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arxiv: 2212.06235 · v2 · pith:GTE52H37new · submitted 2022-12-12 · ⚛️ physics.optics · cond-mat.dis-nn· nlin.CD

Wave-packet spreading in the disordered and nonlinear Su-Schrieffer-Heeger chain

Bertin Many Manda , Vassos Achilleos , Olivier Richoux , Charalampos Skokos , Georgios Theocharis This is my paper

Pith reviewed 2026-05-25 08:56 UTC · model grok-4.3

classification ⚛️ physics.optics cond-mat.dis-nnnlin.CD
keywords wave-packet spreadingSu-Schrieffer-Heeger chaindisordered nonlinear systemstopological phasesAnderson localizationmode-mode interactionsasymptotic dynamics
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The pith

Nonlinearity erases topological distinctions and uniformizes asymptotic wave-packet spreading in the disordered Su-Schrieffer-Heeger chain.

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

The paper numerically studies the long-time evolution of a single-site wave-packet excitation in a disordered nonlinear Su-Schrieffer-Heeger model. In the linear regime, anomalous diffusion occurs near the transition between topological phases while Anderson localization appears inside each phase. Adding on-site nonlinearity introduces mode-mode interactions that remove the anomalous diffusion feature. Direct simulations then show that the characteristics of the asymptotic spreading become identical across the entire parameter space studied. A sympathetic reader would care because the result indicates that nonlinear interactions can override the dynamical signatures of topology.

Core claim

In the linear regime, as the parameters controlling the topology of the system are varied, the transition between two different topological phases is preceded by an anomalous diffusion, in contrast to Anderson localization within these topological phases. In the presence of on-site nonlinearity this feature is lost due to mode-mode interactions. Direct numerical simulations reveal that the characteristics of the asymptotic nonlinear wave-packet spreading are the same across the whole studied parameter space.

What carries the argument

Mode-mode interactions generated by on-site nonlinearity, which eliminate the anomalous diffusion near topological transitions and produce uniform spreading.

If this is right

  • The transition between topological phases no longer produces anomalous diffusion once nonlinearity is introduced.
  • Asymptotic spreading characteristics become independent of the specific topological phase or parameter values.
  • Reliable nonlinear topological markers must incorporate the effects of mode-mode interactions.

Where Pith is reading between the lines

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

  • The same loss of topological distinction may occur in other one-dimensional nonlinear topological chains with disorder.
  • Experimental platforms such as nonlinear photonic lattices could directly measure whether spreading remains uniform when topology is varied.
  • Higher-dimensional extensions of the model might reveal whether the uniformity persists or breaks down with increased connectivity.

Load-bearing premise

The numerical integration reaches true asymptotic long-time behavior without finite-time or finite-size artifacts dominating the observed spreading exponents.

What would settle it

Observing distinctly different spreading exponents in different topological phases after much longer simulation times or in substantially larger lattices would show the claimed uniformity is not reached.

Figures

Figures reproduced from arXiv: 2212.06235 by Bertin Many Manda, Charalampos Skokos, Georgios Theocharis, Olivier Richoux, Vassos Achilleos.

Figure 1
Figure 1. Figure 1: Schematic representation of the disordered SSH [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Topological phase diagram of the disordered [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Time evolution of the averaged amplitude distribution, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Time evolution of the moments (a) M1, (b) M2, (c) M3 and (d) M4 [Eq. (12)], averaged over 9000 configurations of disorder, for the disordered SSH chain of Eq. (1). The blue (b) and red (r) colored curves correspond to (W = 3, m = 0.6) and (W = 6., m = 0.6) respectively. The error bars of the same color as the curves, denote one standard deviation. On the other hand, the peculiar spreading at the topo￾logic… view at source ↗
Figure 5
Figure 5. Figure 5: Dependence of (a) σ 2M1(t) and (b) σ 2M2(t) (c) (σ 4M3(t))1/2 and (d) (σ 6M4(t))1/4 on ln t, ln t/σ, ln t and ln t respectively for several sets of parameters along the topological transition line, depicted in the top panel. The moments are averaged over 9000 configurations of disorder. In addition, σ in each case was numerically computed and reported in the inset of [PITH_FULL_IMAGE:figures/full_fig_p007… view at source ↗
Figure 7
Figure 7. Figure 7: The time evolution of the second moment M2 of the wave-packet for different (W, m) parameter setups of the nonlinear system of Eq. (17) with (a)-(b) g = 3 and (c)- (d) g = 30. Panels (a) and (c) correspond to the (W = 2.04, m = 0.6), (W = 2.04, m = 1.15) and (W = 2.04, m = 1.6) cases [blue (b), green (g) and red (r) curves respectively] and panels (b) and (d) to the ones with (W = 3.0, m = 0.6), (W = 4, m … view at source ↗
Figure 6
Figure 6. Figure 6: Average amplitude distribution h|ψn| 2 i at time t ≈ 105 [dotted curves] and t ≈ 106 [continuous curves] for the disordered nonlinear SSH chain [Eq. (17)], for (a) the case (W = 2.04, m = 0.6) with g = 0 [blue (b) curves] g = 3.0 [green (g) curves] and g = 30 [red (r) curves] and (b) the case (W = 1.0, m = 0.6) with g = 0 [blue (b) curves], g = 1 [green (g) curves] and g = 5 [red (r) curves]. The |φn| 2 va… view at source ↗
Figure 8
Figure 8. Figure 8: Sections of the topological phase diagram at (a) [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Results for representative configurations of disor [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
read the original abstract

We numerically investigate the characteristics of the long-time dynamics of a single-site wave-packet excitation in a disordered and nonlinear Su-Schrieffer-Heeger model. In the linear regime, as the parameters controlling the topology of the system are varied, we show that the transition between two different topological phases is preceded by an anomalous diffusion, in contrast to Anderson localization within these topological phases. In the presence of on-site nonlinearity this feature is lost due to mode-mode interactions. Direct numerical simulations reveal that the characteristics of the asymptotic nonlinear wave-packet spreading are the same across the whole studied parameter space. Our findings underline the importance of mode-mode interactions in nonlinear topological systems, which must be studied in order to define reliable nonlinear topological markers.

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

2 major / 1 minor

Summary. The manuscript numerically investigates long-time wave-packet spreading in a disordered nonlinear Su-Schrieffer-Heeger chain. In the linear regime it reports anomalous diffusion near the topological transition (contrasted with Anderson localization inside the phases); with on-site nonlinearity this feature disappears and the asymptotic spreading characteristics become identical across the studied parameter space. The central claim is that mode-mode interactions erase the linear-regime signature, implying that reliable nonlinear topological markers must account for these interactions.

Significance. If the numerical uniformity holds in the true asymptotic limit, the result would demonstrate that nonlinearity can wash out linear topological signatures in disordered systems, providing a concrete example of how mode coupling alters spreading diagnostics. This is a modest but useful observation for the nonlinear topological physics literature; the work contains no machine-checked proofs or parameter-free derivations.

major comments (2)
  1. [Abstract and numerical-results section] Abstract and numerical-results section: the claim that 'the characteristics of the asymptotic nonlinear wave-packet spreading are the same across the whole studied parameter space' rests on direct numerical simulations, yet the manuscript supplies no information on the integration algorithm, maximum times reached, system sizes, number of disorder realizations, or any convergence tests (e.g., doubling integration time or lattice length). This is load-bearing for the central claim because, near the topological transition, linear localization lengths diverge and relaxation times may be parametrically longer; without explicit checks that the reported spreading diagnostics are stationary with respect to these parameters, apparent uniformity could be a finite-time artifact.
  2. [Numerical diagnostics paragraph] Numerical diagnostics paragraph: the manuscript does not specify how the spreading exponents (or other quantitative measures of 'characteristics') are extracted or averaged, nor does it show that the same diagnostic yields consistent values when the nonlinearity strength or disorder variance is varied while remaining inside the claimed uniform regime. This omission prevents independent assessment of whether the uniformity is robust or an artifact of the chosen observable.
minor comments (1)
  1. [Abstract] The abstract states that the linear-regime anomalous diffusion 'precedes' the transition; a brief clarification of the precise parameter path taken through the topological phase diagram would help readers map the reported behavior onto standard SSH phase boundaries.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and the specific comments on the numerical presentation. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and numerical-results section] Abstract and numerical-results section: the claim that 'the characteristics of the asymptotic nonlinear wave-packet spreading are the same across the whole studied parameter space' rests on direct numerical simulations, yet the manuscript supplies no information on the integration algorithm, maximum times reached, system sizes, number of disorder realizations, or any convergence tests (e.g., doubling integration time or lattice length). This is load-bearing for the central claim because, near the topological transition, linear localization lengths diverge and relaxation times may be parametrically longer; without explicit checks that the reported spreading diagnostics are stationary with respect to these parameters, apparent uniformity could be a finite-time artifact.

    Authors: We agree that the absence of these details weakens the manuscript. The revised version will contain a new 'Numerical Methods' subsection that specifies the integration algorithm, the lattice sizes employed, the longest evolution times reached, the number of disorder realizations, and the convergence tests (doubling both integration time and system size) that were used to confirm stationarity of the spreading diagnostics. These additions will directly address the concern that the reported uniformity might be a finite-time artifact near the topological transition. revision: yes

  2. Referee: [Numerical diagnostics paragraph] Numerical diagnostics paragraph: the manuscript does not specify how the spreading exponents (or other quantitative measures of 'characteristics') are extracted or averaged, nor does it show that the same diagnostic yields consistent values when the nonlinearity strength or disorder variance is varied while remaining inside the claimed uniform regime. This omission prevents independent assessment of whether the uniformity is robust or an artifact of the chosen observable.

    Authors: We accept this point. The revised manuscript will explicitly describe the procedure used to extract and average the spreading exponents (or other diagnostics) and will include additional checks demonstrating that the same diagnostic remains consistent when nonlinearity strength and disorder variance are varied inside the claimed uniform regime. This will allow independent verification of robustness. revision: yes

Circularity Check

0 steps flagged

No circularity: purely numerical observations with no derivation chain

full rationale

The paper consists entirely of direct numerical simulations of wave-packet dynamics in a nonlinear SSH chain. No analytical derivations, fitted parameters presented as predictions, self-definitional relations, or load-bearing self-citations appear in the abstract or described content. The central claim—that asymptotic spreading characteristics become uniform under nonlinearity—is an empirical observation from simulations, not a result obtained by reducing equations to their own inputs. The work is therefore self-contained against external benchmarks with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the chosen numerical scheme faithfully captures long-time asymptotic spreading without artifacts; no new entities or fitted constants are introduced beyond standard model parameters.

axioms (1)
  • domain assumption Standard numerical time-stepping of the discrete nonlinear Schrödinger equation on a finite lattice reaches asymptotic regime within simulated times.
    Implicit in the statement that asymptotic characteristics are observed and uniform.

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discussion (0)

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