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.

arXiv comment24 pages, 11 figures

References in corpus (59)

• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Chern bands
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Non-Hermitian Topology and Exceptional-Point Geometries
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Biorthogonal Quantum Mechanics
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Critical non-Hermitian Skin Effect
• Universal non-Hermitian skin effect in two and higher dimensions
• Reciprocal skin effect and its realization in a topolectrical circuit
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Higher-order non-Hermitian skin effect
• Odd elasticity
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Angle-resolved photoemission spectroscopy and its application to topological materials
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Non-Hermitian band topology and skin modes in active elastic media
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Simple formulas of directional amplification from non-Bloch band theory
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Helical damping and anomalous critical non-Hermitian skin effect
• Exceptional Topological Insulators
• Topological Field Theory of Non-Hermitian Systems
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• DMFT reveals the non-Hermitian topology in heavy-fermion systems
• Magnetic suppression of non-Hermitian skin effects
• Quantized classical response from spectral winding topology
• Non-Bloch bands in two-dimensional non-Hermitian systems
• Non-Hermitian Topological Metamaterials with Odd Elasticity
• Nielsen-Ninomiya Theorem with Bulk Topology: Duality in Floquet and Non-Hermitian Systems
• A non-Hermitian optical atomic mirror
• Geometry-dependent skin effects in reciprocal photonic crystals
• Nonreciprocal Charge and Spin Transport Induced by Non-Hermitian Skin Effect in Mesoscopic Heterojunctions
• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
• Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial
• Non-Hermitian invisibility in tight-binding lattices
• Self-healing of non-Hermitian topological skin modes

Cited by in corpus (26)

• Observation of dynamical degeneracy splitting for the non-Hermitian skin effect
• 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
• Point-Gap Bound States in Non-Hermitian Systems
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• 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
• Interaction-Induced Second-Order Skin Effect
• Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
• Chiral-Extended Photon-Emitter Dressed States in Non-Hermitian Topological Baths
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Loss-induced universal one-way transport in periodically driven systems
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Topological Dynamics and Correspondences in Composite Exceptional Rings
• Dynamical transition in non-Hermitian Chern insulator
• 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