Exceptional Points of Non-hermitian Operators

Abstract

Exceptional points associated with non-hermitian operators, i.e. operators being non-hermitian for real parameter values, are investigated. The specific characteristics of the eigenfunctions at the exceptional point are worked out. Within the domain of real parameters the exceptional points are the points where eigenvalues switch from real to complex values. These and other results are exemplified by a classical problem leading to exceptional points of a non-hermitian matrix.

8 pages, Latex, four figures, submitted to EPJD

References in corpus (1)

• Observation of a Chiral State in a Microwave Cavity

Cited by in corpus (244)

• Non-Hermitian Physics
• The physics of exceptional points
• Loss-induced suppression and revival of lasing
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Pump-induced Exceptional Points in Lasers
• Shell Model in the Complex Energy Plane
• Sensing with exceptional surfaces: combining sensitivity with robustness
• Fast and Unconditional All-Microwave Reset of a Superconducting Qubit
• Spectral singularities and Bragg scattering in complex crystals
• Experimental observation of exceptional surface in synthetic dimensions with magnon polaritons
• Fundamental limits to optical response in absorptive systems
• Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope
• Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system
• Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators
• Coupling of eigenvalues of complex matrices at diabolic and exceptional points
• Fermion doubling theorems in 2D non-Hermitian systems for Fermi points and exceptional points
• Non-Hermitian Hamiltonians and no-go theorems in quantum information
• Observation of an exceptional point in a non-Hermitian metasurface
• Some remarks on 'superradiant' phase transitions in light-matter systems
• Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
• Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre
• Exceptional points in topological edge spectrum of PT symmetric domain walls
• Exceptional Topological Insulators
• Nonlinear modal interactions in parity-time ($\mathcal{P}\mathcal{T}$) symmetric lasers
• Non-Hermitian phase transition from a polariton Bose-Einstein condensate to a photon laser
• Spectral Singularities, Biorthonormal Systems, and a Two-Parameter Family of Complex Point Interactions
• Predicted Impacts of Proton Temperature Anisotropy on Solar Wind Turbulence
• Topological Modes in a Laser Cavity through Exceptional State Transfer
• Symmetry-protected zero-mode laser with a tunable spatial profile
• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• Resonance Phenomenon Related to Spectral Singularities, Complex Barrier Potential, and Resonating Waveguides
• Biorthogonal Quantum Systems
• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
• Parity-time symmetry in optical microcavity systems
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Dark state lasers
• Light transport in PT-invariant photonic structures with hidden symmetries
• Supersymetric laser arrays
• Achieving arbitrary polarization control using complex birefringent meta-materials
• Transport and spectral features in non-Hermitian open systems
• Fundamental limits for reciprocal and non-reciprocal non-Hermitian quantum sensing
• Spectral singularities in PT-symmetric periodic finite-gap systems
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation
• Theory of Exceptional Points of Degeneracy in Uniform Coupled-Waveguides and Balance of Gain and Loss
• Experimental realisation of $\mathcal{P}\mathcal{T}$-symmetric flat bands
• High order exceptional points in ultracold Bose gases
• Self-dual Spectral Singularities and Coherent Perfect Absorbing Lasers without PT-symmetry
• Non-Hermitian lattices with a flat band and polynomial power increase
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Coupled non-identical microdisks: avoided crossing of energy levels and unidirectional far-field emission
• Quasinormal modes and Purcell factors of coupled loss-gain resonators and index-modulated ring resonators near exceptional points
• Non-Hermitian degeneracy of two unbound states
• Classical and Quantum Dynamics of Higher-Derivative Systems
• Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism
• Fundamental limits to near-field optical response, over any bandwidth
• Discovery of exceptional points in the Bose-Einstein condensation of gases with attractive 1/r-interaction
• Transfer Matrices as Non-Unitary S-Matrices, Multimode Unidirectional Invisibility, and Perturbative Inverse Scattering
• Perfect State Transfer in PT-symmetric Non-Hermitian Networks
• Floquet exceptional points and chirality in non-Hermitian Hamiltonians
• Frequency locking and controllable chaos through exceptional point in optomechanics
• Disorder-induced exceptional points and nodal lines in Dirac superconductors
• Exceptional points-based optical amplifiers
• Optical lattices with exceptional points in the continuum
• Scattering in $\mathcal{P}\mathcal{T}$ and $\mathcal{R}\mathcal{T}$ Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension
• Highly Sensitive Coupled Oscillator Based on an Exceptional Point of Degeneracy and Nonlinearity
• Non-Hermitian sensing in the absence of exceptional points
• Non-Hermitian scattering on a tight-binding lattice
• Petermann factors and phase rigidities near exceptional points
• Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
• Contrasting Spectral Signatures and Sensitivities of CPA-Lasing in a $\mathcal{P}\mathcal{T}$-Symmetric Periodic Structure
• Optical Lattices with Higher-order Exceptional Points by Non-Hermitian Coupling
• Jamming anomaly in $\mathcal{P}\mathcal{T}$-symmetric systems
• Exceptional points of degeneracy and $\mathcal{P}\mathcal{T}$-symmetry in photonic coupled chains of scatterers
• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
• Response strengths of open systems at exceptional points
• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
• Non-Hermitian Stark Many-Body Localization
• Spectral Singularities of a General Point Interaction
• Fano resonance scattering in waveguide with an impedance boundary condition
• Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
• Cyclic permutation-time symmetric structure with coupled gain-loss microcavities
• Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
• Hermitian dynamics in a class of pseudo-Hermitian networks
• Exceptional points in anisotropic planar microcavities
• Hybridization and the origin of the Fano resonances in symmetric nanoparticle trimers
• A physical interpretation for the non-Hermitian Hamiltonian
• Asymmetric lasing at spectral singularities
• Spectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer
• Probability-preserving evolution in a non-Hermitian two-band model
• Exponentially-enhanced Quantum Non-Hermitian Sensing via Optimized Coherent Drive
• Universal phenomenology at critical exceptional points of nonequilibrium $O(N)$ models
• Complex magnetic monopoles, geometric phases and quantum evolution in vicinity of diabolic and exceptional points
• Multiparameter estimation perspective on non-Hermitian singularity-enhanced sensing
• Exceptional Points of Degeneracy Directly Induced by Space-Time Modulation of a Single Transmission Line
• Demonstration of a parity-time symmetry breaking phase transition using superconducting and trapped-ion qutrits
• Optical Reciprocity Induced Symmetry of the Scattering Eigenstates in Non-$\mathcal{P}\mathcal{T}$-Symmetric Heterostructures
• Kelvin-Helmholtz instability is the result of parity-time symmetry breaking
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Revisiting the hierarchical construction of higher-order exceptional points
• A brief review of hybrid skin-topological effect
• Higher-order Time-Symmetry-Breaking Phase Transition due to meeting of an Exceptional Point and Fano Resonance
• Exceptional points in coupled dissipative dynamical systems
• Exceptional points and photonic catastrophe
• Non-Hermitian BCS-BEC evolution with a complex scattering length
• Topological Microlaser with A non-Hermitian Topological Bulk
• Interacting non-Hermitian ultracold atoms in a harmonic trap: Two-body exact solution and high-order exceptional point
• Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction
• Shape-preserving beam transmission through non-Hermitian disordered lattices
• Chiral symmetry in non-Hermitian systems: product rule and Clifford algebra
• Quantum interference and exceptional points
• Fano-Feshbach resonances in two-channel scattering around exceptional points
• Exceptional Degeneracies in Traveling Wave Tubes with Dispersive Slow-Wave Structure Including Space-Charge Effect
• Loschmidt echo and fidelity decay near an exceptional point
• Machine learning non-Hermitian topological phases
• Experimental realization of stable exceptional chains protected by non-Hermitian latent symmetries unique to mechanical systems
• Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
• Anomalous Parity-Time Symmetry Transition away from an Exceptional Point
• Exceptional points in quantum and classical dynamics
• Inverse Vernier Effects in Coupled Lasers
• Quantum decay in a topological continuum
• Pontryagin-Optimal Control of a non-Hermitian Qubit
• The infinity-loop microresonator: A new integrated photonic structure working on an exceptional surface
• Non-Hermitian flatband generator in one dimension
• Absorption in atomic wires
• Symmetry protected exceptional points of interacting fermions
• Nonorthogonality constraints in open quantum and wave systems
• Scattering of partially coherent radiation by non-Hermitian localized structures having Parity-Time symmetry
• Scattering properties of anti-parity-time symmetric non-Hermitian system
• QT-Symmetry and Weak Pseudo-Hermiticity
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• Classical oscillator with position-dependent mass in a complex domain
• PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
• Dynamical encircling exceptional point in largely detuned multimode optomechanical system
• Degenerate perturbation theory in thermoacoustics: high-order sensitivities and exceptional points
• Fractional Josephson effect versus fractional charge in superconducting-normal metal hybrid circuits
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model
• A new perspective on the Fano absorption spectrum in terms of complex spectral analysis
• Virtual exceptional points in an electromechanical system
• Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas
• Quasinormal mode analysis of chiral power flow from linearly polarized dipole emitters coupled to index-modulated microring resonators close to an exceptional point
• High-order spectral singularity
• Non-hermiticity in spintronics: oscillation death in coupled spintronic nano-oscillators through emerging exceptional points
• Laser Mode Bifurcations Induced by $\mathcal{P}\mathcal{T}$-Breaking Exceptional Points
• Tweaking Spectral Topology and Exceptional Points by Nonlinearity in Non-Hermitian Polariton Systems
• Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems
• Universal conductance of a PT-symmetric Luttinger liquid after a quantum quench
• Observation of exceptional point in a PT broken non-Hermitian system simulated using a quantum circuit
• Solvable BCS-Hubbard Liouvillians in arbitrary dimensions
• Connecting active and passive $\mathcal{P}\mathcal{T}$-symmetric Floquet modulation models
• Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point
• Detecting the effects of quantum gravity with exceptional points in optomechanical sensors
• Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
• Moving along an exceptional surface towards a higher-order exceptional point
• Classification of multiple arbitrary-order non-Hermitian singularities
• Robust exceptional point of arbitrary order in coupled spinning cylinders
• Quantum tomography of a third-order exceptional point in a dissipative trapped ion
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
• Stochastic feedback control of quantum transport to realize a dynamical ensemble of two nonorthogonal pure states
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Analysis of Dirac exceptional points and their isospectral Hermitian counterparts
• Non-adiabatic transitions in a non-symmetric optical lattice
• Exceptional points of infinite order give a continuous spectrum
• Non-hermitian model for resonant cavities coupled by a chiral mirror
• Self-trapping and skin solitons in two-dimensional non-Hermitian lattices
• Oscillating potential well in complex plane and the adiabatic theorem
• Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
• Level attraction and exceptional points in a resonant spin-orbit torque system
• Excitation Transmission through a non-Hermitian traversable wormhole
• Resonance scattering and singularities of the scattering function
• Mode attraction in Floquet systems with memory: application to magnonics
• An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems
• Analogue Hawking radiation as a tunneling in a two-level $\mathcal{P}\mathcal{T}$-symmetric system
• Metastability and quantum coherence-assisted sensing in interacting parallel quantum dots
• Lasing at a Stationary Inflection Point
• Reconfiguration of quantum states in $\mathcal{P}T$-symmetric quasi-one dimensional lattices
• Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
• Super-enhanced Sensitivity in Non-Hermitian Systems at Infernal Points
• Probing localization properties of many-body Hamiltonians via an imaginary vector potential
• Proposal for measuring Newtonian constant of gravitation at an exceptional point in an optomechanical system
• PHOENIX -- Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions
• Physics of crypto-Hermitian and/or cryptosupersymmetric field theories
• Spin-dependent gain and loss in photonic quantum spin Hall systems
• Correlations at higher-order exceptional points in non-Hermitian models
• Heisenberg and Heisenberg-Like Representations via Hilbert Space Bundle Geometry in the Non-Hermitian Regime
• Collective dynamics of domain walls: an antiferromagnetic spin texture in an optical cavity
• Origin of robust exceptional points: a restricted bulk zero mode
• Control of magnon-photon coupling by spin torque
• Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
• One-transmitter Multiple-receiver Wireless Power Transfer System Using an Exceptional Point of Degeneracy
• Theory for the spectral splitting exponent of exceptional points
• Enhanced quantum sensing with hybrid exceptional-diabolic singularities
• Quantum chaos in PT symmetric quantum systems
• Hamiltonian and Linear-Space Structure for Damped Oscillators: II. Critical Points
• Exceptional Points, Nonnormal Matrices, Hierarchy of Spin Matrices and an Eigenvalue Problem
• Higher-order exceptional points in composite non-Hermitian systems
• Frozen Mode Regime in an Optical Waveguide With Distributed Bragg Reflector
• Metamorphosis of Goldstone and Soft Fluctuation Modes in Polariton Lasers
• Enhanced response at exceptional points in multi-qubit systems for sensing
• Behavior of three modes of decay channels and their self-energies of elliptic dielectric microcavity
• Instabilities, nonhermiticity and exceptional points in the cranking model
• Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Direct Measurement of a Non-Hermitian Topological Invariant in a Hybrid Light-Matter System
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Exceptional Points in Gyrator-Based Circuit and Nonlinear High-Sensitivity Oscillator
• Order-invariant two-photon quantum correlations in PT-symmetric interferometers
• Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems
• Recent advances in the combination of nonlinearity and exceptional points
• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• Multitype entanglement dynamics induced by exceptional points
• Quantum implementation of non-unitary operations with biorthogonal representations
• Asymptotic Exceptional Steady States in Dissipative Dynamics
• Transmission singularities in resonant electron tunneling through double complex potential barrier
• Exceptionally deficient topological square-root insulators
• Exceptional Point Singularities in Multi-Section DFB Lasers
• Scaling of pseudospectra in exponentially sensitive lattices
• Minimal Proper-time in Quantum Field Theory
• Dynamical transition in non-Hermitian Chern insulator
• Disorder-driven exceptional points and concurrent topological phase transitions in non-Hermitian systems
• Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
• Insight of the Green's function as a defect state in a boundary value problem
• Bandstructure of a coupled BEC-cavity system: effects of dissipation and geometry
• Collective terahertz fluctuation modes in a polariton laser
• Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems
• The $\mathcal{P}\mathcal{T}$-symmetry-breaking transition in a chain of trapped interacting ions
• Spectral properties of the Bloch-Torrey operator in three dimensions
• Application of Jordan Decomposition to Non-Hermitian Lattice Models with Spectrally-Isolated Lower Dimensional States
• Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians
• Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems
• Recurrence method in Non-Hermitian Systems
• Stochastic unravelings for Heisenberg picture and trace-nonpreserving dynamics
• Macroscopic entanglement between localized domain walls inside a cavity
• Non-equilibrium Dynamics of Three-Level Absorption Refrigerator at Third-Order Liouvillian Exceptional Points
• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology
• Non-orientable Exceptional Points in Twisted Boundary Systems
• Exceptional-point-controlled mode interaction in three-dimensional microcavities represented by generalized Husimi functions
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers