{"id":"6a40921d-e2d5-48e3-b8ab-24011c27a856","arxiv_id":"2508.09253","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Heat transport between weakly coupled quantum systems is fully controlled by the system's two-point function, and the DSSYK model interpolates between random-matrix and conformal transport regimes.","lead":"This paper computes heat flow between two quantum systems placed at different temperatures, using exactly solvable toy models and the Double-Scaled SYK model. It shows that these models reproduce the full transport story, from transient current peaks to a steady-state current that obeys Fourier's law.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"RMT-DSSYK matching in the low-temperature NESS regime is only shown after normalizing the RMT curve at t=50; the predicted prefactor from eq (4.26) is not tested for the heat current, so the quantitative interpolation claim is not yet established.","rationale":"The reader's verdict of CONDITIONAL is appropriate. The paper's analytic structure is coherent: eq (2.9) is a standard second-order weak-coupling result, the toy models are internally consistent, and the DSSYK derivations in Secs. 4.2-4.3 are plausible. The weakest point for the central claim is the quantitative match between DSSYK and the RMT toy model in the low-temperature NESS regime. Fig. 22b normalizes the RMT heat-current curve at t=50, which removes the overall prefactor that controls the NESS value and conductivity. If the full un-normalized two-point function matches, the concern is resolved and the paper's low-T claims stand; if only the shape matches, the claim should be weakened from 'captures' to 'captures up to an undetermined normalization'. This is addressable with the existing q-series machinery and does not require new physics. I therefore recommend no change to the CONDITIONAL verdict, pending this check. The reader's weakest_assumption partly overlaps with this concern, but emphasizes the conformal-regime 20% discrepancy; I find the RMT normalization issue more directly load-bearing for the central quantitative claim.","tokens_in":31810,"tokens_out":13352,"duration_ms":159961,"concrete_test":"Compute the exact DSSYK two-point function from eqs (4.15) and (B.1) at q=0.4, β=100, for t∈[50,500], and compare it in absolute value with the RMT expression eq (4.25) using the parameter identifications (4.26), with no fitting or normalization freedom. If the ratio differs from 1 by more than 10% over this range, the claimed low-temperature RMT reduction fails quantitatively, and the NESS current prediction is not established. The same test should be applied directly to E_-(t), i.e., reproduce Fig. 22b without rescaling.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the RMT toy model quantitatively captures DSSYK heat transport in the low-temperature/long-time regime. The parameter map (4.26) fixes not only the time dependence but also the overall normalization of the RMT two-point function, and hence the NESS value and conductivity. However, the only direct heat-current comparison in this regime, Fig. 22b, is made by normalizing the RMT result to agree with DSSYK at t=50. This removes exactly the information needed to test the predicted prefactor. The match therefore demonstrates only that the decay shape is roughly right, not that the RMT model reproduces the transport magnitude. The paper's claim that the two-point functions agree 'exactly' in Sec. 4.2.2 is supported by figs. 17-18 for β=1, but no un-normalized low-temperature comparison is shown for the heat current. Because the low-T conductivity statements and the interpolation claim depend on this prefactor, the quantitative content of the central claim is not adequately verified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies heat transport between two quantum systems initialized at different temperatures and weakly coupled at t=0. The central technical result is Eq. (2.9), which expresses the leading-order heat current entirely in terms of the two-point functions of the coupling operators of the two isolated systems. Using this formula, the authors analyze three toy models: an RMT-like model with a semicircle density of states and energy-dependent matrix elements (Sec. 3.1), a conformal model with sinh^{-2m} two-point functions (Sec. 3.2), and a Gaussian model (Sec. 3.3). For each, they characterize the transient peak, the approach to the NESS, and the thermal conductivity. They then turn to DSSYK, reviewing its exact two-point function and showing that in suitable limits it reduces to the RMT and conformal toy models (Secs. 4.2.1–4.2.2). The paper closes with numerical comparisons of heat currents and conductivities, and argues that DSSYK interpolates between the conformal and RMT behaviors, with a crossover governed by the scrambling scale.","tokens_in":32116,"tokens_out":6231,"duration_ms":72474,"significance":"If the central claim is correct, the paper provides a useful analytic laboratory for quantum heat transport beyond quasiparticle descriptions: the heat current is computed exactly (to O(epsilon^2)) from two-point data, and the DSSYK model gives a microscopic realization of a UV-conformal to IR-RMT crossover in a transport setting. The manuscript contains a substantial amount of explicit analytic work: closed-form two-point functions, asymptotic expansions, and parameter maps between models. It also verifies general constraints such as the positivity bound on F_kappa from Ref. [6]. The toy models are simple and potentially reusable for other transport questions. However, the quantitative content of the claimed DSSYK-to-toy-model interpolation is not fully demonstrated, as detailed below.","major_comments":[{"comment":"The central low-temperature claim that DSSYK reduces to the RMT/Cold-RMT model is not quantitatively established by the heat-current data shown. In Fig. 22(b), the RMT result is explicitly normalized to agree with the DSSYK result at t=50. This normalization removes exactly the overall prefactor in the RMT two-point function—the quantity fixed by the parameter map Eq. (4.26)—so the comparison tests only the decay shape, not the transport magnitude. The two-point-function checks in Figs. 17–18 are for beta=1, not in the low-temperature regime. The conductivity comparison in Fig. 23 is a potentially relevant unnormalized test, but the paper does not state clearly whether that comparison is unnormalized or quantify its accuracy over the claimed range. Please provide an unnormalized low-temperature comparison of the heat current (or an explicit, quantified conductivity comparison) using the","section":"§4.3.2, Fig. 22(b), Eq. (4.26)"},{"comment":"The conformal-regime reduction of DSSYK relies on the saddle-point approximation for the partition function and the two-point function, Eqs. (C.2)–(C.8). Fig. 25 shows that the resulting analytical two-point function agrees with numerical DSSYK data only to about 20% at lambda=0.05, and the text itself says the agreement is only “qualitatively well.” Since Eqs. (4.28)–(4.30) use the conformal toy-model form with phi0 determined by the saddle, the finite-lambda conductivity predictions inherit this error. The lambda→0 statement is an asymptotic one, but the paper should state the expected size of subleading corrections and explain how they affect the claimed quantitative agreement in Fig. 23, particularly in the crossover region.","section":"§4.2.1, Appendix C, Fig. 25"},{"comment":"The independence of the toy models is somewhat overstated. The RMT matrix-element ansatz Eq. (3.2) is motivated by the form that appears in the DSSYK edge expansion (see footnote 10), and the Gaussian model is exactly the q→1 limit of DSSYK (Sec. 4.1.1). The parameter map Eq. (4.26) is then derived by matching the same edge data. The agreement between DSSYK and the toy models in those limits is therefore partly by construction. This does not invalidate the toy models as useful parametrizations, but the abstract’s phrase “seemingly distinct toy models” should be tempered, and it would strengthen the paper to test at least one prediction in a regime not used to fix the map.","section":"§3.1, Eq. (3.2); §4.1.1; §4.2.2"}],"minor_comments":[{"comment":"The section title “for t < (1 − q)^{−3/2}” appears inconsistent with the text and figures, which study large times t ≫ (1 − q)^{−3/2}; the inequality sign is probably inverted.","section":"§4.3.2, heading"},{"comment":"In §4.1.1 the text says the Gaussian matrix elements are “identical” to Eq. (3.20) “with γ = 1,” but the parameter γ is not defined in the Gaussian model of §3.3; the symbol used there is q~.","section":"§3.3 and §4.1.1"},{"comment":"The normalization of the DSSYK trace is Tr(I)=1, while the RMT model uses an arbitrary normalization N_r. After matching in Eq. (4.26), the relation between the two conventions is not explicitly discussed; please state the normalization assumptions in the parameter map.","section":"§4.2.2, Eq. (4.25)"},{"comment":"The text uses “exact results” for expressions that are often asymptotic (e.g., Eq. (3.6), Eq. (3.16), Eq. (4.25)). Consider using “closed-form” or “exact in the stated limits” to avoid overstatement.","section":"Abstract and §1"},{"comment":"Several heat-current plots are normalized so that the peak height equals 1. This hides the absolute magnitude, which is important for the quantitative comparisons. Please state in the captions whether and how each curve is normalized.","section":"Figures 4, 9, 13"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope for JHEP and contains much useful analytic material. The main issue is that the headline interpolation claim is not yet backed by an unnormalized quantitative comparison in the low-temperature NESS regime; this is fixable with additional numerics and more careful wording. I would not recommend rejection, because the existing evidence and the asymptotic arguments make the claim plausible, but the current normalization in Fig. 22(b) obscures exactly the prefactor that needs testing."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this about arXiv:2508.09253: it is a genuine exact-results paper, not a repackaging. The authors compute, to leading order in the weak coupling, the full transient and NESS heat current for three toy models (RMT-like, conformal, Gaussian) and then show that DSSYK reduces to each of these in distinct regimes. The transport formula itself, eq (2.9), is from prior work, but the systematic analytics—peak times and heights, power-law vs exponential vs Gaussian approach to NESS, and closed-form conductivities—are new and done carefully.\n\nThe DSSYK part is the main event. They derive a large-time two-point function, eq (4.25), whose form matches RMT, and give an explicit parameter map, eq (4.26), from DSSYK to the RMT model. The analytic derivation is solid; the q-series/Bessel asymptotics in the appendices look right. The conformal regime result, eq (C.8), also matches the expected Schwarzian/SYK behavior, and the comparison to [35] (sigma ~ sqrt(T)) is a nice check.\n\nWhere are the soft spots? The numerical verification is weaker than the analytic claims. Figure 22b, the low-temperature heat-current comparison, normalizes the RMT curve to agree with DSSYK at t=50; that removes exactly the prefactor test. The stress-test note is fair here: the transport-level prefactor from eq (4.26) is not directly checked at low T. It is indirectly supported because the same two-point function amplitude is verified at beta=1 in figures 17-18, but an un-normalized low-temperature comparison would be much more convincing. Likewise, the conformal two-point function agrees to only about 20% (fig 25), so the conductivity formulas (4.29)-(4.30) could shift somewhat. No code or data is provided, which makes these checks hard to reproduce. Also, the RMT toy model is partly chosen because DSSYK has a similar edge expansion; the matching in that limit is thus somewhat by construction. The authors acknowledge this, and it doesn't undermine the independent value of the toy-model results.\n\nOverall, I think the paper holds up. The central interpolation claim is analytically credible and the numerics are suggestive, if not exhaustive. The flaws are addressable and not fatal. I'd bring this to a reading group on SYK transport, and I'd cite it if I worked on that. It deserves a serious referee; my recommendation is that an editor should send it out, with the request that the authors add un-normalized low-temperature comparisons and, ideally, share the code used for the numerics.","headline":"A solid exact-transport paper whose DSSYK interpolation picture is analytically credible but only partially tested numerically.","tokens_in":32567,"tokens_out":4410,"would_cite":true,"duration_ms":44467,"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":"Weakly coupled quantum systems exchange heat at a rate set entirely by the two-point function of the coupling operator, and the double-scaled SYK model interpolates between random-matrix and conformal transport.","keywords":["heat transport","non-equilibrium steady state","DSSYK model","Sachdev-Ye-Kitaev model","random matrix theory","conformal field theory","two-point function","thermal conductivity"],"falsifier":"Compute the full heat current from the exact $q$-series two-point function at finite $\\lambda$ and compare with the conformal-regime conductivity formula (eq. 4.28) at $\\beta\\sqrt{\\lambda} \\sim 1$; a deviation much larger than the roughly 20% seen in the two-point function comparison would falsify the claim that two-point data alone determine transport in this regime.","tokens_in":31704,"feed_emoji":"🔥","tokens_out":4427,"duration_ms":46307,"temperature":0.7,"pith_summary":"This paper tries to establish that heat transport between two weakly coupled quantum systems is exactly computable at leading order in the coupling from the two-point function of the coupling operator alone. It derives a closed formula for the heat current and works it out in three toy models—random-matrix, conformal, and Gaussian—each showing a transient peak, an approach to steady state, and a non-equilibrium steady state obeying Fourier's law. It then shows that the double-scaled SYK model realizes all three toy models in different regimes, interpolating from conformal behavior at high temperature to random-matrix behavior at low temperature, with the crossover at inverse temperature $\\beta \\sim \\lambda^{-3/2}$. If correct, the paper gives a parameter-free way to compute transient peaks and thermal conductivities in a strongly interacting solvable model.","feed_headline":"One correlator fixes heat flow between quantum systems","feed_subtitle":"At leading coupling, transient peaks, steady-state currents, and conductivity all follow from a single two-point function.","key_machinery":"The two-point function $G(t)$ of the operator that couples the hot and cold systems, in particular its frequency-space form satisfying the KMS relation. In the DSSYK model, the exact two-point function is expressed as a sum over chord diagrams, resummed into a $q$-series of Bessel functions; its large-time asymptotics give random-matrix-like power laws, while its $\\lambda\\to 0$ saddle-point evaluation gives the conformal two-point function with Gamma-function quasinormal poles.","core_discovery":"The central claim is that, to leading order in the weak inter-system coupling $\\epsilon$, the heat current is determined entirely by the Wightman two-point functions of the coupling operators: $\\dot E_c(t) = -\\epsilon^2\\,\\mathrm{Im}\\{G_c(t)G_h(t)\\} + \\epsilon^2\\,\\mathrm{Im}\\int_0^t d\\tilde t\\,\\big(G_c(\\tilde t)\\dot G_h(\\tilde t)-\\dot G_c(\\tilde t)G_h(\\tilde t)\\big)$. Consequently, for any system whose two-point function is known—random-matrix, conformal, Gaussian, or DSSYK—the transient peak time and height, the rate of approach to the non-equilibrium steady state, and the steady-state thermal conductivity all follow from that single function. The DSSYK model then serves as a microscopic int","pith_inferences":["If the two-point-function-only formula is general, it suggests a broad dictionary between the analytic structure of $G(t)$ and transport universality classes: poles give exponential approach, branch cuts give power laws, and Gaussian forms give ultra-fast approach.","The conformal-to-random-matrix interpolation seen in DSSYK could be a template for other disordered fermion models, including chains of DSSYK systems, where a similar temperature-driven crossover should appear.","The conductivity result for unequal operator dimensions (eq. 3.18) may extend naturally to charge transport if the coupling operator is replaced by a conserved charge current, giving a solvable route to electrical conductivity in the same toy-model family.","The paper leaves open higher-order corrections in $\\epsilon$; if those corrections are controlled, the same chord-diagram machinery could compute leading anharmonic corrections to heat transport."],"forward_implications":["The transient current peak, the time at which it occurs, and the approach to the steady state are all computable from two-point data alone, without solving the full nonequilibrium dynamics.","Different two-point decay profiles produce distinct signatures: random-matrix models approach the steady state as a power law $t^{-5}$, conformal models exponentially, and Gaussian models with a Gaussian falloff.","The DSSYK model interpolates between conformal and random-matrix transport as temperature varies, giving a concrete microscopic realization of an RG-like flow between the two toy-model descriptions.","The explicit conductivity formulas in the conformal regime, $\\sigma \\sim \\lambda^{-2m}\\beta^{1-4m}$ at low temperature and $\\sigma \\sim \\sqrt{\\lambda}\\,\\beta^2$ at high temperature, reproduce earlier coupled-SYK results with now-controlled prefactors.","The integrated energy-flux bound $F_\\kappa \\ge 0$ for $\\kappa \\ge 2/\\beta_h$ is verified in every model considered."],"supporting_citations":[{"why":"Supplies the typical transient-peak, NESS, thermalization picture and the integrated-energy-flux bound that the paper verifies in each model.","marker":"[6]"},{"why":"Earlier coupled-SYK transport study whose weak-coupling $\\sqrt{T}$ and strong-coupling $T$ conductivity scalings are reproduced in the conformal regime.","marker":"[35]"},{"why":"Chord-diagram technique giving the exact DSSYK partition function and two-point function as resummed sums over chord states.","marker":"[39]"},{"why":"Provides the $q$-series expansions of the partition function and $Z_k(\\beta)$ used for numerical evaluation and long-time asymptotics.","marker":"[40]"},{"why":"Defines the double-scaled SYK limit and its triple-scaling low-energy Schwarzian regime, used to map the toy-model regimes.","marker":"[38]"},{"why":"Supplies the conformal-regime two-point function of DSSYK that matches the conformal toy model.","marker":"[58]"},{"why":"Establishes the low-energy conformal two-point function and Schwarzian physics of SYK that motivate the conformal toy model.","marker":"[19]"},{"why":"Continuous $q$-Hermite polynomial orthogonality used to derive structural properties of $Z_k(\\beta)$ and the two-point function.","marker":"[56]"}],"fun_headline_variants":["Heat flow from one two-point function","Single correlator sets quantum heat current","Two-point function governs heat transport","Heat current follows from one Green's function","Leading order heat current from single correlator"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The central premise is that the saddle-point and large-time asymptotic approximations used to evaluate the DSSYK two-point function in the conformal and random-matrix regimes control the transport observables; if subleading corrections are larger than the numerics indicate, the quantitative conductivity predictions could shift.","fun_headline_variants_meta":{"raw":{"variants":["Heat flow from one two-point function","Single correlator sets quantum heat current","Two-point function governs heat transport","Heat current follows from one Green's function","Leading order heat current from single correlator"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000162,"raw_usage":{"total_tokens":1082,"prompt_tokens":757,"completion_tokens":325,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":501,"completion_tokens_details":{"reasoning_tokens":263}},"tokens_in":501,"tokens_out":325,"duration_ms":3636,"temperature":1.0,"reasoning_tokens":263,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T21:11:28.013455+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the full heat current from the exact $q$-series two-point function at finite $\\lambda$ and compare with the conformal-regime conductivity formula (eq. 4.28) at $\\beta\\sqrt{\\lambda} \\sim 1$; a deviation much larger than the roughly 20% seen in the two-point function comparison would falsify the claim that two-point data alone determine transport in this regime.","supporting_citations":[{"cited_title":"Universal constraints on energy flow and syk thermalization,","cited_arxiv_id":null,"evidence_quote":"Supplies the typical transient-peak, NESS, thermalization picture and the integrated-energy-flux bound that the paper verifies in each model."},{"cited_title":"Energy transport across two interacting quantum baths without quasiparticles,","cited_arxiv_id":null,"evidence_quote":"Earlier coupled-SYK transport study whose weak-coupling $\\sqrt{T}$ and strong-coupling $T$ conductivity scalings are reproduced in the conformal regime."},{"cited_title":"Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction,","cited_arxiv_id":null,"evidence_quote":"Chord-diagram technique giving the exact DSSYK partition function and two-point function as resummed sums over chord states."},{"cited_title":"Towards a full solution of the large N double-scaled SYK model,","cited_arxiv_id":null,"evidence_quote":"Provides the $q$-series expansions of the partition function and $Z_k(\\beta)$ used for numerical evaluation and long-time asymptotics."},{"cited_title":"Black Holes and Random Matrices,","cited_arxiv_id":null,"evidence_quote":"Defines the double-scaled SYK limit and its triple-scaling low-energy Schwarzian regime, used to map the toy-model regimes."},{"cited_title":"Large p SYK from chord diagrams,","cited_arxiv_id":null,"evidence_quote":"Supplies the conformal-regime two-point function of DSSYK that matches the conformal toy model."},{"cited_title":"Remarks on the sachdev-ye-kitaev model,","cited_arxiv_id":null,"evidence_quote":"Establishes the low-energy conformal two-point function and Schwarzian physics of SYK that motivate the conformal toy model."},{"cited_title":"Continuous q-Hermite polynomials — Wikipedia, the free encyclopedia","cited_arxiv_id":null,"evidence_quote":"Continuous $q$-Hermite polynomial orthogonality used to derive structural properties of $Z_k(\\beta)$ and the two-point function."}],"review_version":1}