop calculation captures the low-density decay rate of the retarded Green's function.","tokens_in":18182,"tokens_out":3230,"duration_ms":36655,"significance":"If established, the spectral-function KPZ collapse would provide a new, experimentally accessible diagnostic of KPZ universality in driven-dissipative bosonic systems and would extend the earlier work on correlation functions. The tensor-network framework for Lindblad steady states and dynamical two-point functions is a useful methodological contribution, especially the use of a positive-semidefinite L†L minimization and block-sparse symmetry exploitation. The study is also valuable for delineating the narrow parameter window in which semiclassical KPZ behavior survives and for showing that the quantum model at the same microscopic parameters sits in a different density regime. However, the central KPZ spectral-linewidth claim is currently supported by a collapse with a fitted amplitude exponent that is inconsistent with the quoted scaling form, and the one-loop comparison is partly a consistency check rather than an independent prediction. These issues affect the strength of the main conclusions.","major_comments":[{"comment":"The central evidence for z = 3/2 is the collapse of spectral lines in Fig. 6 using the scaling variable (ω−ω_k)/|k|^z. However, Eq. (26) has a fixed amplitude prefactor |k|^{-(2χ+d+z)} = |k|^{-7/2} in d = 1, while the collapse multiplies by |k|^{1.89} and footnote 1 explicitly states that the amplitude prefactor does not match pure KPZ. Since α is fitted, the collapse in the frequency variable alone is a weaker test of KPZ universality and could in principle be achieved with other values of z and α. The authors should either demonstrate the full scaling form including the amplitude, or provide a quantitative finite-window/finite-size justification for the mismatch. In addition, the linewidth exponents in Fig. 5 are extracted from Lorentzian fits without error bars or fitting ranges; error bars are needed to assess whether the k^{3/2} dependence is distinguishable from k^2 and k^{3/2} ove","section":"§III C, Eq. (26), Fig. 6, footnote 1"},{"comment":"The agreement between the one-loop result and the tensor-network data in Fig. 9 is presented as a successful prediction, but the lattice-spacing parameter ã is determined from the numerically fitted exponential decay of G^R(k=0,t), as stated in the text: 'From the numerically fitted exponential decay of G^R(k=0,t), we determine the lattice spacing ã'. Using the same data to fix the conversion parameter and then comparing with the same data makes the comparison at least partially circular. The authors should present this as a one-parameter consistency check, not as an ab initio prediction, and should quantify the sensitivity to the fitting procedure and to the small system size (L=3, Ns=5). Without an independent determination of ã, Fig. 9 does not validate the one-loop calculation.","section":"§IV C, Fig. 9"},{"comment":"The abstract and introduction state the spectral-function KPZ result for the driven-dissipative Bose-Hubbard model, but the evidence is obtained in a semiclassical regime with density ρ0 ≈ 15.2 a^{-1} and U = 10^{-3}. The manuscript itself shows that the KPZ scaling is lost when the density decreases by 25% or when L < 2^8 (Fig. 2), and Appendix A demonstrates that the fully quantum model at the same microscopic parameters has mean filling ⟨n⟩ ≈ 0.2 and lies in a different density regime. Thus the KPZ spectral-linewidth claim is not established for the quantum lattice model, only for the semiclassical large-filling limit. The authors should state this limitation explicitly in the abstract and conclusions, and should avoid wording that implies the result applies to the full model Hamiltonian (2).","section":"§III B, Fig. 2, Appendix A"},{"comment":"The mapping from |g^(1)| to the phase-phase correlator assumes small density fluctuations (Eq. (19)), and Fig. 1 shows that this holds only in a limited time window. The authors should state the range of times and momenta over which Eq. (19) is used in the spectral-function analysis, and explain how violations of this assumption affect the extracted linewidth exponent. This is important because the spectral function is computed from the full complex field, not from the phase alone, so the KPZ collapse could be contaminated by density fluctuations outside the quoted window.","section":"§III A, Eq. (19)"}],"minor_comments":[{"comment":"The fitted decay points are shown without statistical uncertainties; adding error bars would also let the reader judge the deviation from the k^{3/2} and k^2 lines at small k.","section":"Fig. 5"},{"comment":"The statement that the linewidth depends weakly on wavevector is based on two fitting methods (Lorentzian and HWHM), but the scatter between these methods appears larger than the claimed k-dependence. Please quantify this uncertainty.","section":"§IV B, Fig. 8"},{"comment":"The y-axis label 'S_k(ω) k' is ambiguous; the rescaling by |k|^{1.89} is only described in the caption. Please make the plotted quantity explicit in the axis label.","section":"Fig. 6"},{"comment":"The level-crossing analysis is based on exact diagonalization for L=4, Ns=3. It would be helpful to state the dependence of the crossing position and overlap curves on L and Ns, since the conclusion that the gap does not close is limited to these sizes.","section":"§IV E, Fig. 12/13"},{"comment":"The notation Δt in Eq. (20) and in figure axes is used both as a time step and as the unit of frequency; please distinguish the numerical time step from the physical time unit τ.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about the Fig. 6 amplitude exponent is valid and is acknowledged in the manuscript's own footnote. The paper would be considerably stronger if the authors either provide the full KPZ scaling collapse including the amplitude or reframe the claim as evidence for z=3/2 with the amplitude mismatch as a quantitative finite-window effect. The one-loop comparison in Sec. IV C should be reframed as a consistency check. The methodological contribution and the careful parameter-window study are solid and worth publishing after these issues are addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a real paper, not a packaging exercise. It has two genuinely new results—a measurable spectral-linewidth signature of KPZ dynamics (Γ∼k^{3/2} instead of k^2) and a one-loop Keldysh linewidth formula with two-body losses—and it ships a working tensor-network workflow for NESS and dynamics. It deserves a serious referee. But the central scaling claim is not as clean as the text implies. The KPZ collapse in Fig. 6 uses a fitted amplitude exponent α≈1.89; the full KPZ form predicts |k|^{-7/2}. Footnote 1 acknowledges the mismatch, and the collapse is therefore partly a test of the exponent z only, with the amplitude free to absorb whatever prefactor is needed. That doesn't invalidate the z=3/2 linewidth claim—Fig. 5 shows a distinct power law in the width—but it does mean the spectral-function collapse is a weaker test than presented, and the paper should say so.\n\nWhat else is good: The paper is honest about the narrow parameter window for KPZ (Fig. 2 shows the scaling fades at L=2^7 and when density drops 25%). The tensor-network machinery, including the U(1) block-sparse structure for the Liouvillian, is a contribution in itself. The strong-interaction regime results—no closing of the Liouvillian gap, a level crossing where the slowest mode changes from a uniform density fluctuation to a staggered annihilation mode—are new and thought-provoking, though \"localized to extended\" in the abstract is not what the body actually shows (the overlaps are with a staggered operator, not a spatial localization analysis). Minor.\n\nThe soft spots, in order: (1) Fig. 9's \"prediction\" fits the lattice rescaling ã from the same numerical decay it claims to reproduce. That's circular; the authors should fix ã independently or at least flag the fit. (2) The extracted exponents β≈0.31, χ≈0.48 have no error bars, and the linewidth fits in Fig. 5 are Lorentzian fits without uncertainties. (3) The collapse amplitude issue above. None of these is obviously fatal, but together they mean the paper's strongest claim—that the spectral function directly reveals z=3/2—is plausible, not proven.\n\nWho should read it: anyone working on driven-dissipative condensates, KPZ universality in 1D polariton systems, or tensor network methods for open bosons. It's not a field-reorganizing paper (everything important relies on known KPZ mapping), but it opens a concrete experimental probe.\n\nRecommendation: Send it to peer review. The authors should be pushed to add error bars, show the full KPZ scaling form including the amplitude, and resolve the circular fit. But the work is serious and worth refereeing.","headline":"Genuinely new results and a usable tensor-network workflow; the KPZ linewidth claim is plausible but the spectral collapse is a weaker test than presented because the amplitude exponent is fitted, and the one-loop comparison has a circular fit.","tokens_in":18722,"tokens_out":2573,"would_cite":true,"duration_ms":28841,"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":"This paper claims that in a one-dimensional driven-dissipative Bose-Hubbard model, the spectral-function linewidth in the weakly interacting, large-filling regime follows Kardar-Parisi-Zhang scaling, growing as k^z with z=3/2 rather than th","keywords":["driven-dissipative Bose-Hubbard","Kardar-Parisi-Zhang universality","spectral function","linewidth scaling","Liouvillian gap","tensor networks","Gross-Pitaevskii equation","Keldysh formalism"],"falsifier":"Measure or simulate the spectral function of a one-dimensional driven-dissipative condensate at the parameters of Eq. (20) with large filling and system size L≥2^8: if the extracted linewidth follows Γ(k) ~ k^2 over a range of k instead of collapsing onto Γ(k) ~ k^{3/2}, the central claim fails. Equivalently, in numerics, reducing the density by 25% at fixed other parameters should destroy the k^{3/2} collapse; observing k^{3/2} even at low density would contradict the claimed parameter window.","tokens_in":17746,"feed_emoji":"⚛️","tokens_out":4974,"duration_ms":50206,"temperature":0.7,"pith_summary":"The paper argues that a one-dimensional driven-dissipative Bose-Hubbard model with incoherent pump and one- and two-body losses can be understood through its two-point space-time correlations in two complementary regimes. In the weakly interacting, large-filling regime, phase fluctuations are governed by KPZ universality, and the spectral linewidth scales as k^{3/2} instead of the Bogoliubov k^2, offering a directly measurable signature. In the strongly interacting, low-filling regime, a tensor-network calculation shows that the mean-field threshold is not accompanied by a closing Liouvillian gap; instead, the slowest excitation undergoes a level crossing, changing from a uniform density mode to a staggered single-particle mode. These results connect universal dynamical scaling to experimentally accessible spectral observables and clarify what survives of the mean-field transition in one dimension.","feed_headline":"A 3/2 exponent replaces 2 in the linewidth of driven 1D bosons","feed_subtitle":"Spectral lines of a 1D driven Bose gas confirm Kardar–Parisi–Zhang scaling, giving an observable probe of the exponent.","key_machinery":"The argument is carried by the mapping from the driven-dissipative Gross-Pitaevskii equation to the KPZ equation for the condensate phase, valid when density fluctuations are negligible so that |g^{(1)}(x,t)| ≈ exp(−C_{θθ}(x,t)/2). This relation turns the KPZ phase-growth scaling into a prediction for the spectral linewidth: Γ(k) ~ k^z with z=3/2. In the quantum regime, the key tool is a matrix-product-operator representation of the Liouvillian, with DMRG-based steady-state search and TEBD/TDVP time evolution to obtain retarded Green's functions, complemented by a one-loop Keldysh self-energy calculation for the weak-interaction linewidth.","core_discovery":"The central claim is that in the semi-classical regime the momentum dependence of the spectral linewidth is governed by KPZ scaling, Γ(k) ~ k^z with z=3/2, in contrast to the Bogoliubov prediction z=2. The authors establish this by simulating the stochastic driven-dissipative Gross-Pitaevskii equation at parameters where phase fluctuations dominate, verifying KPZ exponents (β≈1/3, χ≈1/2) and Tracy-Widom statistics, and showing that spectral lines at different momenta collapse when rescaled by k^{3/2}. A second, independent claim is that in the fully quantum model the Liouvillian gap does not close when crossing the mean-field transition point; instead, the longest-lived excitation changes it","pith_inferences":["If the spectral-linewidth collapse is confirmed in polariton experiments, it would provide a simpler probe of KPZ universality than full space-time correlation measurements, which are harder to access.","The level-crossing mechanism in the quantum regime may be a finite-size precursor of the higher-dimensional dissipative transition, suggesting that in one dimension the transition is replaced by a crossover in excitation structure that could persist at larger U/J.","Because the KPZ linewidth is lost when density fluctuations grow, tuning the two-body loss rate may offer a control knob to switch between Bogoliubov and KPZ behavior in the same device.","The strong discrepancy between semi-classical and quantum steady-state densities for the same microscopic parameters implies that reaching KPZ scaling in a fully quantum simulation would require much larger fillings and system sizes than currently accessible."],"forward_implications":["The spectral function provides a direct, experimentally accessible observable to detect KPZ scaling in one-dimensional driven-dissipative condensates, such as exciton-polariton systems.","Bogoliubov linear-response theory fails to capture the long-time phase dynamics; at low momenta the nonlinear KPZ term dominates and changes the linewidth exponent from 2 to 3/2.","In one dimension, the mean-field pump-loss threshold does not correspond to a genuine dissipative phase transition: the steady state varies smoothly, but the slowest relaxation mode changes its nature at a level crossing.","One-loop Keldysh perturbation theory quantitatively captures the temporal decay of the retarded Green's function in the weak-interaction, low-filling quantum regime, including the linear-in-γ₂ₗ contribution from two-body losses.","KPZ scaling in the linewidth is fragile: it requires sufficiently large systems (L ≥ 2^8) and sufficiently high density (within 25% of the KPZ parameter set), and is lost when vortices or solitons appear."],"fun_headline_variants":["KPZ exponent 3/2 found in linewidth of driven 1D bosons","Driven 1D bosons prove KPZ scaling: z=3/2 replaces 2","Linewidth of 1D driven bosons shows KPZ 3/2, not 2","Spectral linewidth of driven Bose gas verifies KPZ 3/2"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The KPZ linewidth claim rests on the assumption that density fluctuations are negligible, so that the first-order correlation function is set entirely by phase fluctuations (Eq. 19), and that the chosen parameters (Eq. 20) place the system inside the KPZ basin, away from vortex and soliton sectors; the paper itself shows the scaling fades when the density drops by 25% or the system size falls below L=2^8.","fun_headline_variants_meta":{"raw":{"variants":["KPZ exponent 3/2 found in linewidth of driven 1D bosons","Driven 1D bosons prove KPZ scaling: z=3/2 replaces 2","Linewidth of 1D driven bosons shows KPZ 3/2, not 2","Spectral linewidth of driven Bose gas verifies KPZ 3/2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000247,"raw_usage":{"total_tokens":1360,"prompt_tokens":706,"completion_tokens":654,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":450,"completion_tokens_details":{"reasoning_tokens":557}},"tokens_in":450,"tokens_out":654,"duration_ms":6919,"temperature":1.0,"reasoning_tokens":557,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T02:12:45.450099+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure or simulate the spectral function of a one-dimensional driven-dissipative condensate at the parameters of Eq. (20) with large filling and system size L≥2^8: if the extracted linewidth follows Γ(k) ~ k^2 over a range of k instead of collapsing onto Γ(k) ~ k^{3/2}, the central claim fails. Equivalently, in numerics, reducing the density by 25% at fixed other parameters should destroy the k^{3/2} collapse; observing k^{3/2} even at low density would contradict the claimed parameter window.","supporting_citations":[],"review_version":1}