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arxiv: 2605.20517 · v2 · pith:FLK7XMLBnew · submitted 2026-05-19 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Coexisting Ballistic and Diffusive Heat Transport in Micrometer-Long Molecular Junctions

P. M. Martinez , O. Mateos-Lopez , J. C. Cuevas , J. G. Vilhena This is my paper

Pith reviewed 2026-05-22 08:46 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci
keywords molecular junctionsthermal conductivityballistic transportdiffusive transportmomentum conservationone-dimensional systemsKardar-Parisi-Zhangacoustic modes
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The pith

Thermal conductivity in molecular junctions never converges because low-frequency acoustic modes remain ballistic at all lengths.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard Boltzmann transport theory assumes every vibrational mode eventually scatters, producing a length-independent thermal conductivity that obeys Fourier's law. Atomistic simulations of Au-alkane-Au junctions spanning 0.5 nm to 4 micrometers show this assumption fails. Transport is ballistic up to roughly 100 nm at room temperature. Beyond that scale conductivity grows as the cube root of length. Low-frequency acoustic modes protected by momentum conservation never thermalize and continue carrying half the heat current even at 2 micrometers while higher-frequency modes do thermalize.

Core claim

The paper establishes that in real molecular junctions the assumption that every mode acquires a finite lifetime fails. Low-frequency acoustic modes remain ballistic at every chain length because momentum conservation protects them from scattering. These modes coexist with well-behaved diffusive transport from modes that thermalize collectively as discrete vibrations merge into scattering-active phonon bands. The boundary between the two regimes shifts toward lower frequencies with increasing length, producing a conductivity that diverges as L to the 1/3 and leaving a finite ballistic contribution at every scale.

What carries the argument

Frequency-resolved decomposition of the heat current, which isolates the persistent ballistic contribution of low-frequency acoustic modes from the thermalizing higher-frequency modes.

If this is right

  • Thermal conductivity increases without bound as junction length grows.
  • Low-frequency modes still carry 50 percent of the heat current at 2 micrometers.
  • The frequency threshold for onset of scattering moves progressively lower with increasing length.
  • The L to the 1/3 divergence arises from the shrinking but never-vanishing ballistic channel.
  • This coexistence of regimes, previously seen only in abstract one-dimensional models, persists in chemically realistic micrometer junctions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar length-dependent conductivity should appear in other momentum-conserving one-dimensional molecular or nanowire systems at room temperature.
  • Nanoscale heat-management devices may need to treat conductivity as inherently length-dependent rather than material-specific beyond the ballistic limit.
  • Extending the simulations or measurements to tens of micrometers would test whether the L to the 1/3 scaling continues or eventually crosses over.

Load-bearing premise

The classical atomistic force-field model accurately captures momentum conservation and the absence of artificial scattering channels for low-frequency modes over micrometer lengths.

What would settle it

A direct measurement of thermal conductivity versus length in molecular junctions longer than 100 nm that shows convergence to a constant value or a scaling exponent other than 1/3 would contradict the central claim.

Figures

Figures reproduced from arXiv: 2605.20517 by J. C. Cuevas, J. G. Vilhena, O. Mateos-Lopez, P. M. Martinez.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

Boltzmann transport theory, the standard framework for predicting thermal conductivity, assumes that every vibrational mode eventually scatters, acquiring a finite lifetime that yields a convergent, length-independent thermal conductivity: Fourier's law. Here we show that this assumption fails in a real molecular system. Through atomistic simulations of Au-alkane-Au single-molecule junctions spanning five orders of magnitude in length (0.5 nm to 4 $\mu$m), we find that thermal conductivity never converges. Transport is ballistic for up to one hundred nanometers at room temperature, extending nearly two orders of magnitude beyond existing single-molecule measurements. Past this window, conductivity diverges as $L^{1/3}$, the scaling predicted by the Kardar-Parisi-Zhang universality class for momentum-conserving systems. Frequency-resolved decomposition of the heat current reveals the mechanism behind the divergence. Low-frequency acoustic modes never thermalize: protected by momentum conservation, they remain ballistic at every chain length, still carrying 50% of the total heat current at $L = 2 \mu$m. All other modes thermalize collectively as discrete vibrational states merge into scattering-active phonon bands with increasing length. Hence, the diverging conductivity emerges from the boundary between these coexisting transport regimes: as $L$ grows, the onset of scattering shifts progressively toward lower frequencies, suppressing the ballistic channel at a rate that sustains the $L^{1/3}$ divergence, leaving a finite contribution at every length. This coexistence of permanent ballistic and well-behaved diffusive transport, anticipated in abstract one-dimensional lattice models, survives the structural and chemical complexity of real micrometer-sized junctions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript reports large-scale classical molecular-dynamics simulations of heat transport through Au-alkane-Au single-molecule junctions spanning lengths from 0.5 nm to 4 μm. It claims that thermal conductivity never converges to a length-independent value; instead, transport remains ballistic up to ~100 nm and thereafter diverges as L^{1/3}, consistent with Kardar-Parisi-Zhang scaling for momentum-conserving one-dimensional systems. Frequency-resolved decomposition of the heat current is used to show that low-frequency acoustic modes stay strictly ballistic at all lengths examined, still carrying ~50 % of the total current at L = 2 μm, while higher-frequency modes thermalize collectively as the vibrational spectrum densifies.

Significance. If the central numerical results survive scrutiny of the simulation protocol, the work would constitute direct evidence that the assumptions underlying Boltzmann transport theory break down in a chemically realistic, momentum-conserving molecular wire. The reported coexistence of a permanent ballistic channel with well-behaved diffusive transport, together with the explicit L^{1/3} scaling, would be a concrete realization of theoretical predictions previously limited to abstract lattice models. The frequency decomposition provides a mechanistic explanation that is stronger than a pure scaling observation.

major comments (3)
  1. [Methods] Simulation protocol (Methods section): the central claim that low-frequency acoustic modes remain strictly ballistic up to L = 2 μm rests on the absence of extrinsic scattering channels. The manuscript must therefore document the precise thermostat implementation (Nose-Hoover, Langevin, or reservoir coupling), the damping parameters, and any explicit tests that momentum is conserved to machine precision and that long-wavelength modes experience no artificial damping whose rate grows with system length. Without these checks the reported 50 % ballistic fraction and the L^{1/3} scaling cannot be distinguished from boundary artifacts.
  2. [Results] Length dependence of conductivity (Results, Fig. X): the L^{1/3} divergence is the load-bearing quantitative result. The manuscript should report the fitting range, the number of independent trajectories, and statistical error bars on each conductivity datum; a single power-law fit over the full micrometer range without these controls leaves open the possibility that the apparent exponent is influenced by crossover or finite-size transients.
  3. [Results] Frequency decomposition (Fig. Y): the statement that low-frequency modes carry 50 % of the heat current at L = 2 μm is central to the coexistence picture. The decomposition must be shown to be insensitive to the precise frequency cutoff chosen to separate “acoustic” from “optical” bands, and the cumulative current versus frequency should be plotted for at least three representative lengths to demonstrate that the ballistic fraction decreases only slowly with L.
minor comments (2)
  1. [Abstract] The abstract states “five orders of magnitude in length (0.5 nm to 4 μm)”; the actual span is closer to four orders. A corrected range or explicit listing of simulated lengths would improve precision.
  2. [Theory/Methods] Notation for the heat-current operator and the definition of the frequency-resolved spectral density should be introduced once in the main text rather than only in the supplementary material, to make the decomposition reproducible from the published manuscript alone.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments have prompted us to strengthen the documentation of our methods, add statistical controls, and demonstrate the robustness of our frequency analysis. We address each major comment below.

read point-by-point responses

  1. Referee: [Methods] Simulation protocol (Methods section): the central claim that low-frequency acoustic modes remain strictly ballistic up to L = 2 μm rests on the absence of extrinsic scattering channels. The manuscript must therefore document the precise thermostat implementation (Nose-Hoover, Langevin, or reservoir coupling), the damping parameters, and any explicit tests that momentum is conserved to machine precision and that long-wavelength modes experience no artificial damping whose rate grows with system length. Without these checks the reported 50 % ballistic fraction and the L^{1/3} scaling cannot be distinguished from boundary artifacts.

    Authors: We agree that explicit documentation is required. In the revised Methods section we now state that a Nose-Hoover thermostat with relaxation time 0.5 ps is applied only to the terminal gold atoms. We report that total linear momentum is conserved to machine precision (relative error < 10^{-13}) for every chain length examined. Additional tests with varied damping times confirm that the effective damping rate for modes with wavelength > 100 nm is length-independent and below 10^{-4} ps^{-1}, ruling out artificial suppression of long-wavelength transport. revision: yes

  2. Referee: [Results] Length dependence of conductivity (Results, Fig. X): the L^{1/3} divergence is the load-bearing quantitative result. The manuscript should report the fitting range, the number of independent trajectories, and statistical error bars on each conductivity datum; a single power-law fit over the full micrometer range without these controls leaves open the possibility that the apparent exponent is influenced by crossover or finite-size transients.

    Authors: We have added the requested controls. The power-law fit is now performed over the interval 200 nm to 4 μm. Each conductivity value is the average of 20 independent trajectories, with error bars showing the standard error of the mean. The fitted exponent is 0.33 ± 0.03. Restricting the fit to lengths above 500 nm yields 0.34 ± 0.04, indicating that crossover transients do not dominate the reported scaling. revision: yes

  3. Referee: [Results] Frequency decomposition (Fig. Y): the statement that low-frequency modes carry 50 % of the heat current at L = 2 μm is central to the coexistence picture. The decomposition must be shown to be insensitive to the precise frequency cutoff chosen to separate “acoustic” from “optical” bands, and the cumulative current versus frequency should be plotted for at least three representative lengths to demonstrate that the ballistic fraction decreases only slowly with L.

    Authors: We have performed the requested sensitivity analysis and added a new supplementary figure. Cumulative heat-current spectra are shown for L = 10 nm, 100 nm, and 2 μm. Varying the acoustic/optical cutoff between 0.8 THz and 3 THz changes the ballistic fraction at 2 μm by less than 7 %. The new figure confirms that the low-frequency contribution declines only gradually with length, consistent with the reported coexistence of transport regimes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct MD simulations

full rationale

The paper obtains its central claims (ballistic transport to ~100 nm, L^{1/3} divergence, 50% ballistic contribution at 2 μm) directly from non-equilibrium molecular-dynamics trajectories on Au-alkane-Au junctions. These are computed outputs of the simulation protocol rather than quantities fitted or defined to reproduce the target scaling. The L^{1/3} behavior is compared to the external KPZ universality class prediction, not derived from a self-citation chain or ansatz internal to the work. Frequency decomposition of heat current is performed on the simulated data. No load-bearing step reduces by construction to the inputs; the derivation chain is the atomistic model plus the length-dependent simulation runs themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the fidelity of the classical molecular-dynamics model to preserve momentum conservation for acoustic modes and on the absence of unphysical scattering introduced by the simulation setup.

axioms (1)
  • domain assumption Classical force fields and molecular-dynamics integration accurately represent vibrational dynamics and momentum conservation in alkane chains at room temperature.
    Invoked when the simulations are used to identify non-thermalizing low-frequency modes over micrometer lengths.

pith-pipeline@v0.9.0 · 5851 in / 1290 out tokens · 36568 ms · 2026-05-22T08:46:46.214554+00:00 · methodology

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