Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics

Abstract

Non-Hermitian skin effect, namely that the eigenvalues and eigenstates of a non-Hermitian tight-binding Hamiltonian have significant differences under open or periodic boundary conditions, is a remarkable phenomenon of non-Hermitian systems. Inspired by the presence of the non-Hermitian skin effect, we study the evolution of wave-packets in non-Hermitian systems, which can be determined using the single-particle Green's function. Surprisingly, we find that in the thermodynamical limit, the Green's function does not depend on boundary conditions, despite the presence of skin effect. We proffer a general proof for this statement in arbitrary dimension with finite hopping range, with an explicit illustration in the non-Hermitian Su-Schrieffer-Heeger model. We also explore its applications in non-interacting open quantum systems described by the master equation, where we demonstrate that the evolution of the density matrix is independent of the boundary condition.

arXiv comment5 pages, 3 figures

References in corpus (62)

• Topological Insulators
• Topological insulators and superconductors
• Topological Photonics
• Classification of topological quantum matter with symmetries
• Edge states and topological invariants of non-Hermitian systems
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Non-Hermitian Physics
• Topological Insulator Materials
• Colloquium: Topological Band Theory
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• 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
• Spawning rings of exceptional points out of Dirac cones
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• 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
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• 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 topology and its bulk-edge correspondence in an active mechanical metamaterial
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Exceptional Points of Non-hermitian Operators
• Non-Hermitian Topological Invariants in Real Space
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Reciprocal skin effect and its realization in a topolectrical circuit
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• New topological invariants in non-Hermitian systems
• 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
• Topological states of non-Hermitian systems
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Simultaneous Observation of Topological Edge State and Exceptional Point in an Open and Non-Hermitian System
• Observation of non-Bloch parity-time symmetry and exceptional points
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Topological phases and edge states in a non-Hermitian trimerized optical lattice
• Simple formulas of directional amplification from non-Bloch band theory
• Non-Hermitian Linear Response Theory
• Hall Conductance of a Non-Hermitian Chern Insulator
• Magnetotransport of dirty-limit van Hove singularity quasiparticles
• Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
• Observation of non-Hermitian topology with non-unitary dynamics of solid-state spins
• Quantized classical response from spectral winding topology
• Symmetry protected topological phases characterized by isolated exceptional points
• High order exceptional points in ultracold Bose gases
• Topological Phase Transition Independent of System Non-Hermiticity
• Symmetry-Protected Scattering in Non-Hermitian Linear Systems
• Untying links through anti-parity-time-symmetric coupling

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• Topological Non-Hermitian skin effect
• Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas
• Liouvillian Skin Effect in an Exactly Solvable Model
• Non-Hermitian skin effect as an impurity problem
• Engineering Non-Hermitian Skin Effect with Band Topology in Ultracold Gases
• Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
• Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths
• Dynamic skin effects in non-Hermitian systems
• Bound states and photon emission in non-Hermitian nanophotonics
• Edge theory of non-Hermitian skin modes in higher dimensions
• Skin Effect in Quadratic Lindbladian Systems: an Adjoint Fermion Approach
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Space-Time Duality between Quantum Chaos and Non-Hermitian Boundary Effect
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Non-Bloch dynamics and topology in a classical non-equilibrium process
• Abnormal Frequency Response Determined by Saddle Points in Non-Hermitian Crystal Systems
• Real-time edge dynamics of non-Hermitian lattices
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Topology of the generalized Brillouin zone of one-dimensional models
• Anomalous Point-Gap Interactions Unveil the Mirage Bath
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
• Recurrence method in Non-Hermitian Systems