The physics of exceptional points

Abstract

A short resume is given about the nature of exceptional points (EPs) followed by discussions about their ubiquitous occurrence in a great variety of physical problems. EPs feature in classical as well as in quantum mechanical problems. They are associated with symmetry breaking for $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians, where a great number of experiments have been performed in particular in optics, and to an increasing extent in atomic and molecular physics. EPs are involved in quantum phase transition and quantum chaos, they produce dramatic effects in multichannel scattering, specific time dependence and more. In nuclear physics they are associated with instabilities and continuum problems. Being spectral singularities they also affect approximation schemes.

13 pages, 2 figures

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• Topological Band Theory for Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Anomalous edge state in a non-Hermitian lattice
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• Scalar Active Mixtures: The Non-Reciprocal Cahn-Hilliard Model
• Experimental observation of exceptional surface in synthetic dimensions with magnon polaritons
• General Theory of Spontaneous Emission Near Exceptional Points
• Non-Hermitian band topology and skin modes in active elastic media
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point
• Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
• Parity-time-symmetric topological superconductor
• Observation of PT-symmetric quantum interference
• Dissipation Induced Structural Instability and Chiral Dynamics in a Quantum Gas
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• Higher-order exceptional point in a cavity magnonics system
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
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• Non-Hermitian topology: a unifying framework for the Andreev versus Majorana states controversy
• Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model
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• Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
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• Non-Hermitian disorder in two-dimensional optical lattices
• Generalized bulk-edge correspondence for non-hermitian topological systems
• Experimental demonstration of an anisotropic exceptional point
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• Incident Direction Independent Wave Propagation and Unidirectional Lasing
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• Breaking of PT-symmetry in bounded and unbounded scattering systems
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• Topological classification of non-Hermitian bands
• Surface and 3D quantum Hall effects from engineering of exceptional points in nodal-line semimetals
• Symmetry classes of open fermionic quantum matter
• Kondo effect in a parity-time-symmetric non-Hermitian Hamiltonian
• Perspective: non-Hermitian physics in magnetic systems
• Non-Hermitian skin clusters from strong interactions
• Exceptional Bound States and negative Entanglement Entropy
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• Exceptional Points and Asymmetric Mode Switching in Plasmonic Waveguides
• Resonances in open quantum systems
• Topological Wave-Guiding Near an Exceptional Point: Defect-Immune, Slow-Light, Loss-Immune Propagation
• Exceptional Point and Cross-Relaxation Effect in a Hybrid Quantum System
• Group theoretic approach to many-body scar states in fermionic lattice models
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• Hunting for the non-Hermitian exceptional points with fidelity susceptibility
• Optimized heat transfer at exceptional points in quantum circuits
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• Exact spectral solution of two interacting run-and-tumble particles on a ring lattice
• Hybrid exceptional point created from type III Dirac point
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• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Classification of Exceptional Nodal Topologies Protected by $\mathcal{P}\mathcal{T}$ Symmetry
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• Observing exceptional point degeneracy of radiation with electrically pumped photonic crystal coupled-nanocavity lasers
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• Symmetry and topological classification of Floquet non-Hermitian systems
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• Highly Sensitive Coupled Oscillator Based on an Exceptional Point of Degeneracy and Nonlinearity
• Anyonic-parity-time symmetry in complex-coupled lasers
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• A model of three coupled wave guides and third order exceptional points
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• Topological Gapless Matters in Three-dimensional Ultracold Atomic Gases
• Self-hybridization within non-Hermitian plasmonic systems
• Distinguishing phases using the dynamical response of driven-dissipative light-matter systems
• Correlations at PT-symmetric quantum critical point
• Non-Markovian Quantum Exceptional Points
• $\mathcal{P}\mathcal{T}$ phase transition in open quantum systems with Lindblad dynamics
• Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
• Topology protects chiral edge currents in stochastic systems
• Spectral singularities in PT-symmetric Bose-Einstein condensates
• Macroscopic degeneracy of zero-mode rotating surface states in 3D Dirac and Weyl semimetals under radiation
• Noise Constraints for Nonlinear Exceptional Point Sensing
• Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport
• Exceptional points in anisotropic planar microcavities
• Transparency in a periodic chain of quantum emitters strongly coupled to a waveguide
• Encircling exceptional points as a non-Hermitian extension of rapid adiabatic passage
• Hybridization and the origin of the Fano resonances in symmetric nanoparticle trimers
• Coherent coupling between multiple ferrimagnetic spheres and a microwave cavity in the quantum-limit
• The fate of reentrant localization phenomenon in the one-dimensional dimerized quasiperiodic chain with long-range hopping
• Fourth-Order Exceptional Points in Correlated Quantum Many-Body Systems
• Quantum information dynamics in a high-dimensional parity-time-symmetric system
• Continuum of Bound States in a Non-Hermitian Model
• Real spectra in non-Hermitian topological insulators
• Controlling Exceptional Points with Light
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Amplification of quantum signals by the non-Hermitian skin effect
• On the time evolution at a fluctuating exceptional point
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Symmetry recovery of exceptional points and their dynamical encircling in a two-state system
• Spectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer
• Wave emission and absorption at spectral singularities
• Exponentially-enhanced Quantum Non-Hermitian Sensing via Optimized Coherent Drive
• Optimized Steering: Quantum State Engineering and Exceptional Points
• Third-order Exceptional Point and Successive Switching among Three States in a Degenerate Optical Microcavity
• Vortices in Bose-Einstein condensates with $\mathcal{P}\mathcal{T}$-symmetric gain and loss
• Unitarity corridors to exceptional points
• Bound states and photon emission in non-Hermitian nanophotonics
• Topology of multipartite non-Hermitian one-dimensional systems
• Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates
• Imaginary couplings in non-Hermitian coupled-mode theory: Effects on exceptional points of optical resonators
• Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models
• Microscopic origin of level attraction for a coupled magnon-photon system in a microwave cavity
• Anderson localization transitions in disordered non-Hermitian systems with exceptional points
• Experimental observation of exceptional bound states in a classical circuit network
• Exceptional Points in the Flatland: A Non-Hermitian Line-Wave Scenario
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• Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice
• Odd Cosserat elasticity in active materials
• Non-abelian nature of systems with multiple exceptional points
• Giant Emitters in a Structured Bath with Non-Hermitian Skin Effect
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• Dissipative analog of four-dimensional quantum Hall physics
• Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
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• Dynamical scaling of Loschmidt echo in non-Hermitian systems
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• Exceptional points in coupled dissipative dynamical systems
• Acoustic metamaterials with spinning components
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• Analysis of a Triple-cavity Photonic Molecule Based on Coupled Mode Theory
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• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
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• Excitation of absorbing exceptional points in the time domain
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• Semiclassical Dynamics, Berry Curvature and Spiral Holonomy in Optical Quasicrystals
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• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Dispersive readout of a weakly coupled qubit via the parity-time-symmetric phase transition
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• Realization of complex conjugate media using non-PT-symmetric photonic crystals
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• Active Brownian Particles in a Circular Disk with an Absorbing Boundary
• Near-unit efficiency of chiral state conversion via hybrid-Liouvillian dynamics
• Three solvable matrix models of a quantum catastrophe
• Behavior of eigenvalues in a region of broken-PT symmetry
• Harmonic inversion analysis of exceptional points in resonance spectra
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Exceptional degeneracies in non-Hermitian Rashba semiconductors
• Symmetry protected exceptional points of interacting fermions
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• Making topologically trivial non-Hermitian systems nontrivial via gauge fields
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• Exceptional point description of one-dimensional chiral topological superconductors/superfluids in BDI class
• Nonequilibrium transition between dissipative time crystals
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Nonlinearity Induced Anomalous Mode Collapsing and Non-chiral Asymmetric Mode Switching around multiple Exceptional Points
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model
• Fractional Josephson effect versus fractional charge in superconducting-normal metal hybrid circuits
• Exceptional points as signatures of dynamical magnetic phase transitions
• Non-Hermitian Floquet invisibility
• Enhanced Purcell factor for nanoantennas supporting interfering resonances
• Experimental Observation of Partial Parity-Time Symmetry and Its Phase Transition with a Laser-Driven Cesium Atomic Gas
• Enhanced response of non-Hermitian photonic systems near exceptional points
• Exceptional Points of Resonant States on a Periodic Slab
• Dynamics of finite dimensional non-hermitian systems with indefinite metric
• Complex symmetric Hamiltonians and exceptional points of order four and five
• Degenerate perturbation theory in thermoacoustics: high-order sensitivities and exceptional points
• Quasinormal modes and excitation factors of Kerr black holes
• Acoustic Bound States in the Continuum in Coupled Helmholtz Resonators
• Topological superconductivity enhanced by exceptional points
• Exceptional point induced lasing dynamics in a non-Hermitian system
• Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation
• Emergent phases and novel critical behavior in a non-Markovian open quantum system
• Acceleration toward polarization singularity inspired by relativistic ExB drift
• From unexceptional to doubly exceptional surface waves
• Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems
• Unification of quantum Zeno-anti Zeno effects and parity-time symmetry breaking transitions
• Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems
• Discussion of the adiabatic hypothesis in control schemes using exceptional points
• Emergence of tunable exceptional points in altermagnet-ferromagnet junctions
• Indirect link between resonant and guided modes on uniform and periodic slabs
• Virtual exceptional points in an electromechanical system
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Fano resonances in scattering: an alternative perspective
• Initial experimental results on a superconducting-qubit reset based on photon-assisted quasiparticle tunneling
• Non-Hermitian heterostructure for two-parameter sensing
• Dynamical signature of moire pattern in non-Hermitian ladder
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Coalescence of non-Markovian dissipation, quantum Zeno effect and non-Hermitian physics, in a simple realistic quantum system
• Recent Developments in Quantum-Circuit Refrigeration
• Higher order topological degeneracies and towards unique successive state-switching in a four-level open system
• Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate
• Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system
• Mechanism of dynamical phase transitions: The complex-time survival amplitude
• Signature of exceptional point phase transition in Hermitian systems
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• Gain-Loss Coupled Systems
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Electromagnetic fields in a time-varying medium: Exceptional points and operator symmetries
• Tweaking Spectral Topology and Exceptional Points by Nonlinearity in Non-Hermitian Polariton Systems
• Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
• Quasinormal mode analysis of chiral power flow from linearly polarized dipole emitters coupled to index-modulated microring resonators close to an exceptional point
• Dissipative dynamics in open XXZ Richardson-Gaudin models
• Non-hermiticity in spintronics: oscillation death in coupled spintronic nano-oscillators through emerging exceptional points
• Characterizing and Tuning Exceptional Points Using Newton Polygons
• Self-stabilization of light sails by damped internal degrees of freedom
• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Pseudomagnetic suppression of non-Hermitian skin effect
• Topological transitions in quantum jump dynamics: Hidden exceptional points
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• Stability and collisions of quantum droplets in PT -symmetric dual-core couplers
• Massive scalar perturbations in Kerr Black Holes: near extremal analysis
• Resonant generation of $p$-wave Cooper pair in non-Hermitian Kitaev chain at exceptional point
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Dynamic gain and frequency comb formation in exceptional-point lasers
• Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model
• PT-symmetry breaking in resonant tunneling heterostructures
• Many-body phase transitions in a non-Hermitian Ising chain
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Holonomic Gates in Pseudo-Hermitian Quantum Systems
• Exceptional Non-Hermitian Phases in Disordered Quantum Wires
• Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point
• Anomalous dynamical response of non-Hermitian topological phases
• Hermitian Topologies originating from non-Hermitian braidings
• Real-space topological invariant for time-quasiperiodic Majoranas
• Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation
• $PT$-symmetric graphene under a magnetic field
• Giant Amplification of Small Perturbations in Frictional Amorphous Solid
• Non-Hermitian topological Fermi superfluid near the $p$-wave unitary limit
• Integrable nonlinear parity-time symmetric optical oscillator
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• Observables in non-Hermitian systems: A methodological comparison
• Amplified and directional spontaneous emission from arbitrary composite bodies: self-consistent treatment of Purcell effect below threshold
• Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling
• Theory of response to perturbations in non-Hermitian systems using five-Hilbert-space reformulation of unitary quantum mechanics
• Enhancing the sensitivity of nonlinearity sensors through homodyne detection in dissipatively coupled systems
• Boundary Effects of Weak Nonlocality in Multilayered Dielectric Metamaterials
• Subthreshold phonon generation in an optomechanical system with an exceptional point
• Exceptional Degeneracy in a Waveguide Periodically Loaded with Discrete Gain and Radiation Loss Elements
• Optical Limiter Based on PT-Symmetry Breaking of Reflectionless Modes
• Analytic structure of eigenvalues of coupled quantum systems
• Mesoscopic transport signatures of disorder-induced non-Hermitian phases
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Complex BPS solitons with real energies from duality
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Symmetrically Tuned Large-Volume Conic Shell-Cavities for Axion Searches
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• A high order continuation method to locate exceptional points and to compute Puiseux series with applications to acoustic waveguides
• Magnetic degeneracy points in interacting two-spin systems: geometrical patterns, topological charge distributions, and their stability
• Critical and non critical non-Hermitian topological phase transitions in one dimensional chains
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Signatures of avoided energy-level crossings in entanglement indicators obtained from quantum tomograms
• Exceptional points and exponential sensitivity for periodically driven Lindblad equations
• Non-Hermitian boost deformation
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Experimental observation of the avoided crossing of two $S$-matrix resonance poles in an ultracold atom collider
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Thermal induced monochromatic microwave generation in magnon-polariton
• Dynamically Induced Exceptional Phases in Quenched Interacting Semimetals
• Black hole quasinormal mode resonances
• Hilbert space inner products for PT-symmetric Su-Schrieffer-Heeger models
• Stochastic feedback control of quantum transport to realize a dynamical ensemble of two nonorthogonal pure states
• Oscillation death in coupled counter-rotating identical nonlinear oscillators
• Correlations in non-Hermitian systems and Diagram techniques for the steady state
• Resonant spectra of quadrupolar anions
• Dissipative light-matter coupling and anomalous dispersion in nonideal cavities
• Imperfect chirality at exceptional points in optical whispering-gallery microcavities
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Nonlocality of local Andreev conductances as a probe for topological Majorana wires
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Effect of loss on the topological features of dimer chain described by the extended Aubry-André-Harper model
• Gain assisted controllable fast light generation in cavity magnomechanics
• Jordan blocks and the Bethe ansatz I: The eclectic spin chain as a limit
• Discriminant indicators with generalized inversion symmetry
• Exceptional point in a coupled Swanson system
• Experimental observation of exceptional points in coupled pendulums
• Surface exceptional points in a topological Kondo insulator
• A topological fluctuation theorem
• Anomalous mechanisms of the loss of observability in non-Hermitian quantum models
• Quantum mold casting for topological insulating and edge states
• Transition from degeneracy to coalescence: theorem and applications
• Universal quantum control by non-Hermitian Hamiltonian
• Metastable two-component solitons near an exceptional point
• Two-dimensional phase-space picture of the photonic crystal Fano laser
• Liouvillian and Hamiltonian exceptional points of atomic vapors: The spectral signatures of quantum jumps
• Information constraint in open quantum systems
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations
• Quantum Metrology with Higher-order Exceptional Points in Atom-cavity Magnonics
• Spectral and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric tight-binding chain with gain and loss
• Bosonic Josephson effect in the Fano-Anderson model
• Symmetry properties of non-Hermitian PT-symmetric quantum field theories
• Liouvillian exceptional points of an open driven two-level system
• Simple models of three coupled $\mathcal{P}\mathcal{T}$-symmetric wave guides allowing for third-order exceptional points
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Interplay between tilt, disorder, and Coulomb interaction in type-I Dirac fermions
• $\mathcal{P}\mathcal{T}$-Symmetry in Hartree-Fock Theory
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Phase transitions in a non-Hermitian Su-Schrieffer-Heeger model via Krylov spread complexity
• Edge states in a non-Hermitian topological crystalline insulator
• Multitude of exceptional points in van der Waals magnets
• Exceptional Point-enhanced Rydberg Atomic Electrometers
• Counting Majorana bound states using complex momenta
• Non-Hermitian semi-Dirac semi-metals
• Quantum features of the transport through ion channels in the soft knock-on model
• Quantum memories for squeezed and coherent superpositions in a driven-dissipative nonlinear oscillator
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator
• A Unified View on Geometric Phases and Exceptional Points in Adiabatic Quantum Mechanics
• Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
• KPZ fluctuations in finite volume
• Level attraction and exceptional points in a resonant spin-orbit torque system
• Non-Hermitian generalizations of the Yao-Lee model augmented by SO(3)-symmetry-breaking terms
• Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Oscillating potential well in complex plane and the adiabatic theorem
• Perfectly matched layer method for optical modes in dielectric cavities
• Exceptional points treatment of cavity spectroscopies
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• Loss compensation symmetry of unequally sized dielectric cylinders with gain and loss
• Mode attraction in Floquet systems with memory: application to magnonics
• Resonant spectra of multipole-bound anions
• Weyl points and exceptional rings with polaritons in bulk semiconductors
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields
• Anomalous Hall effect from a non-Hermitian viewpoint
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Controlled probing of localization effects in the non-Hermitian Aubry-André model via topolectrical circuits
• Probing eigenfunction nonorthogonality by parametric shifts of resonance widths
• General theory for infernal points in non-Hermitian systems
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Phase Transitions and Virtual Exceptional Points in Quantum Emitters Coupled to Dissipative Baths
• Non-Hermitian superconducting diode effect
• Complex entanglement entropy for complex conformal field theory
• Exceptional points in single open acoustic resonator due to the symmetry breaking
• Emergent localized states at the interface of a twofold $\mathcal{P}\mathcal{T}$-symmetric lattice
• Reconfiguration of quantum states in $\mathcal{P}T$-symmetric quasi-one dimensional lattices
• Topological Singularities in Metasurface Scattering Matrices: From Nodal Lines to Exceptional Lines
• Non-Hermitian Numerical Renormalization Group: Solution of the non-Hermitian Kondo model
• Lasing at a Stationary Inflection Point
• Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model
• Retardaion-induced exceptional point
• How to Project onto an Arbitrary Single-Photon Wavepacket
• On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials
• Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase
• Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
• Nonlinear Hall effects with an exceptional ring
• Analogue Hawking radiation as a tunneling in a two-level $\mathcal{P}\mathcal{T}$-symmetric system
• Non-Markovian Dynamics of Open Quantum Systems via Auxiliary Particles with Exact Operator Constraint
• Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings
• Parsing skin effect in a non-Hermitian spinless BHZ-like model
• Unconventional steady states and topological phases in an open two-level non-Hermitian system
• A unifying asymptotic approach for nonadiabatic transitions near pairs of real or complex turning points
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model
• Liouvillian exceptional points in continuous variable system
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Hidden exceptional point, localization-delocalization phase transition in Hermitian bosonic Kitaev model
• Dynamic transition from insulating state to eta-pairing state in a composite non-Hermitian system
• Broken Hermiticity phase transition in Bose-Hubbard model
• Topological states at exceptional points
• Riemann surfaces for integer counting processes
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Jordan blocks and the Bethe ansatz II: The eclectic spin chain beyond $K=1$
• Enhanced quantum sensing in time-modulated non-Hermitian systems
• Non-Hermitian Floquet-Free Analytically Solvable Time Dependant Systems
• PHOENIX -- Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
• Parity-Time Symmetry and Exceptional points: A Tutorial
• Nodal phases in non-Hermitian wallpaper crystals
• Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model
• Level attraction from interference in two-tone driving
• Proposal for measuring Newtonian constant of gravitation at an exceptional point in an optomechanical system
• Spontaneous Formation of Exceptional Points at the Onset of Magnetism
• Probing localization properties of many-body Hamiltonians via an imaginary vector potential
• Long-time memory effects in a localizable central spin problem
• Exceptional points in cylindrical elastic media with radiation loss
• Correlations at higher-order exceptional points in non-Hermitian models
• BIC in waveguide arrays within a symmetry classification scheme
• A controllable anti-P-pseudo-Hermitian mechanical system and its application
• Néel vector controlled exceptional contours in $p$-wave magnet-ferromagnet junctions
• Spin-dependent gain and loss in photonic quantum spin Hall systems
• Topological Phase Transition of A Non-Hermitian Crosslinked Chain
• A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians
• Excitonic transverse and amplitude fluctuations in the noncollinear and charge-ordered RbFe${}^{2+}$Fe${}^{3+}$F${}_6$
• Essential implications of similarities in non-Hermitian systems
• Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction
• Plunging in the Dirac sea using graphene quantum dots
• Loss revives bistable state near the exceptional point in a non-Hermitian microwave photonic meta-molecule
• Exact density profile in a tight-binding chain with dephasing noise
• Observation of Braid-Protected Unpaired Exceptional Points
• Winding Topology of Multifold Exceptional Points
• Non-Hermitian theory of valley excitons in two-dimensional semiconductors
• Heat transport through an open coupled scalar field theory hosting stability-to-instability transition
• Breakdown of Linear Spin-Wave Theory in a Non-Hermitian Quantum Spin Chain
• Correlated Nonreciprocity around Conjugate Exceptional Points
• Spontaneous symmetry breaking in non-steady modes of open quantum many-body systems
• Topological Operations Around Exceptional Points via Shortcuts to Adiabaticity
• Enhanced quantum sensing with hybrid exceptional-diabolic singularities
• One-transmitter Multiple-receiver Wireless Power Transfer System Using an Exceptional Point of Degeneracy
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Spectra, eigenstates and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric ring
• Defect production due to time-dependent coupling to environment in the Lindblad equation
• Dynamical Phase Transitions in Open Quantum Walks
• Theory for the spectral splitting exponent of exceptional points
• Superradiance in finite quantum systems randomly coupled to continuum
• Frozen Mode Regime in an Optical Waveguide With Distributed Bragg Reflector
• Implications of exceptional points for few-photon transport in waveguide quantum electrodynamics
• An attractor dynamics in a non-Hermitian two-level system
• New insights into mode behaviours in waveguides with impedance boundary conditions
• Topological Dynamics and Correspondences in Composite Exceptional Rings
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Recent advances in the combination of nonlinearity and exceptional points
• Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
• Non-Hermitian physics and engineering in silicon photonics
• Exceptional deficiency of non-Hermitian systems
• Exceptional Points in Gyrator-Based Circuit and Nonlinear High-Sensitivity Oscillator
• Electromagnetic Eigenvalue Problems and Nonhermitian Effects in Linear and Saturable Scattering
• Non-Hermitian Josephson junctions with four Majorana zero modes
• Artificial Hawking radiation, weak pseudo-Hermiticity and Weyl semimetal blackhole analogy
• Oblique scattering from non-Hermitian optical waveguides
• Exceptional points in perturbed dielectric spheres: A resonant-state expansion study
• Supersymmetrically bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Evolution of electric-field-induced quasibound states and resonances in one-dimensional open quantum systems
• Slow approach to adiabaticity in many-body non-Hermitian systems: the Hatano-Nelson Model
• Alternating quantum-emitter chains: Exceptional-point phase transition, edge state, and quantum walks
• Non-Hermitian skin effect and electronic nonlocal transport
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Almost All Quantum Channels Are Diagonalizable
• Enhanced response at exceptional points in multi-qubit systems for sensing
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Coalescing hardcore-boson condensate states with nonzero momentum
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Topological Engineering of High-Order Exceptional Points through Transformation Optics
• Complex modes in an open lossless periodic waveguide
• State conversions around exceptional points
• Magnetization in a non-equilibrium quantum spin system
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Observing S-Matrix Pole Flow in Resonance Interplay: Cold Collisions of Ultracold Atoms in a Miniature Laser-based Accelerator
• Exotic light transition between superluminal and subliminal group velocity in a $\mathcal{P}\mathcal{T}$ coupled slab waveguide
• Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions
• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• Spatial transient behavior in waveguides with lossy impedance boundary conditions
• Chiral state conversion in a levitated micromechanical oscillator with in situ control of parameter loops
• Apodized photonic crystals: A non-dissipative system hosting multiple exceptional points
• Quantum implementation of non-unitary operations with biorthogonal representations
• Stochastic light in a cavity: A Brownian particle in a scalar potential?
• Zero Curvature Condition for Quantum Criticality
• Exceptional points in SSH-like models with hopping amplitude gradient
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Topologically protected two-fluid edge states
• Exceptionally deficient topological square-root insulators
• Complex energy structures of exceptional point pairs in two level systems
• Building ground states of Hubbard model by time-ordered bound-pair injection
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Exceptional Points, Bulk-Boundary Correspondence, and Entanglement Properties for a Dimerized Hatano-Nelson Model with Staggered Potentials
• Few-grid-point simulations of Big Bang singularity in quantum cosmology
• Witnessing criticality in non-Hermitian systems via entropic uncertainty relation
• From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
• Simulating the spectral gap with polariton graphs
• Asymptotic Exceptional Steady States in Dissipative Dynamics
• Steady-states and response functions of the periodically driven O(N) scalar field theory
• Singularities of Floquet Scattering and Tunneling
• A Passive $\mathcal{P}\mathcal{T}$-Symmetric Floquet-Coupler
• Perfectly absorbed and emitted currents by complex potentials in nonlinear media
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Intrinsic exceptional point -- a challenge in quantum theory
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• Topological spin textures in electronic non-Hermitian systems
• Topological bosonic Bogoliubov excitations with sublattice symmetry
• $\mathcal{P}\mathcal{T}$-symmetry in compact phase space for a linear Hamiltonian
• Exceptional points in the elliptical three-disk scatterer using semiclassical periodic orbit quantization
• Exceptional Spectral Phase in a Dissipative Collective Spin Model
• Higher order coherence as witness of exceptional point in Hermitian bosonic Kitaev dimer
• Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
• Universal quantum control over non-Hermitian continuous-variable systems
• Non-hermitian off-diagonal magnetic response of Dirac fermions
• Bi-stability and period-doubling cascade of frequency combs in exceptional-point lasers
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model
• Experimental Realization of Non-Abelian Permutations in a Three-State Non-Hermitian System
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Exceptional point rings and $PT$-symmetry in the non-Hermitian XY model
• Observation of novel robust edge states without bulk-boundary correspondence in non-Hermitian quantum walks
• Anderson Impurities In Edge States with Nonlinear and Dissipative Perturbations
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Exceptional points and defective resonances in an acoustic scattering system with sound-hard obstacles
• Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Finite Rectangular Domain with Absorbing Boundary Conditions
• Entanglement generation across exceptional points in two-qubit open quantum system -- the role of initial states
• Loss-driven gain enhancements driven by topological singularities in non-Hermitian photonic crystals defects
• Dissipation-Induced Super Scattering and Lasing PT-Spaser
• Quantum jumps in open cavity optomechanics and Liouvillian versus Hamiltonian exceptional points
• A Hermitian bypass to the non-Hermitian quantum theory
• Homodyne Measurement of a Non-Hermitian Qubit Undergoing Fluorescence
• Non-Hermitian magnetic moment
• Third-order exceptional surface in a pseudo-Hermitian superconducting circuit
• Nodal Spectral Functions Stabilized by Non-Hermitian Topology of Quasiparticles
• Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Transition-Path Times, Survival Probability, and First-Passage Time
• Tunable Localisation in Parity-Time-Symmetric Resonator Arrays with Imaginary Gauge Potentials
• Stronger sum uncertainty relations for non-Hermitian operators
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• Dynamic Moiré-like pattern in non-Hermitian Wannier-Stark ladder system
• Exceptional Points of Degeneracy and Branch Points for Transmission-Line Problems - Linear Algebra and Bifurcation Theory Perspectives
• Exceptional Lines and Excitation of (Nearly) Double-Pole Quasinormal Modes: A Semi-Analytic Study in the Nariai Black Hole
• Phase transitions in quasi-Hermitian quantum models at exceptional points of order four
• In-Plane Linear Stress Waves in Layered Media: I. Non-Hermitian Degeneracies and Modal Chirality
• Non-orientability induced PT phase transition in Moebius ladder lattices
• Bandstructure of a coupled BEC-cavity system: effects of dissipation and geometry
• Odd elasticity in disordered chiral active materials
• An exact solution to dispersion of a passive scalar by a periodic shear flow
• Electromagnetic surface waves at exceptional points
• Entanglement properties of bound and resonant few-body states
• Collective actuation in active solids in the presence of a polarizing field: a systematic analysis of the dynamical regimes
• Signatures of nonclassical effects in tomograms
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics
• Non-Markovian renormalization of optomechanical exceptional points
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Anomalous Non-Hermitian Topological Anderson Insulator
• Non-Markovian exceptional points in waveguide quantum electrodynamics
• Spectroscopic Signatures of a Liouvillian Exceptional Spectral Phase in a Collective Spin
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance
• Non-Hermiticity induced thermal entanglement phase transition
• Nonreciprocal flow of fluctuations, populations and correlations between doubly coupled bosonic modes
• Emergence and localization of exceptional points in an exactly solvable toy model
• Hexagonal Warping Control of Exceptional Points in Topological Insulator--Ferromagnetic Heterojunctions
• Probing phase transitions in non-Hermitian systems with quantum entanglement
• Observation of non-Hermitian point gap in photonic crystals
• Parity violating spectral dynamics of black holes in dynamical Chern-Simons gravity
• Stochastic unravelings for Heisenberg picture and trace-nonpreserving dynamics
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics
• Characterizing Liouvillian Exceptional Points Through Newton Polygons and Tropical Geometry
• Dynamical Quantum Phase Transitions and Many-Body Backflow in Open Quantum Systems
• Impact of noise on nonlinear-exceptional-point-based sensors
• Zero Indirect Band Gap in Non-Hermitian Systems
• Exceptional flat bands in bipartite non-Hermitian lattices
• The analytically tractable zoo of similarity-induced exceptional structures
• 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
• Synthetic high-order PT symmetry in a single coil resonator
• Functional renormalization group for non-Hermitian and $\mathcal{P}\mathcal{T}$-symmetric systems
• Complex analysis of divergent perturbation theory at finite temperature
• Wave Propagation in Electric Periodic Structure in Space with Modulation in Time (2D+1). I. Theory
• PT symmetry and the evolution speed in open quantum systems
• Non-Hermitian Lindhard function and Friedel oscillations
• Supermetal-insulator transition in a non-Hermitian network model
• Unidirectional weak visibility in band gap and singular scattering in conduction band of one-dimensional parity-time symmetric photonic crystal
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model
• Hierarchic superradiant phases in anisotropic Dicke model
• Non-Hermitian Higher-Order Dirac Semimetals
• Chiral modes near exceptional points in symmetry broken H1 photonic crystal cavities
• Fast recovery of parametric eigenvalues depending on several parameters and location of high order exceptional points
• Characteristic influence of exceptional points in quantum dynamics
• Metastable quantum entrainment
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
• A weak pseudo-Hermitian two band model, artificial Hawking radiation and tunneling
• Pseudo-Jahn-Teller interaction among electronic resonant states of H3
• Emergence of Hermitian topology from non-Hermitian knots
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
• Complex time method for quantum dynamics when an exceptional point is encircled in the parameter space
• Weak-coupling bound states in semi-infinite topological waveguide QED
• High-order exceptional points and enhanced sensing in subwavelength resonator arrays
• Accelerated Non-Reciprocal Transfer of Energy Around an Exceptional Point
• State Diagram of the Non-Reciprocal Cahn-Hilliard Model and the Effects of Symmetry
• Pursuing complex optical energy through Exceptional Points of Degeneracy (EPDs)
• Local perfect chirality at reflection-zeros away from exceptional points in optical whispering gallery microcavity
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
• Passive leakage removal unit based on a disordered transmon array
• Landau-Zener transitions through a pair of higher order exceptional points
• A simple tool for the optimization of 1D phononic and photonic bandgap filters
• Recurrence method in Non-Hermitian Systems
• Anisotropy and asymptotic degeneracy of the physical-Hilbert-space inner-product metrics in an exactly solvable crypto-unitary quantum model
• Breakdown of the Meissner effect at the zero exceptional point in non-Hermitian two-band BCS model
• All-Dielectric Nanophotonic Structures: Exploring the Magnetic Component of Light
• Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems
• Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians
• The Control of the Oscillation Threshold with Asymmetric Gain in Operational Amplifiers
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description
• Electronic states in a bilayer graphene quantum ripple
• Collective Resonances in Nanoparticle Oligomers
• Probability of a single current
• A unifying E2-quasi-exactly solvable model
• The $\mathcal{P}\mathcal{T}$-symmetry-breaking transition in a chain of trapped interacting ions
• Non-Markovianity Benefits Quantum Dynamics Simulation
• Evolution of Gaussian mixed states under the Markovian master equation for a driven quantum oscillator
• Chiral behaviour for three wave guides at an exceptional point of third order
• Nonreciprocal Coupling Induced Non-Hermitian Entanglement in Optomechanical Systems
• Exceptional Luttinger Liquids from sublattice dependent interaction
• Triple exceptional point with unitary paths of unfolding in a three-site fermionic Swanson-like model
• Out-of-time-order correlators for Swanson Hamiltonian with interaction terms