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arxiv: 2604.18990 · v2 · submitted 2026-04-21 · 🪐 quant-ph

Scale-Free Response with Directional Amplification in Critical Non-Hermitian Systems

Kunling Zhou , Zihe Yang , Bowen Zeng , Yong Hu This is my paper

Pith reviewed 2026-05-10 02:58 UTC · model grok-4.3

classification 🪐 quant-ph
keywords non-Hermitian skin effectHatano-Nelson modelscale-free responsedirectional amplificationtopological winding numberperturbed open boundary conditionsGreen's functionfinite-size effects
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The pith

Perturbed open boundaries in the Hatano-Nelson model produce scale-free directional amplification characterized by a winding number.

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

The paper establishes that applying perturbed open boundary conditions to the Hatano-Nelson model yields a directional response that amplifies signals from one end to the other without depending on the chain length. This scale-free behavior stems from a first-order boundary effect and is topologically characterized by a winding number computed on a continuous generalization of the finite-size Brillouin zone. A reader would care because standard non-Hermitian amplification changes sharply with size or disorder, while this version remains stable and thus more feasible for devices. The work focuses on the end-to-end Green's function as the observable that benefits from the robustness.

Core claim

In the Hatano-Nelson model under perturbed open boundary conditions, the system exhibits a scale-free, topological, and directionally amplified response. This response is attributed to the first order boundary effect and characterized by a winding number defined on a continuous generalization of the finite-size Brillouin zone, a concept introduced in this work. Such scale-free behavior endows the end-to-end Green's function with significant robustness and makes it promising for practical applications.

What carries the argument

The first-order boundary effect under perturbed open boundary conditions, which produces size-independent amplification, together with the winding number defined on the continuous generalization of the finite-size Brillouin zone.

If this is right

  • The end-to-end Green's function becomes robust against variations in system size.
  • The directional amplification factor stays stable under local disorder.
  • Topological characterization remains valid for finite systems with the introduced boundary perturbations.
  • The response gains practical viability for implementations where exact length control is difficult.

Where Pith is reading between the lines

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

  • The same boundary perturbation strategy might produce analogous scale-free effects in other non-Hermitian lattice models.
  • The continuous finite-size Brillouin zone construction could be applied to analyze topology in additional finite non-Hermitian settings.
  • Photonic or acoustic lattice experiments could directly measure the predicted robustness of the amplification.
  • Testing the effect of higher-order boundary perturbations would clarify the range where scale-freeness holds.

Load-bearing premise

The boundary perturbation must create a true first-order effect that eliminates size dependence in the amplification without introducing other length scales or dependencies that the new winding number definition fails to capture.

What would settle it

Direct computation of the end-to-end Green's function across multiple chain lengths showing that the amplification factor changes by more than a small constant factor when length varies, or the winding number failing to match the observed direction and magnitude of amplification.

Figures

Figures reproduced from arXiv: 2604.18990 by Bowen Zeng, Kunling Zhou, Yong Hu, Zihe Yang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

The non-Hermitian skin effect can lead to directional amplification of response, with the associated end-to-end Green's function generally exhibiting size dependence. Any deviation in length or local disorder can drastically alter the amplification factor, rendering the response fragile in practical implementations. In this work, we identify a new type of scale-free, topological, and directionally amplified response in a Hatano-Nelson model under perturbed open boundary conditions. The scale-free response can be attributed to the first order boundary effect and characterized by a winding number defined on a continuous generalization of the finite-size Brillouin zone-a concept introduced in this work. Such scale-free behavior endows the end-to-end Green's function with significant robustness and making it promising for practical applications.

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.

Circularity Check

0 steps flagged

No significant circularity; derivation relies on introduced concept without reduction to inputs by construction.

full rationale

The paper introduces a continuous generalization of the finite-size Brillouin zone as a new concept and defines a winding number on it to characterize the scale-free response attributed to first-order boundary effects in the perturbed Hatano-Nelson model. No load-bearing steps reduce by definition, fitting, or self-citation chain to the target claim itself. The scale-free property is presented as following from the boundary effect and topology, with the new coordinate system serving as an analytical tool rather than a tautological redefinition. This is the common honest case of a self-contained derivation against external benchmarks like standard non-Hermitian skin effect.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only; no explicit free parameters or standard axioms listed. One new conceptual entity is introduced.

invented entities (1)
  • continuous generalization of the finite-size Brillouin zone no independent evidence
    purpose: To define a winding number that characterizes the scale-free topological response
    Introduced in this work per the abstract to handle finite-size effects in the non-Hermitian model.

pith-pipeline@v0.9.0 · 5419 in / 1152 out tokens · 82442 ms · 2026-05-10T02:58:08.933806+00:00 · methodology

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Reference graph

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