Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems.

In this Letter, we introduce the concept of dynamical degeneracy splitting to describe the anisotropic decay behaviors in non-Hermitian systems. We demonstrate that systems with dynamical degeneracy splitting exhibit two distinctive features: (i) the system shows frequency-resolved non-Hermitian skin effect; (ii) Green's function exhibits anomalous behavior at given frequency, leading to uneven broadening in spectral function and anomalous scattering. As an application, we propose directional invisibility based on wave packet dynamics to investigate the geometry-dependent skin effect in higher dimensions. Our work elucidates a faithful correspondence between non-Hermitian skin effect and Green's function, offering a guiding principle for exploration of novel physical phenomena emerging from this effect.