Quasi-Non-Hermitian Edge Bursts Induced by Nonuniform Loss

This paper investigates how spatially nonuniform loss (dissipation) influences non-Hermitian boundary phenomena, specifically the non-Hermitian edge burst (NHEB). While the conventional NHEB is typically attributed to the interplay between the non-Hermitian skin effect (NHSE) and a gapless imaginary spectrum, the authors explore whether nonuniform loss alone can generate similar boundary-localized loss anomalies in the absence of the NHSE.

The researchers analyze a one-dimensional non-Hermitian tight-binding model consisting of two coupled sublattice chains. Non-Hermiticity is introduced via position-dependent imaginary on-site potentials on one sublattice, while magnetic flux is introduced via Peierls substitution to control the NHSE. The authors quantify the NHSE using the mean inverse participation ratio (MIPR) and evaluate the dynamical behavior of a quantum walker to identify the emergence of edge bursts under varying flux and loss profiles.

The study identifies a phenomenon termed the quasi-non-Hermitian edge burst (quasi-NHEB). Unlike the conventional NHEB, which requires the NHSE, the quasi-NHEB emerges at zero magnetic flux where the NHSE is absent. The authors demonstrate that this effect is driven by the loss gradient rather than the skin effect. Furthermore, they show that the quasi-NHEB follows a distinct bulk-edge scaling relation compared to the conventional NHEB, and that nonuniform loss can partially decouple spectral structure from eigenstate localization.

This work expands the understanding of non-Hermitian boundary phenomena by showing that spatially structured dissipation serves as an independent control mechanism. By demonstrating that boundary-localized loss anomalies can exist without the NHSE, the authors provide a broader platform for engineering non-Hermitian systems, offering new possibilities for controlling quantum transport and dissipation in open systems.