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arxiv: 2604.12939 · v1 · submitted 2026-04-14 · ❄️ cond-mat.mes-hall · cond-mat.dis-nn· cond-mat.quant-gas· quant-ph

Dynamical Poles in Non-Hermitian Impurity Scattering

Ao Yang , Kai Zhang , Chen Fang This is my paper

Pith reviewed 2026-05-10 14:12 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.dis-nncond-mat.quant-gasquant-ph
keywords non-Hermitianimpurity scatteringdynamical polesGreen's functionbound stateslattice modelsreal-time dynamicsanalytic continuation
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The pith

In non-Hermitian lattices, late-time impurity signals arise from dynamical poles in the real-time Green's function rather than static bound states.

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

In Hermitian systems, each isolated late-time exponential decay after impurity scattering directly fingerprints a bound state. This paper shows the correspondence breaks down for non-Hermitian bands. The late-time signal is instead controlled by isolated complex frequencies called dynamical poles, which are selected by the analytic continuation of the Green's function that applies to real-time dynamics. Dynamical poles need not match static bound states found from the eigenvalue problem; a pole can exist without a bound-state counterpart, and a bound state can remain invisible in the dynamics. The incoherent remainder of the signal is set by the complex edges of the continuum, so the real-time analytic structure of the Green's function organizes the scattering.

Core claim

For a single impurity in a non-Hermitian lattice, the late-time signal is controlled by isolated complex frequencies selected by the analytic continuation of the Green's function relevant to real-time dynamics, which are termed dynamical poles. These dynamical poles need not coincide with static bound states: one may appear without any bound-state counterpart, while a static bound state may be dynamically invisible. The remainder of the signal is an incoherent background set by complex continuum edges. This establishes that the real-time analytic structure of the Green's function, not the static eigenvalue problem alone, organizes non-Hermitian impurity scattering.

What carries the argument

Dynamical poles: isolated complex frequencies selected by the analytic continuation of the Green's function that is relevant to real-time dynamics.

If this is right

  • Late-time exponential decays become fingerprints of dynamical poles instead of bound states.
  • A dynamical pole can exist without any corresponding static bound state.
  • A static bound state can be invisible to real-time dynamics.
  • The incoherent background signal is fixed by the complex edges of the continuum.
  • Scattering structure is determined by the real-time analytic properties of the Green's function.

Where Pith is reading between the lines

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

  • This separation may require new numerical methods that focus on time-domain continuations rather than static spectra in non-Hermitian models.
  • Experimental probes of relaxation or transport in open systems could miss equilibrium features that are dynamically invisible.
  • Material design could target dynamical poles independently to control late-time responses without altering static spectra.
  • The same distinction might appear in multi-impurity or higher-dimensional non-Hermitian setups and could be checked in concrete lattice calculations.

Load-bearing premise

The analytic continuation of the Green's function chosen for real-time dynamics correctly selects the physically relevant poles that dominate late-time behavior.

What would settle it

A calculation or measurement in which the observed late-time decay rates fail to match the imaginary parts of the dynamical poles predicted by the Green's function continuation, or in which a known static bound state visibly contributes to the dynamics.

Figures

Figures reproduced from arXiv: 2604.12939 by Ao Yang, Chen Fang, Kai Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) Red solid ellipse: spectrum of the perturbed HN model. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Illustration of the branch-point criterion for ˜g [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a1) Perturbed OBC spectrum of the model in Fig. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

In Hermitian impurity scattering, each isolated late-time exponential is the fingerprint of a bound state. We show that this correspondence breaks down in non-Hermitian bands. For a single impurity in a non-Hermitian lattice, the late-time signal is controlled by isolated complex frequencies selected by the analytic continuation of the Green's function relevant to real-time dynamics, which we term dynamical poles (DPs). DPs need not coincide with static bound states: one may appear without any bound-state counterpart, while a static bound state may be dynamically invisible. The remainder of the signal is an incoherent background set by complex continuum edges. Our results establish that the real-time analytic structure of the Green's function, not the static eigenvalue problem alone, organizes non-Hermitian impurity scattering.

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

0 major / 3 minor

Summary. The paper claims that the standard correspondence between isolated late-time exponentials and bound states in Hermitian impurity scattering breaks down for non-Hermitian lattices. For a single impurity, late-time dynamics are instead controlled by isolated complex frequencies—termed dynamical poles (DPs)—selected via analytic continuation of the Green's function appropriate to real-time evolution. These DPs need not coincide with static bound states obtained from the eigenvalue problem: a DP can exist without a static counterpart, and a static bound state can be dynamically invisible. The residual signal forms an incoherent background set by the complex continuum edges. The central organizing principle is therefore the real-time analytic structure of the Green's function rather than the static spectrum alone.

Significance. If the derivations and examples hold, the result is significant for non-Hermitian physics. It demonstrates that real-time dynamics in impurity scattering are governed by a distinct analytic continuation of the Green's function, not reducible to the static bound-state problem. This distinction is relevant to open quantum systems, PT-symmetric lattices, and experimental platforms such as photonic or mechanical arrays where non-Hermiticity is engineered. The introduction of dynamical poles as a concrete, selectable feature of the Green's function provides a falsifiable organizing principle that could guide both theory and measurement of late-time signals in non-Hermitian bands.

minor comments (3)
  1. §2.2, around Eq. (8): the branch-cut prescription for the continuum contribution is stated but the explicit contour deformation that isolates the dynamical pole is not shown; adding a short diagram or one-line justification would strengthen the separation between pole and background.
  2. Figure 3 caption: the time-domain plot overlays the full signal, the DP contribution, and the continuum; labeling the decay rates extracted from each component would make the numerical confirmation of the analytic claim immediate.
  3. §4.1: the statement that a static bound state can be 'dynamically invisible' is illustrated for one parameter set; a brief remark on the measure of parameter space where this occurs would clarify how generic the phenomenon is.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading and positive evaluation of our manuscript. Their summary accurately reflects the central claims regarding the distinction between dynamical poles and static bound states in non-Hermitian impurity scattering. As no specific major comments are provided in the report, we have no individual points to rebut or revise at this stage. We remain available to incorporate any minor revisions requested by the editor.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper derives the distinction between dynamical poles (selected via analytic continuation of the Green's function for real-time dynamics) and static bound states through explicit construction of the continuation, demonstration that continuum contributions decay faster, and concrete lattice-model examples of DPs without static counterparts (and vice versa). These steps are supported by derivations and numerical checks internal to the models considered, with no reduction of the central claim to self-definition, fitted inputs renamed as predictions, or load-bearing self-citations. The selection rule is the derived quantity rather than a tautological input, rendering the argument self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on the assumption that real-time dynamics are captured by a specific analytic continuation of the Green's function and on the introduction of dynamical poles as the organizing objects.

axioms (1)
  • domain assumption The real-time dynamics of the impurity problem are determined by the analytic continuation of the Green's function into the complex frequency plane.
    Invoked in the abstract to define dynamical poles and select which poles control late-time behavior.
invented entities (1)
  • dynamical poles (DPs) no independent evidence
    purpose: Isolated complex frequencies that govern late-time exponential signals in non-Hermitian impurity scattering.
    New term introduced to label the poles selected by real-time analytic continuation.

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