Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems

Abstract

In this paper, 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 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.

24 pages, 11 figures

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• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Edge theory of non-Hermitian skin modes in higher dimensions
• Non-Hermitian Skin Effect in Periodically-Driven Dissipative Ultracold Atoms
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Point-Gap Bound States in Non-Hermitian Systems
• Observation of Impurity-Induced Scale-Free Localization in a Disordered Non-Hermitian Electrical Circuit
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Versatile Control of Nonlinear Topological States in Non-Hermitian Systems
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
• Interaction-Induced Second-Order Skin Effect
• Chiral-Extended Photon-Emitter Dressed States in Non-Hermitian Topological Baths
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Loss-induced universal one-way transport in periodically driven systems
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Topological Dynamics and Correspondences in Composite Exceptional Rings
• Non-Hermitian gravitational effects on Bose-Einstein condensate
• Robustness of tripartite entangled states in passive PT-symmetric qubits
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems