Simple formulas of directional amplification from non-Bloch band theory

Abstract

Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is complicated by the high sensitivity of energy spectrums to boundary conditions, which invalidates the straightforward generalization of Hermitian formulas. Here, based on the non-Bloch band theory, we obtain simple Green's function formulas of general one-dimensional non-Hermitian bands. Furthermore, in the large-size limit, these formulas dramatically reduce to finding the roots of a simple algebraic equation. As an application, our formulation provides the desirable formulas for the defining quantities, the gain and directionality, of directional amplification. Thus, our formulas provide an efficient guide for designing directional amplifiers.

11 pages, 7 figures, including Supplemental Material

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• Exceptional Bound States and negative Entanglement Entropy
• Quantized classical response from spectral winding topology
• Exact solution of single impurity problem in non-reciprocal lattices: impurity induced size-dependent non-Hermitian skin effect
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
• Zoology of non-Hermitian spectra and their graph topology
• Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
• Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification
• Connections between the Open-boundary Spectrum and Generalized Brillouin Zone in Non-Hermitian Systems
• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
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• Dissipative Spin-wave Diode and Nonreciprocal Magnonic Amplifier
• Non-Hermitian boundary spectral winding
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• Manipulating non-Hermitian skin effect via electric fields
• Anatomy of open-boundary bulk in multiband non-Hermitian systems
• Giant Emitters in a Structured Bath with Non-Hermitian Skin Effect
• Edge theory of non-Hermitian skin modes in higher dimensions
• Direction reversal of non-Hermitian skin effect via coherent coupling
• Green's functions of multiband non-Hermitian systems
• Universal scalefree non-Hermitian skin effect near the Bloch point
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Non-Bloch band theory for non-Hermitian continuum systems
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Exact formulas of the end-to-end Green's functions in non-Hermitian systems
• Localized states and skin effect around non-Hermitian impurities in tight-binding models
• Steady-state edge burst: From free-particle systems to interaction-induced phenomena
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Exponentially Enhanced non-Hermitian Cooling
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Point-Gap Bound States in Non-Hermitian Systems
• Optomechanically induced transparency and directional amplification in a non-Hermitian optomechanical lattice
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
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• Constraints of internal symmetry on the non-Hermitian skin effect and bidirectional skin effect under the action of the Hermitian conjugate of time-reversal symmetry
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Complex semiclassical theory for non-Hermitian quantum systems
• Effective impurity behavior emergent from non-Hermitian proximity effect
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
• Dynamics in non-Hermitian systems with nonreciprocal coupling
• Symmetry classes of dissipative topological insulators with edge dark state
• Unconventional and robust light-matter interactions based on the non-Hermitian skin effect
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• Entangelment Entropy on Generalized Brillouin Zone
• Non-Hermitian physics of levitated nanoparticle array
• Emergent $\mathcal{P}\mathcal{T}$-symmetry breaking of collective modes with topological critical phenomena
• Anomalous hybridization of spectral winding topology in quantized steady-state responses
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Formal Green's function theory in non-Hermitian lattice systems
• Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
• Abnormal Frequency Response Determined by Saddle Points in Non-Hermitian Crystal Systems
• Inverse Design of Winding Tuple for Non-Hermitian Topological Edge Modes
• Real-time edge dynamics of non-Hermitian lattices
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• Non-Hermitian Hopf insulators
• Topological and fractal defect states in non-Hermitian lattices
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Beyond characteristic equations: A unified one-dimensional non-Bloch band theory via wavefunction data
• Scaling rule in critical non-Hermitian skin effect
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems
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• Topology of the generalized Brillouin zone of one-dimensional models
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field