Dynamical Poles in Non-Hermitian Impurity Scattering

TL;DR

This paper reveals that in non-Hermitian impurity scattering, late-time dynamics are governed by complex frequencies called dynamical poles, which differ from static bound states and are determined by the Green's function's analytic structure.

Contribution

It introduces the concept of dynamical poles in non-Hermitian systems and shows their role in organizing real-time impurity scattering beyond static bound states.

Findings

Dynamical poles can exist without static bound states.

Late-time signals are controlled by complex frequencies from Green's function.

The real-time Green's function structure governs non-Hermitian impurity scattering.

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.