Dynamical Poles in Non-Hermitian Impurity Scattering

• URL: http://arxiv.org/abs/2604.12939v1
• Date: Tue, 14 Apr 2026 16:29:05 GMT
• Title: Dynamical Poles in Non-Hermitian Impurity Scattering
• Abstract summary: In Hermitian impurity scattering, each isolated late-time exponential is the fingerprint of a bound state.<n>We show that this correspondence breaks down in non-Hermitian bands.<n>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.
• Score: 16.562827543427623
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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