{"id":"137bf32e-0491-41d3-9316-58b75d92b6ff","arxiv_id":"2501.16705","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Convection modulation in a coupled ring chain realizes non-Hermitian topological edge modes and an extended-localized transition in thermal diffusion.","lead":"This paper shows that rotating thermal rings with speeds that vary from ring to ring can create the thermal equivalent of a topological insulator, with heat localized at the edges. It also shows that a quasiperiodic speed pattern makes heat switch from spreading evenly to gathering in moving hot spots, which could be a knob for reconfigurable heat control.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The m=1 sector maps cleanly, but the full thermal field also contains a decoupled m=0 sector with no convection potential and slower decay; unless the displayed temperature fields are filtered to m=1, the claimed criticality may be a post-processing artifact.","rationale":"The reader's weakest assumption concerns the plane-wave ansatz and m=1 truncation. I agree that this is the right area, but the more specific and testable risk is not that higher modes change β; rather, the azimuthal modes are decoupled, so the full system is a stack of independent chains. The m=1 chain maps cleanly to Eq. (1) up to a harmless constant shift S, and the COMSOL eigenvalue simulations in Fig. 3 provide independent support for that sector. The weak point is the temperature-field evidence: those simulations probe the whole ring, including the m=0 sector, which has no convection sensitivity and longer-lived modes. Without an explicit azimuthal Fourier filter or a pure-m=1 initial condition, the extended-localized criticality shown in Fig. 6 could be an artifact of post-processing rather than a property of the raw thermal metamaterial. This does not overturn the central theoretical mapping, but it makes the observational claim conditional on a check that is straightforward to perform. The constant S issue raised by the reader is real but not load-bearing, since it is a uniform shift that leaves eigenstates unchanged. Because the reader's verdict is already CONDITIONAL and the proposed test can resolve the concern, no verdict change is needed.","tokens_in":11486,"tokens_out":29552,"duration_ms":304800,"concrete_test":"Re-run the COMSOL transient of Fig. 6 (V=h, 2h, 3h) and decompose each ring's circumferential temperature into azimuthal Fourier modes T_j(x,t)=Σ_m T_j^{(m)}(t)e^{imx/R}. Plot the m=1 component after the same normalization used in Fig. 6 and confirm that it shows the extended/localized/critical distinction while the m=0 component is either negligible or explicitly subtracted. Equivalently, initialize with a pure m=1 single-ring profile (T_j∝A_j cos(x/R+φ_j) plus a small offset) and check whether the V=2h transition still appears; if it does not, the raw thermal field does not exhibit the claimed criticality without m=0 filtering.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (3) is reduced to Eq. (4) by substituting T_j = A_j e^{i(βx−ωt)} and keeping β=1/R (m=1). Since v_j is independent of x, different azimuthal orders m are decoupled: each m obeys its own tight-binding chain with onsite βv_j = (m/R)v_j and uniform loss S_m = −D(m/R)^2 − 2h. The m=1 chain is the one claimed to match Eq. (1). But the m=0 sector has β=0, hence no convection-induced imaginary potential, and its decay rates reach 0 (the uniform steady state). Any transient initialized with a generic excitation—including the 'linear' initial condition of Fig. 6—populates m=0. The long-time temperature field is then dominated by this trivial diffusive sector, not by the m=1 AAH physics, unless the plotted observable explicitly removes the ring-averaged component. The paper defines a normalized field for Fig. 4 but does not specify such an m=0 filter for Fig. 6. If the displayed localization is produced by subtracting the azimuthal average in post-processing, the claim that 'the coupled ring chain structure exhibits the thermal behaviour of the theoretical model' is not supported for the raw thermal field; the criticality would be a property of the m=1 projection, not of the physical temperature field. This is the load-bearing weakness: the eigenvalue spectra in Figs. 2, 3, and 5 are m=1-sector quantities, whereas the temperature-field demonstrations in Figs. 4 and 6 must be shown to be m=1-sector observables.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a thermal-metamaterial realization of the non-Hermitian Aubry-André-Harper (AAH) model with a purely imaginary onsite potential. The key idea is a chain of coupled rings whose rotation velocities are modulated sinusoidally as v_j = R V sin(2πα j + δ), so that advection in each ring acts as an effective imaginary potential after a plane-wave ansatz is made for the azimuthal temperature dependence. For α = 1/4 the authors predict topological edge modes inside an imaginary band gap, and for α = (√5−1)/2 they predict an extended-localized transition at V = 2h. The claims are supported by tight-binding spectra, polarization calculations, COMSOL eigenvalue simulations, transient temperature-field simulations, and a disorder-robustness test. The central mapping from the diffusion equation to the tight-binding model, Eq. (3) to Eq. (4), is standard but relies on a single-mode (m = 1) truncation and omits the effect of the m = 0 sector.","tokens_in":11786,"tokens_out":3825,"duration_ms":37763,"significance":"If the mapping is valid, the work makes a useful contribution to topological thermotics by showing that a dynamically tunable parameter—convection—can implement non-Hermitian topological phases and localization criticality in a purely dissipative platform. The proposed design is physically concrete and the simulations include explicit COMSOL spectra, eigenfields, and transient temperature fields, giving the paper a practical character. A notable strength is that the connection between the diffusion equation and the non-Hermitian tight-binding model is derived without fitted parameters, and the disorder test in Appendix C addresses robustness explicitly. The main significance, however, is conditional on the m = 1 projection: if the observable temperature fields are not filtered to the m = 1 sector, the claimed edge-mode localization and the V = 2h criticality are not properties of the physical temperature field, because the decoupled m = 0 sector dominates at long times and contains no convection-induced imaginary potential.","major_comments":[{"comment":"The reduction from Eq. (3) to Eq. (4) uses the ansatz T_j = A_j e^{i(βx−ωt)} with β = m/R. Because the velocity modulation v_j is independent of x, different azimuthal orders m are decoupled: each m satisfies its own tight-binding chain with onsite term β v_j = (m/R) v_j and uniform loss S_m = −D(m/R)^2 − 2h. The m = 0 sector has β = 0, so it has no convection-induced imaginary potential and its decay rate is simply −2h, which is slower than the m = 1 decay rate. The manuscript never states whether the transient temperature-field simulations in Figs. 4 and 6 are filtered to m = 1 or intended to show the raw temperature field. The linear initial condition described in Appendix B certainly contains an m = 0 component. If the plotting or analysis subtracts the azimuthal average, this must be stated explicitly; otherwise the displayed localization and criticality may be artifacts of the m = 1 projection rather than of the physical temperature field.","section":"Sec. II, Eq. (4)"},{"comment":"The sentence 'the coupled ring chain Hamiltonian Eq. 4 has the same form with the model Hamiltonian Eq. 1, differing only by a factor of i' is incomplete. Eq. (4) contains the uniform imaginary onsite term iS, with S = −[β²κ/(ρC) + 2h], in addition to the modulated term. The uniform shift iS does not change eigenstates but it does shift all decay rates and therefore affects the quantitative comparison in Fig. 4(d), where the reported edge-mode decay rate −Im(ω)_edge = 0.101 rad/s includes the contribution of S. The exact relation is Eq. (4) = iH + iS (with t = h), not merely a factor of i. Please state this explicitly and account for S when comparing decay rates.","section":"Sec. II, paragraph after Eq. (4)"},{"comment":"The statement that 'only the slowest decaying mode can be observed in diffusion systems' does not justify the choice m = 1, because the m = 0 mode decays with rate −2h, which is slower than the m = 1 mode. If the slowest-decay argument is used, it selects m = 0, not m = 1. The choice m = 1 must be justified either by the initial excitation (preparation of a specific azimuthal profile) or by an explicit statement that the m = 0 component is removed from the observables. As written, the selection of m = 1 is an ad hoc truncation that is load-bearing for all subsequent claims about edge modes and criticality.","section":"Sec. II, justification of m = 1 truncation"},{"comment":"The extended-localized transition at V = 2h is demonstrated for the tight-binding model in Fig. 5, and the temperature-field simulations in Fig. 6 are presented as supporting evidence. But if the temperature field is not restricted to the m = 1 sector, the agreement between Fig. 5 and Fig. 6 is not a test of the criticality claim. In particular, the m = 0 sector always contributes a uniform, slowly decaying component, so the 'extended' temperature field at V = h and the 'localized' temperature field at V = 3h need to be shown to be m = 1 observables. Please specify how the m = 0 sector is handled in the transient simulation and in the displayed temperature fields.","section":"Sec. IV, Figs. 5 and 6"}],"minor_comments":[{"comment":"The phrase 'fantastic tunability' is informal for a journal article; consider replacing it with a more quantitative or precise statement about the tunability of convection.","section":"Abstract and Sec. I"},{"comment":"There are several typographical artifacts, including 'di ffusion' in the abstract and main text; these should be corrected to 'diffusion'.","section":"Throughout"},{"comment":"The interlayer coupling terms h[T_{j−1} − T_j] + h[T_{j+1} − T_j] need a brief statement of the open boundary condition for j = 1 and j = N, since the summation limits are not specified in the text.","section":"Appendix B, Eq. (3)"},{"comment":"The sentence 'the times of sampling is 50' is a grammatical error; it should read 'the number of disorder samples is 50.'","section":"Appendix C"},{"comment":"The color name 'modena' is not standard; please provide an RGB value or a conventional color name for the cold source.","section":"Appendix F, Fig. 11 caption"}],"recommendation":"major_revision","confidential_remarks":"The paper is a competent numerical study that maps a diffusion problem to a known non-Hermitian tight-binding model. The main reservation is the m = 0 sector: the central physical observable—the temperature field—appears to contain a slowly decaying, convection-independent component that is not discussed. If the authors can clarify that their displayed fields are m = 1 projections or that the m = 0 component is negligible under their initial conditions, the manuscript would be considerably stronger. The novelty relative to prior work on imaginary-AAH models and on diffusive quasicrystals is incremental, but the convection-based implementation is potentially interesting for applied thermal metamaterials. The fit to the journal's scope is acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper does something concrete: it maps convection in a coupled ring chain onto the imaginary-onsite AAH Hamiltonian and shows numerically that periodic and quasiperiodic convection modulation produce topological edge modes and an extended-localized transition in the m=1 sector. The new bit is not the Hamiltonian—that is Takata-Notomi / Zhu et al. / Pereira et al.—but the thermal realization and the diffusive temperature-field behavior, particularly the mobile multiple localization centers in the localized phase. That is a fair contribution, and the authors credit the prior work properly.\n\nWhat it does well: the derivation from the diffusion equation to Eq. (4) is standard and clean; the COMSOL eigenvalue simulations reproduce the theoretical spectra and eigenfield localization; the disorder test and the no-convection control in Appendix E are the right checks. The IPR and Lyapunov exponent analysis of the quasiperiodic case is consistent with the known transition at V=2h. No constants are fit; the simulation is a consistency check, which is fine.\n\nThe soft spots are addressable. First, the m=0 azimuthal sector is completely decoupled from the convection potential (beta=0) and contains a persistent uniform component with zero decay. The paper claims m=1 is the slowest decaying mode, which is not true—m=0, k=0 never decays. Any initial condition with a ring-averaged component leaves a constant offset that dominates long-time absolute temperature fields. Figures 4 and 6 look like they must use a filtered observable (range-based normalization in Fig. 4(c) does filter m=0, but the Fig. 6 temperature fields are not specified). The authors need to state explicitly that the displayed fields are m=1-sector observables or that the azimuthal average is removed. Second, dropping the constant imaginary shift S in Eq. (4) is harmless (global decay) but unflagged. Third, there is no experiment and no code or data files; all evidence is numerical. Those are conditions, not fatal flaws. The central mapping is not circular; it transfers known non-Hermitian AAH physics to a new platform.\n\nIf I were editor, I would send this to review. The m=0 issue is substantive enough that a referee should see it, but it is fixable in revision and does not undermine the eigenvalue results.","headline":"A clean numerical transfer of the imaginary-AAH model to convection-driven thermal rings; the m=1 sector works, but the temperature-field claims need an explicit m=0 filter.","tokens_in":12333,"tokens_out":5433,"would_cite":true,"duration_ms":54511,"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":"Sinusoidally modulated ring rotations make thermal diffusion reproduce a non-Hermitian tight-binding model with imaginary on-site potential, producing exponentially localized topological edge modes and an extended-localized transition at…","keywords":["thermal metamaterials","topological edge modes","non-Hermitian physics","Aubry-André-Harper model","extended-localized transition","convection modulation","coupled ring chain","diffusion systems"],"falsifier":"Measure the azimuthal temperature profile on the rings in the $\\alpha=1/4$ configuration, or simulate Eq. (3) without the $m=1$ truncation: if modes other than $m=1$ carry significant amplitude, the imaginary spectrum should show no protected gap and the edge-ring temperature should decay at a rate different from the predicted $-\\mathrm{Im}(\\omega)_{\\mathrm{edge}}=0.101$ rad/s.","tokens_in":11242,"feed_emoji":"🔥","tokens_out":13938,"duration_ms":119387,"temperature":0.7,"pith_summary":"Thermal diffusion is normally purely dissipative, but this paper claims that adding a spatially modulated convection term—spinning each ring of a coupled ring chain at a sinusoidally varying speed—makes the diffusion equation behave like a non-Hermitian tight-binding model with an imaginary on-site potential. With a periodic modulation ($\\alpha=1/4$), the temperature field develops topological edge modes localized at the boundary rings, decaying exponentially at a fixed rate and remaining robust against disorder in the ring speeds. With a quasiperiodic modulation ($\\alpha=(\\sqrt{5}-1)/2$), the bulk modes undergo an extended-localized transition at a critical convection amplitude $V=2h$, visible in the inverse participation ratio and Lyapunov exponent and in the simulated temperature fields. The advantage the authors emphasize is tunability: convection can be adjusted dynamically, so the same structure can switch between uniform heat spreading and localized or edge-trapped heat flow. This suggests a route to reconfigurable thermal devices that do not require changing material thermal conductivity.","feed_headline":"Spinning rings make heat mimic non-Hermitian topology","feed_subtitle":"Periodic and quasiperiodic ring speeds pin heat at edges or switch it between spread and localized flow.","key_machinery":"The mechanism is the advection-to-imaginary-potential mapping in a coupled ring chain. Each ring obeys the diffusion-convection equation $\\partial_t T_j = (\\kappa/\\rho C)\\partial_x^2 T_j + v_j\\partial_x T_j + h(T_{j-1}+T_{j+1}-2T_j)$; the plane-wave ansatz $T_j=A_j e^{i(\\beta x-\\omega t)}$ converts the rotating-velocity term $v_j\\partial_x T_j$ into $i\\beta v_j A_j$. With the fundamental azimuthal mode $\\beta=1/R$ and the choice $v_j=R V\\sin(2\\pi\\alpha j+\\delta)$, this becomes the imaginary on-site potential $iV_j$ of the non-Hermitian Aubry–André–Harper (AAH)-type Hamiltonian, while the coupling $h$ plays the role of the hopping $t$. The periodic case $\\alpha=1/4$ gives the imaginary band gap and edge modes protected by non-Hermitian particle-hole symmetry; the quasiperiodic case $\\alpha=(\\sqrt{5}-1)/2$ gives the extended-localized transition, with IPR and Lyapunov exponent as diagnostics. This same machinery is what lets the simulated temperature fields exhibit the predicted localization and critical behavior.","core_discovery":"At the center of the paper is the claim that a chain of coupled rotating rings can translate thermal convection into the imaginary on-site potential of a non-Hermitian tight-binding model. Starting from Fourier's law with a convection term, the authors substitute the plane-wave ansatz $T_j=A_j e^{i(\\beta x-\\omega t)}$ and keep only the fundamental azimuthal mode ($m=1$, so $\\beta=1/R$). The effective Hamiltonian then has the same form as $\\hat{H}=t\\sum_j(a_j^\\dagger a_{j+1}+\\mathrm{H.c.})+i\\sum_j V_j a_j^\\dagger a_j$, up to an overall factor $i$ and a constant shift, with $V_j=V\\sin(2\\pi\\alpha j+\\delta)$ when each ring rotates at $v_j=R V\\sin(2\\pi\\alpha j+\\delta)$. For $\\alpha=1/4$ the imaginary spectrum develops a gap containing topological edge modes whose temperature fields decay exponentially at the boundary rings; the non-Hermitian electric polarization takes the quantized value $|p_x|=1/2$ in the nontrivial phase. For $\\alpha=(\\sqrt{5}-1)/2$ the bulk modes undergo an extended-localized transition at $V=2h$, confirmed by the inverse participation ratio, the Lyapunov exponent, and transient temperature simulations in which the localized phase shows moving multiple localization centers.","pith_inferences":["Editorial inference: the same convection-modulation mapping should work for higher azimuthal modes ($m>1$), yielding effective tight-binding models with different parameters or longer-range couplings and thereby a broader family of thermal Hamiltonians than the AAH form considered here.","Editorial inference: since rotation speeds can be varied in time, sweeping the phase $\\delta$ or the amplitude $V$ slowly should realize adiabatic topological pumping of heat across the chain, a dynamical protocol the paper does not discuss.","Editorial inference: the mechanism is not obviously restricted to one-dimensional chains; a two-dimensional lattice of rotating rings could realize imaginary-potential landscapes that produce corner modes or skin-effect-like heat accumulation, which the paper leaves unexamined."],"forward_implications":["A thermal device built on this scheme can hold heat at its boundary rings and release it with a controlled exponential decay rate, with the edge mode surviving disorder in the ring rotation velocities.","The quasiperiodic modulation gives a heat-flow switch: below $V=2h$ the temperature field stays extended and nearly stationary, while above $V=2h$ it breaks into moving localized hotspots, so the convection amplitude controls whether heat spreads uniformly or concentrates.","Because the control parameter is rotation speed rather than material thermal conductivity, the same ring chain can be reconfigured dynamically, offering a practical route to programmable thermal routing.","In the localized phase the moving multiple localization centers can drive thermoelectric generation, e.g., as a double-trace generator that powers two loads simultaneously.","The observed signatures are inherently diffusive: the topological edge mode decays in time rather than propagating, so experimental tests should look at transient cooling of edge rings, not steady-state wave transport."],"supporting_citations":[{"why":"Supplies the quasiperiodic tight-binding model whose self-duality yields the extended-localized transition at a finite potential strength.","marker":"[7]"},{"why":"Shows that a gain/loss sequence with period four alone induces photonic topological edge modes, the periodic case this paper transplants to heat.","marker":"[19]"},{"why":"Provides the non-Hermitian quasiperiodic lattice model used for the bulk extended-localized criticality.","marker":"[26]"},{"why":"Gives the eigenstate-localization diagnostics (IPR and Lyapunov exponent) used to identify the transition.","marker":"[28]"},{"why":"Defines the imaginary on-site potential model and the non-Hermitian polarization/Wilson-loop method used to characterize the edge modes.","marker":"[33]"},{"why":"The engineered-loss photonic array that realized topological edge modes and criticality, the wave-system counterpart this work converts to diffusion.","marker":"[34]"},{"why":"Introduces the coupled ring chain thermal structure and its diffusion-convection equation, the platform realizing the model.","marker":"[56]"},{"why":"Shows extended-localized transitions in diffusive quasicrystals, the prior diffusion result this work extends to convection modulation.","marker":"[58]"}],"fun_headline_variants":["Spinning rings create topological heat modes","Rotating rings make heat show non-Hermitian physics","Thermal metamaterials get topological edge states from convection","Heat edge modes from rotating rings","Spinning rings control heat localization and topology"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything rests on the assumption that the temperature around each ring is a single rotating wave with one wavelength around the circumference, so the rotation speed becomes a clean imaginary on-site potential and the constant shift can be dropped; if higher-order azimuthal modes or geometry-dependent coupling change that wavelength, the predicted edge modes and transition need not appear.","fun_headline_variants_meta":{"raw":{"variants":["Spinning rings create topological heat modes","Rotating rings make heat show non-Hermitian physics","Thermal metamaterials get topological edge states from convection","Heat edge modes from rotating rings","Spinning rings control heat localization and topology"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00055,"raw_usage":{"total_tokens":2631,"prompt_tokens":960,"completion_tokens":1671,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":1603}},"tokens_in":576,"tokens_out":1671,"duration_ms":12400,"temperature":1.0,"reasoning_tokens":1603,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T11:16:36.211991+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the azimuthal temperature profile on the rings in the $\\alpha=1/4$ configuration, or simulate Eq. (3) without the $m=1$ truncation: if modes other than $m=1$ carry significant amplitude, the imaginary spectrum should show no protected gap and the edge-ring temperature should decay at a rate different from the predicted $-\\mathrm{Im}(\\omega)_{\\mathrm{edge}}=0.101$ rad/s.","supporting_citations":[{"cited_title":"Aubry and G","cited_arxiv_id":null,"evidence_quote":"Supplies the quasiperiodic tight-binding model whose self-duality yields the extended-localized transition at a finite potential strength."},{"cited_title":"Takata and M","cited_arxiv_id":null,"evidence_quote":"Shows that a gain/loss sequence with period four alone induces photonic topological edge modes, the periodic case this paper transplants to heat."},{"cited_title":"Jiang, L","cited_arxiv_id":null,"evidence_quote":"Gives the eigenstate-localization diagnostics (IPR and Lyapunov exponent) used to identify the transition."},{"cited_title":"Zhu, L.-J","cited_arxiv_id":null,"evidence_quote":"Defines the imaginary on-site potential model and the non-Hermitian polarization/Wilson-loop method used to characterize the edge modes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The engineered-loss photonic array that realized topological edge modes and criticality, the wave-system counterpart this work converts to diffusion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the coupled ring chain thermal structure and its diffusion-convection equation, the platform realizing the model."},{"cited_title":"Liu, P.-C","cited_arxiv_id":null,"evidence_quote":"Shows extended-localized transitions in diffusive quasicrystals, the prior diffusion result this work extends to convection modulation."}],"review_version":1}