{"id":"f9d69b2b-1f46-4360-ad91-25e5367c43d7","arxiv_id":"2411.18768","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Moving impurities in a 2D disordered system convert Anderson-localized wavefunctions into diffusive ones with D about hbar over m, a coefficient the paper calls Planckian diffusion.","lead":"This paper reports simulations in which a moving disordered medium destroys Anderson localization and replaces it with a universal diffusion coefficient of order hbar over mass, the Planckian diffusion constant. The authors argue the same effect explains linear-in-temperature resistivity in several settings, including a 1980s experiment on electrons on solid hydrogen.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The D≈ℏ/m plateau in Figs. 3–5 is extracted from finite-window MSD slopes without ensemble averaging or convergence checks, so a transient pre-diffusive slope may be mistaken for the asymptotic diffusion coefficient.","rationale":"The reader's weakest assumption identifies the same load-bearing issue: the diffusion coefficient is read off finite-window MSD slopes without realization averaging, error bars, or convergence checks, so the central universality claim is numerically under-supported. I agree with that assessment and with the CONDITIONAL verdict. The paper presents a plausible mechanism—moving disorder scrambles the phase coherence needed for Anderson localization—and cites supportive independent cases (the solid-hydrogen experiment and prior lattice-vibration simulations), but none of that substitutes for a statistically robust extraction of D in the new model. The absence of deposited code and the unfinished figure caption further weaken confidence. I do not see an internal inconsistency that would force rejection; the gap is evidential rather than logical. The requested additional analysis—ensemble averages, error bars, finite-size and duration checks, and a code/parameter deposit—would settle whether the plateau is real. Until then, CONDITIONAL is the right verdict, and this stress test does not move it.","tokens_in":9091,"tokens_out":3873,"duration_ms":40685,"concrete_test":"Recompute the v=2000 m/s point of Figure 3 with an independent split-operator code using at least 20 fresh random impurity configurations, a simulation box large enough that the MSD radius stays below one-quarter of the box side for the whole run, and an evolution time at least four times the current window. Extract D by linear fitting over successive sub-windows and report the median and interquartile range. If the median slope or its dependence on fit window falls outside 0.5–2ℏ/m, the claimed Planckian plateau is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of universal Planckian diffusion rests on the numerical values of D in Figures 3–5. Those values come from the slope of the mean square displacement over a finite simulation window, apparently for a single disorder realization, with no reported ensemble averaging, error bars, system-size scan, or check that the MSD has reached its long-time linear regime. Section II defines D by a t→∞ limit, but the paper does not demonstrate that the finite-time slopes in Figures 1, 3, 4, and 5 have converged to that limit. This matters because a Gaussian wavepacket launched with zero average momentum initially spreads ballistically, and in a finite moving-disorder medium the MSD slope can pass through ℏ/m during a crossover even when the true asymptotic diffusivity is different. The claim that D is independent of impurity speed, coupling strength, and temperature is built directly on these slopes, so if the window or realization biases them, the universality statement loses its numerical support. The phenomenological chamber model in Section IV does not repair this gap: it assumes a one-level-spacing broadening τ=ℏρ=mA/h, which by construction yields D≈ℏ/m independent of A; it illustrates the idea but cannot validate the numerics. The manuscript also flags its own limitations: no exact data points are plotted in the adiabatic regime because the authors state they 'cannot accurately gauge diffusion,' and the caption of Figure 8 contains a placeholder ('Lorem ipsum00'), indicating an unfinished numerical record. These are secondary, but they reinforce that the load-bearing numerical evidence is under-documented.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims that when Anderson localization is destroyed by the motion of a disordered medium, the ensuing diffusion is universal: D = αℏ/m with α of order unity, independent of impurity speed, coupling strength, impurity mass, temperature, and even of the existence of thermal equilibrium. The argument combines (i) time-dependent Schrödinger simulations of a Gaussian wavepacket among thousands of moving Bessel-shaped impurities in two dimensions, with D read off the slopes of the mean square displacement (Figures 3–5); (ii) a phenomenological chamber model; (iii) an earlier experiment on electrons on solid hydrogen; and (iv) the authors' prior strange-metal simulations. A Drude/Einstein conversion turns the temperature-independent D into a Planckian scattering rate τ = αℏ/k_BT and linear-in-T resistivity. The paper distinguishes a semi-adiabatic regime (D ≪ ℏ/m), a broad 'ghost' Planckian regime (0.5–2ℏ/m), and a high-velocity classical regime (D ≫ 2ℏ/m).","tokens_in":9402,"tokens_out":13909,"duration_ms":121252,"significance":"If the claim holds, it would be a striking unification: a universal quantum diffusion constant ℏ/m emerging from broken Anderson localization, independent of coupling and temperature and not requiring thermal equilibrium, with direct consequences for the Planckian dissipation phenomenology. The design of the central computation is honest—D is measured from MSD slopes with parameters varied rather than fitted—and the paper makes a concrete, falsifiable experimental proposal (deliberately disturbing the localized states of ref. [26] and measuring D). It also flags its own limitations, including the absence of data in the adiabatic regime. However, as presented, the numerical evidence does not yet distinguish an asymptotic universal regime from a finite-window crossover, the 'Planckian window' is defined to coincide with the claimed range of α, and one of the experimental supporting figures is an uncorrected placeholder. The significance is potentially high but conditional on the statistical and convergence analysis requested below.","major_comments":[{"comment":"The central numerical claim—that D plateaus at αℏ/m over a wide parameter range—is built on slopes of the mean square displacement taken over finite simulation windows, but the manuscript provides no ensemble averaging, no statistical error bars, no system-size scan, and no demonstration that these slopes have converged to the t→∞ limit defining D in Section II. This is not a routine omission: the text itself notes that the wavepacket is kept away from the boundary 'to make the most use of the window size,' so the reported slopes are window-averaged quantities, and a zero-mean Gaussian wavepacket spreads ballistically at early times, so its local MSD slope can cross ℏ/m during a crossover even when the asymptotic diffusivity is different. Since the claimed independence of D from impurity speed, potential height, impurity mass, and temperature is inferred from these slopes, the universality statement currently rests on unquantified finite-window data; I ask for ensemble-averaged MSDs with errors, a check that the local slope is stationary in a linear regime (e.g., a local log-log exponent consistent with 1 over a substantial time interval), and a convergence test in system size and window duration.","section":"Section II, Section III B, Figs. 3–5"},{"comment":"The acceptance window for the claim is the claim itself: the abstract asserts α ∈ [0.5, 2], and Section III B defines the 'Planckian regime' as D between 0.5ℏ/m and 2ℏ/m. With no error bars on the individual points in Figures 3–5, every plotted datum inside the pink box automatically counts as agreement, and the phrase 'diffusion coefficient quickly rises to the Planckian regime' carries no quantitative content beyond 'the points are inside the box.' The case for universality would be materially strengthened by reporting fitted values of α (with uncertainties) as a function of the control parameters and showing that they cluster around a single value rather than merely lying within a factor-of-two band.","section":"Abstract and Section III B"},{"comment":"The chamber model derives D ≈ ℏ/m by assuming that a single-channel leak broadens each level by one level spacing (τ = ℏρ = mA/h) and then combining this with d = √A and D = d²/(4τ). Because the assumption fixes τ to be of order ℏρ, the final result D = h/(4m) is independent of A by construction; the model illustrates how a Planckian D could arise but provides no independent check on the simulations, since the one-level-spacing broadening is asserted rather than derived or tested. Section VI counts this model among the 'four cases' supporting universality, so I ask that it be explicitly relabeled as a consistency check and that the level-broadening assumption be justified (or at least tested) rather than posited.","section":"Section IV"},{"comment":"The manuscript reports no data in the adiabatic/semi-adiabatic regime—'No exact data points are plotted in the adiabatic regime in Figure 3, because for such very slow movement we cannot accurately gauge diffusion'—yet Section VI states that the diffusion coefficient 'rises very rapidly but smoothly from zero to the Planckian rate' and uses the adiabatic limit to engage with the conjectured Planckian bound on transport (refs. [24,25]). The assertion of a smooth (or any particular) transition, and the claimed bearing on the Planckian bound, are unsupported by plotted measurements; either the low-velocity data should be provided or these statements should be restricted to what the data show.","section":"Section III B and Section VI"},{"comment":"Figure 8, which presents the solid-hydrogen experiment as a confirming case, cannot currently be evaluated: its caption contains the literal placeholder text 'Lorem ipsum00', and no data plot with axes is identifiable. Since Section VI explicitly counts this experiment among the 'four cases' that 'all indicate' a universal outcome, the evidential base for the experimental claim is incomplete; the figure must be restored, and the caption should clarify whether the quoted slope D = 0.3ℏ/me is the original experiment's interpretation or the present authors' re-analysis of the inverse residual mobility.","section":"Section V A, Figure 8"}],"minor_comments":[{"comment":"The heading 'AKNOWLEDGEMENTS' should read 'ACKNOWLEDGEMENTS'.","section":"Section VIII"},{"comment":"Typos should be corrected: 'Panckian' (first word of Section VI), 'intricaces' (Section III B), 'givn' and 'stange metals' (Figure 9 caption), 'supercedes' (Abstract), 'furthers tests' (Section VI), and 'we have find' (Section VII).","section":"Throughout"},{"comment":"References [15] and [16] are the same article (Aydin et al., PNAS 121:2404853121, 2024) and should be merged or one removed.","section":"References"},{"comment":"The sentence beginning 'Referring to recent work We have shown...' is grammatically incomplete and should be rewritten.","section":"Section VII"},{"comment":"Please report the numerical simulation parameters (box size, grid spacing, time step, number of impurities, number of disorder realizations) so that the MSD measurements are reproducible.","section":"Section II"},{"comment":"Add one sentence explaining how the diffusion coefficient is extracted from the inverse residual mobility in the Corbino geometry; as written, the connection between the measured mobility and D = 0.3ℏ/me is asserted without derivation.","section":"Section V A"},{"comment":"The phrase 'Planckian diffusion supercedes the Planckian speed limit' should be softened to reflect that the relation τ = αℏ/k_BT follows from D together with the Einstein relation in thermal systems; as written the implication structure is unclear.","section":"Abstract"},{"comment":"Clarify the direction of the inequality when connecting the adiabatic regime to the Planckian bound in refs. [24,25]: as stated, going 'below the Planckian limit' in the adiabatic regime is a statement about a nonuniversal crossover, and the relevance to the bound on transport needs a sentence of elaboration.","section":"Section VI"}],"recommendation":"major_revision","confidential_remarks":"The manuscript appears to be an unfinished draft: the Lorem ipsum placeholder in Figure 8, the duplicated reference, and the typographical density suggest it was submitted before final polishing. The novelty increment relative to the authors' own recent work (refs. [12]–[16], especially the PNAS 2024 paper) should be stated explicitly; as it stands, Section V B largely re-cites that work as a 'supporting case' rather than deriving new results from it. On scope, the paper is a condensed-matter transport claim presented in a quant-ph venue; that is defensible given the Anderson-localization and ultracold-atom community, but the editor may wish to consider whether the revised version's evidence level matches the journal's standards for a universality claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the numerical demonstration: a Gaussian wavepacket in a 2D moving-impurity model diffuses with D near hbar/m over a wide range of impurity speeds, potential strengths, temperatures, and masses, and even 10% moving impurities is enough to break localization. That is a concrete, falsifiable observation that I have not seen in the cited literature. The paper also does something useful in connecting this to the solid-hydrogen/adsorbed-helium experiment and to the earlier thermal deformation-potential work. The chamber model in Section IV is a nice pedagogical illustration, though not evidence.\n\nThe soft spots are real and mostly about documentation. The MSD slopes in Figures 3–5 are extracted from a finite simulation window with no ensemble averaging, no error bars, no system-size scan, and no explicit convergence check to the t→∞ limit. That matters because a transient ballistic-to-diffusive crossover can pass through hbar/m even when the true asymptotic diffusivity is different. The stress-test note is right about this. The authors also admit they cannot accurately gauge diffusion in the adiabatic regime, which is exactly where the curve is omitted—so the clean rise to the Planckian plateau is partly asserted rather than shown. Defining the Planckian regime as 0.5–2 hbar/m makes the match generous. The chamber model assumes a one-level-spacing broadening, which encodes D ~ hbar/m by construction; it illustrates the mechanism but cannot validate the numerics. Finally, the Figure 8 caption contains an unfinished “Lorem ipsum00” placeholder, and the re-drawn experimental data deserve a cleaner presentation. None of these are fatal—the central idea is coherent and the simulations are plausible—but the paper currently argues for universality on a thin evidentiary base.\n\nWho gets value from this: people working on Planckian transport, transient localization, and strange-metal phenomenology. It is a thought-provoking single-particle mechanism that could be important if the numerics hold up. It deserves peer review—a serious referee can push for the missing convergence and averaging checks, and ask the authors to deposit code and parameters. The universality claim should be softened to match what is actually demonstrated. I would not cite it in my own work until the numerical evidence is solid, but I would read the revised version. Bring it to reading group, if only to debate whether the chamber model is illuminating or circular—both sides have a point.","headline":"Plausible and potentially important claim that moving impurities convert Anderson localization into universal D ~ hbar/m diffusion, but the numerical support is under-documented and the paper overreaches in its universality language.","tokens_in":9925,"tokens_out":1231,"would_cite":false,"duration_ms":14165,"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":"The paper claims that a moving random medium turns Anderson localization into a universal Planckian diffusion, with $D = \\alpha\\hbar/m$ and $\\alpha$ about 0.5 to 2.","keywords":["Anderson localization","Planckian diffusion","dynamic disorder","moving impurities","quantum transport","linear resistivity","strange metals","wavepacket simulation"],"falsifier":"A direct check would be to repeat the moving-impurity simulation for many independent disorder realizations and much longer times: if the ensemble-averaged slope of the mean-square displacement does not approach a stable value in the range $0.5$ to $2$ times $\\hbar/m$, or if the slope drifts with system size and runtime, the claimed universal plateau is a finite-window artifact.","tokens_in":8902,"feed_emoji":"👻","tokens_out":9845,"duration_ms":83097,"temperature":0.7,"pith_summary":"The paper sets out to show that Anderson localization, the freezing of quantum waves in a static disordered medium, is replaced by a universal Planckian diffusion, $D = \\alpha\\hbar/m$ with $\\alpha$ of order one, as soon as the disorder starts to move. It argues that this constant is independent of how fast the impurities move over a wide range, how strongly they scatter, their mass, and the temperature, and that it does not even require thermal equilibrium. If true, this would mean the much-studied Planckian scattering time $\\tau \\approx \\hbar/(k_B T)$ is a corollary of a deeper, more general transport constant. The evidence comes from numerical wavepacket propagation in two dimensions, a simple chamber model, and a re-analysis of an existing experiment.","feed_headline":"When Anderson localization dies, Planckian diffusion takes over","feed_subtitle":"A moving random medium destroys wave localization and locks diffusion at ℏ/m, with linear resistivity as a corollary.","key_machinery":"The load-bearing mechanism is the moving random potential: impurity motion scrambles the phase relations among multiply scattered waves before Anderson localization can lock them in, so the wavefunction diffuses instead of localizing. The key identity in the chamber model is the quantum dwell-time relation: a two-dimensional box of area $A$ has density of states $\\rho = 2\\pi m A/h^2$, and a single-channel leak broadens each level by one spacing, giving dwell time $\\tau = m A/h$; with a random-walk step $\\sqrt{A}$ this yields $D = d^2/4\\tau = 2\\pi\\hbar/4m \\approx \\hbar/m$, independent of $A$. In the simulations, the diffusion coefficient is extracted from the time-derivative of the mean-square displacement of a Gaussian wavepacket propagated numerically.","core_discovery":"The paper's central claim is that the destruction of Anderson localization by a time-dependent random medium gives rise to a universal quantum diffusion constant, $D = \\alpha\\hbar/m$, with $\\alpha$ of order unity, rather than a material-specific transport coefficient. This Planckian diffusion is claimed to be insensitive to impurity speed, carrier-impurity coupling strength, impurity mass, and temperature, and to hold even when no thermal equilibrium exists. The claim is supported by a two-dimensional wavepacket simulation with thousands of moving impurities, by a phenomenological morphing-chambers model based on the scaling theory of localization, and by re-interpreting an experiment on electrons on solid hydrogen. In thermal systems the same constant implies the conventional Planckian scattering rate $\\tau = \\alpha\\hbar/(k_B T)$, but the paper argues that the diffusion constant itself is the more fundamental statement.","pith_inferences":["If the universality holds, the Planckian scattering rate $\\tau \\approx \\hbar/(k_B T)$ would be a symptom of the same mechanism rather than an independent bound, and could appear in non-thermal driven systems at zero temperature.","A direct experimental test could use ultracold atoms in a disorder potential whose pattern is made to drift or fluctuate; the measured diffusion constant should fall near $\\hbar/m$ and be insensitive to the drift speed over a wide window.","A natural numerical follow-up is to ensemble-average over many disorder realizations and extend the time window; this would map the boundaries of the plateau and test whether it is a true long-time limit or a finite-window crossover.","The chamber model suggests searching for Planckian diffusion in other wave systems, such as acoustic or photonic media with moving scatterers, where the predicted diffusion constant should again be near $\\hbar/m_\\text{eff}$."],"forward_implications":["In a thermal system, the mobility-diffusion relation turns $D = \\alpha\\hbar/m$ into the Planckian scattering time $\\tau = \\alpha\\hbar/(k_B T)$, so resistivity is linear in temperature down to at least 1 K.","The universal diffusion does not require thermal equilibrium; it holds for driven, nonthermal impurity motion as well, making it a broader statement than the Planckian speed limit.","Only about 10% of impurities need to move to break Anderson localization and produce diffusion at the Planckian rate.","The diffusion coefficient remains near $\\hbar/m$ across impurity speeds from roughly sound speed upward, potential heights, impurity masses from 10 to 10000 electron masses, and temperatures from 1 K to 500 K.","The chamber model gives $D = 2\\pi\\hbar/4m \\approx \\hbar/m$ independent of chamber area, showing a geometric mechanism for the same constant."],"supporting_citations":[{"why":"Defines Anderson localization, the phenomenon whose breakdown is the paper's central subject.","marker":"[1]"},{"why":"Supplies the numerical propagation and mean-square-displacement method, and the earlier strange-metal simulations shown in Figure 9.","marker":"[16]"},{"why":"Provides the relation between diffusion coefficient and scattering time used to convert $D$ into linear resistivity.","marker":"[19]"},{"why":"Provides the scaling theory of localization that the phenomenological chamber model is meant to realize.","marker":"[20]"},{"why":"Supplies numerical localization studies underlying the chamber model's scaling reasoning.","marker":"[21]"},{"why":"Experiments on electrons on solid hydrogen with adsorbed helium, treated as a confirming case of Planckian diffusion.","marker":"[22]"},{"why":"Data re-drawn in the paper's Figure 8, whose slope gives $D = 0.3\\hbar/m_e$, supporting the universality claim.","marker":"[23]"},{"why":"Counterexample to the conjectured Planckian bound, cited to support the claim that diffusion can fall below the Planckian limit in the adiabatic regime.","marker":"[25]"}],"fun_headline_variants":["Moving disorder kills localization, births Planckian diffusion","Universal diffusion D=αħ/m replaces Anderson localization","Anderson localization dies to moving disorder, diffusion fixed at ħ/m","Planckian diffusion: the universal heir to Anderson localization"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the slope of the mean-square displacement over the finite simulation window equals the true long-time diffusion constant, even though no ensemble averaging, error bars, or convergence checks are reported.","fun_headline_variants_meta":{"raw":{"variants":["Moving disorder kills localization, births Planckian diffusion","Universal diffusion D=αħ/m replaces Anderson localization","Anderson localization dies to moving disorder, diffusion fixed at ħ/m","Planckian diffusion: the universal heir to Anderson localization"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000598,"raw_usage":{"total_tokens":2776,"prompt_tokens":903,"completion_tokens":1873,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":519,"completion_tokens_details":{"reasoning_tokens":1807}},"tokens_in":519,"tokens_out":1873,"duration_ms":108368,"temperature":1.0,"reasoning_tokens":1807,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T10:54:12.372186+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct check would be to repeat the moving-impurity simulation for many independent disorder realizations and much longer times: if the ensemble-averaged slope of the mean-square displacement does not approach a stable value in the range $0.5$ to $2$ times $\\hbar/m$, or if the slope drifts with system size and runtime, the claimed universal plateau is a finite-window artifact.","supporting_citations":[{"cited_title":"Quantum acoustics unravels Planckian resistivity","cited_arxiv_id":"2303.06077","evidence_quote":"Supplies the numerical propagation and mean-square-displacement method, and the earlier strange-metal simulations shown in Figure 9."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the relation between diffusion coefficient and scattering time used to convert $D$ into linear resistivity."},{"cited_title":"Scaling theory of localization: Absence of quantum diffusion in two di- mensions","cited_arxiv_id":null,"evidence_quote":"Provides the scaling theory of localization that the phenomenological chamber model is meant to realize."},{"cited_title":"Numerical studies of lo- calization in disordered systems","cited_arxiv_id":null,"evidence_quote":"Supplies numerical localization studies underlying the chamber model's scaling reasoning."},{"cited_title":"Adams and Mikko A","cited_arxiv_id":null,"evidence_quote":"Experiments on electrons on solid hydrogen with adsorbed helium, treated as a confirming case of Planckian diffusion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Data re-drawn in the paper's Figure 8, whose slope gives $D = 0.3\\hbar/m_e$, supporting the universality claim."},{"cited_title":"Coun- terexample to the conjectured planckian bound on trans- port","cited_arxiv_id":null,"evidence_quote":"Counterexample to the conjectured Planckian bound, cited to support the claim that diffusion can fall below the Planckian limit in the adiabatic regime."}],"review_version":1}