Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum

Abstract

We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors.

Revised version, accepted for publication in J. Math. Phys

References in corpus (7)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Supersymmetry and the spontaneous breakdown of PT symmetry
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials
• Quantum Complex Henon-Heiles Potentials
• On an exactly solvable $B_N$ type Calogero model with nonhermitian PT invariant interaction
• Conservation of pseudo-norm in PT symmetric quantum mechanics
• PT - symmetrized supersymmetric quantum mechanics

Cited by in corpus (492)

• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Non-Hermitian Physics
• The physics of exceptional points
• Symmetry and Topology in Non-Hermitian Physics
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• PT-symmetric laser-absorber
• Non-Hermitian Chern bands
• Pseudo-Hermitian Representation of Quantum Mechanics
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Non-reciprocal phase transitions
• Non-Hermitian Topology and Exceptional-Point Geometries
• Edge states and topological phases in non-Hermitian systems
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Second-Order Topological Phases in Non-Hermitian Systems
• Exact PT-Symmetry Is Equivalent to Hermiticity
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Must a Hamiltonian be Hermitian?
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• New topological invariants in non-Hermitian systems
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• The ODE/IM Correspondence
• Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• Optical realization of relativistic non-Hermitian quantum mechanics
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Observation of non-Bloch parity-time symmetry and exceptional points
• The Naimark dilated PT-symmetric brachistochrone
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Parity-time-symmetric topological superconductor
• Invisibility and PT-symmetry
• Quantum noise and self-sustained radiation of PT-symmetric systems
• Perspective on topological states of non-Hermitian lattices
• Local PT symmetry violates the no-signaling principle
• Higher-order exceptional point in a cavity magnonics system
• Mathematical and physical aspects of complex symmetric operators
• PT-Symmetric Plasmonic Metamaterials
• Pseudospectra in non-Hermitian quantum mechanics
• PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model
• Supersymmetry-generated complex optical potentials with real spectra
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Time evolution of non-Hermitian Hamiltonian systems
• Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems
• Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• Many-body approach to non-Hermitian physics in fermionic systems
• Pseudo-Hermiticity for a Class of Nondiagonalizable Hamiltonians
• Non-Hermitian dynamics without dissipation in quantum systems
• PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues
• Exceptional points in topological edge spectrum of PT symmetric domain walls
• Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential
• Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
• Spectral Singularities, Biorthonormal Systems, and a Two-Parameter Family of Complex Point Interactions
• Three-Hilbert-Space Formulation of Quantum Mechanics
• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics
• Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
• Integrable nonlocal vector nonlinear Schrödinger equation with self-induced parity-time-symmetric Potential
• Quantum sensing with a single-qubit pseudo-Hermitian system
• Quantum Mechanics of Klein-Gordon-Type Fields and Quantum Cosmology
• Explicit definition of $\mathcal{P}\mathcal{T}$ symmetry for non-unitary quantum walks with gain and loss
• Perspective: non-Hermitian physics in magnetic systems
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Delta-Function Potential with a Complex Coupling
• Biorthogonal Quantum Systems
• Quasi-Hermiticity in infinite-dimensional Hilbert spaces
• Consistency of PT-symmetric quantum mechanics
• Topological phases in Kitaev chain with imbalanced pairing
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
• Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
• Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures
• Parity-time symmetry in optical microcavity systems
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• The non-Hermitian Swanson model with a time-dependent metric
• Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method
• Geometric Phase in PT-Symmetric Quantum Mechanics
• A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
• Completeness and Orthonormality in PT-symmetric Quantum Systems
• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Quantum master equation with balanced gain and loss
• Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians
• Spectra of PT-Symmetric Operators and Perturbation Theory
• The Quantum Deformed Mirror TBA I
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Non-Hermitian Photonic Lattices: tutorial
• Introduction to Supersymmetric Theory of Stochastics
• Theory of Exceptional Points of Degeneracy in Uniform Coupled-Waveguides and Balance of Gain and Loss
• Complex Correspondence Principle
• Higher-order exceptional point in a pseudo-Hermitian cavity optomechanical system
• Self-dual Spectral Singularities and Coherent Perfect Absorbing Lasers without PT-symmetry
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Second order SUSY transformations with `complex energies'
• On the invariant method for the time-dependent non-Hermitian Hamiltonians
• Eigenvalue structure of a Bose-Einstein condensate in a PT-symmetric double well
• Non-Hermitian supersymmetry and singular PT symmetrized oscillators
• Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
• Quantum Mechanics of Klein-Gordon Fields I: Hilbert Space, Localized States, and Chiral Symmetry
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Goldstone bosons and the Englert-Brout-Higgs mechanism in non-Hermitian theories
• Complex Optical Potentials and Pseudo-Hermitian Hamiltonians
• Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Pseudo-Hermiticity, weak pseudo-Hermiticity and eta-orthogonality condition
• Transfer Matrices as Non-Unitary S-Matrices, Multimode Unidirectional Invisibility, and Perturbative Inverse Scattering
• Cosmological Perturbations in Conformal Gravity
• Time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics in generic non-Hermitian systems
• Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
• Semiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• Cubic-scaling iterative solution of the Bethe-Salpeter equation for finite systems
• Uniqueness and Self-Conjugacy of Dirac Hamiltonians in arbitrary Gravitational Fields
• Supersymmetry vs ghosts
• Energy Observable for a Quantum System with a Dynamical Hilbert Space and a Global Geometric Extension of Quantum Theory
• Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report
• Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model
• On the pseudo-Hermitian nondiagonalizable Hamiltonians
• Solution of the problem of uniqueness and hermiticity of hamiltonians for Dirac particles in gravitational fields
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Higher winding number in a non-unitary photonic quantum walk
• Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
• Discrete PT-symmetric models of scattering
• Detection sensitivity enhancement of magnon Kerr nonlinearity in cavity magnonics induced by coherent perfect absorption
• Non-Hermitian Hamiltonians of Lie algebraic type
• Asymmetric transmission through a flux-controlled non-Hermitian scattering center
• Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators
• Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay
• Scattering theory using smeared non-Hermitian potentials
• Nonlinear quantum dynamics in a PT-symmetric double well
• Application of Pseudo-Hermitian Quantum Mechanics to a PT-Symmetric Hamiltonian with a Continuum of Scattering States
• A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields
• Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model
• PT/Non-PT Symmetric and Non-Hermitian Poschl-Teller-Like Solvable Potentials via Nikiforov-Uvarov Method
• The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes
• Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
• $\mathcal{P}\mathcal{T}$-symmetric, non-Hermitian quantum many-body physics -- a methodological perspective
• Exceptional points of degeneracy and $\mathcal{P}\mathcal{T}$-symmetry in photonic coupled chains of scatterers
• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
• Erratum: Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians [J. Math. Phys. 43, 6343 (2002); math-ph/0207009]
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• (1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric
• Semiclassical Analysis of Spectral Singularities and Their Applications in Optics
• Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?
• Irreversibility of the renormalization group flow in non-unitary quantum field theory
• Static correlation beyond the random phase approximation: Dissociating H2 with the Bethe-Salpeter equation and time-dependent GW
• Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
• Spectral Singularities of a General Point Interaction
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• Hybrid higher-order skin-topological effect in hyperbolic lattices
• Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
• PT symmetry of a conditionally exactly solvable potential
• Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point
• On Hamiltonians Generating Optimal-Speed Evolutions
• Non-self-adjoint hamiltonians defined by Riesz bases
• Conditional observability
• Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
• Operator equations and Moyal products -- metrics in quasi-hermitian quantum mechanics
• Fragile PT-symmetry in a solvable model
• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Constructible reality condition of pseudo entropy via pseudo-Hermiticity
• Non-Hermitian quantum systems and their geometric phases
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• $\eta$-weak-Pseudo-Hermiticity generators and exact solvability
• Non-Hermitian d-dimensional Hamiltonians with position dependent mass and their $\eta$-pseudo-Hermiticity generators
• New Quasi-Exactly Solvable Sextic Polynomial Potentials
• Continuum of Bound States in a Non-Hermitian Model
• Moyal products -- a new perspective on quasi-hermitian quantum mechanics
• Real spectra in non-Hermitian topological insulators
• Coupled-channel version of PT-symmetric square well
• Wave emission and absorption at spectral singularities
• A new class of non-Hermitian Hamiltonians with real spectra
• Non-Hermitian skin effect edge
• Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics
• Exactly Solvable Quasi-hermitian Transverse Ising Model
• CPA-Lasing in Thin-Elastic Plates via Exceptional Points
• On the Real Spectra of Calogero Model with Complex Coupling
• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• P,T,PT, and CPT invariance of Hermitian Hamiltonians
• PT-symmetric models in curved manifolds
• Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry
• Level statistics of a pseudo-Hermitian Dicke model
• Vortices in Bose-Einstein condensates with $\mathcal{P}\mathcal{T}$-symmetric gain and loss
• Quantum Mechanics of Proca Fields
• An exactly solvable PT symmetric potential from the Natanzon class
• Unitarity of loop diagrams for the ghost-like $1/(k^2-M_1^2)-1/(k^2-M_2^2)$ propagator
• Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates
• Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models
• Anderson localization transitions in disordered non-Hermitian systems with exceptional points
• Generalized Swanson models and their solutions
• Real Description of Classical Hamiltonian Dynamics Generated by a Complex Potential
• $PT$ symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
• From Generalized Dirac Equations to a Candidate for Dark Energy
• Appropriate Inner Product for PT-Symmetric Hamiltonians
• Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem
• The quantum brachistochrone problem for non-Hermitian Hamiltonians
• Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions
• $J$-self-adjoint operators with $\mathcal{C}$-symmetries: extension theory approach
• C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians
• Quantum Mechanics of a Photon
• Analytically Solvable PT-Invariant Periodic Potentials
• Entanglement, non-Hermiticity, and duality
• Kelvin-Helmholtz instability is the result of parity-time symmetry breaking
• Dirac Operator on Fuzzy AdS_2
• A generalized non-Hermitian oscillator Hamiltonian, N-fold supersymmetry and position-dependent mass models
• Quadratic PT-symmetric operators with real spectrum and similarity to self-adjoint operators
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• Probability Density in the Complex Plane
• Higher-order exceptional point in a blue-detuned non-Hermitian cavity optomechanical system
• Mathematical aspects of intertwining operators: the role of Riesz bases
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation
• Transport properties in a Non-Hermitian triple-quantum-dot structure
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical Applications
• Field Theory of Dissipative Systems with Gapped Momentum States
• Non-Hermitian von Roos Hamiltonian's $\eta$-weak-pseudo-Hermiticity, isospectrality and exact solvability
• Maximal quantum entanglement at exceptional points via unitary and thermal dynamics
• Generation of Bell, W and GHZ states via exceptional points in non-Hermitian quantum spin systems
• PT-symmetry and its spontaneous breakdown explained by anti-linearity
• Pseudo-Hermitian Quantum Dynamics of Tachyonic Spin-1/2 Particles
• Interplay between Fano resonance and $\mathcal{P}\mathcal{T}$ symmetry in non-Hermitian discrete systems
• Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry
• Matching method and exact solvability of discrete PT-symmetric square wells
• Universal scalefree non-Hermitian skin effect near the Bloch point
• Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians
• Bose-Einstein condensates with balanced gain and loss beyond mean-field theory
• Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• First-order intertwining operators with position dependent mass and $\eta$- weak-psuedo-Hermiticity generators
• Pseudo Hermitian Generalized Dirac Oscillators
• A note on topological insulator phase in non-hermitian quantum systems
• Non-Bloch band theory for non-Hermitian continuum systems
• Quantum Phase Transition in a Pseudo-hermitian Dicke model
• Emergent Mott insulators and non-Hermitian conservation laws in an interacting bosonic chain with noninteger filling and nonreciprocal hopping
• Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
• Weak Ergodicity Breaking in Non-Hermitian Many-body Systems
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Long-range entangled zero-mode state in a non-Hermitian lattice
• Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
• Pontryagin-Optimal Control of a non-Hermitian Qubit
• Propagation of Electromagnetic Waves in Linear Media and Pseudo-Hermiticity
• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Quantum parameter estimation of non-Hermitian systems with optimal measurements
• Pseudo supersymmetric partners for the generalized Swanson model
• Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
• Dispersive readout of a weakly coupled qubit via the parity-time-symmetric phase transition
• Geometric phase and phase diagram for non-Hermitian quantum XY model
• Spiked potentials and quantum toboggans
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials
• Real spectra for non-Hermitian Dirac equation in 1+1 dimensions with a most general coupling
• Discrete quantum square well of the first kind
• Restoring number conservation in quadratic bosonic Hamiltonians with dualities
• Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models
• Basics of Quantum Mechanics, Geometrization and some Applications to Quantum Information
• Non-Hermitian Holography
• On the Pseudo-Hermiticity of a Class of PT-Symmetric Hamiltonians in One Dimension
• Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry
• QT-Symmetry and Weak Pseudo-Hermiticity
• Quantum centrality testing on directed graphs via PT-symmetric quantum walks
• Scattering of partially coherent radiation by non-Hermitian localized structures having Parity-Time symmetry
• Complex Berry phase and imperfect non-Hermitian phase transitions
• On the Role of the Normalization Factors ${\kappa }_n$ and of the Pseudo-Metric $\mathcal{P}\ne {\mathcal{P}}^{†}$ in Crypto-Hermitian Quantum Models
• $S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians
• Dynamics of finite dimensional non-hermitian systems with indefinite metric
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• Classical oscillator with position-dependent mass in a complex domain
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
• Charge Conjugation Invariance of the Vacuum and the Cosmological Constant Problem
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• PT-Invariant Periodic Potentials with a Finite Number of Band Gaps
• Alternative descriptions and bipartite compound quantum systems
• Chern number in Ising models with spatially modulated real and complex fields
• Ising chain with topological degeneracy induced by dissipation
• Quantum state discrimination in a PT-symmetric system
• Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction
• Non-Hermitian noncommutative quantum mechanics
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• Local photons
• Gain-Loss Coupled Systems
• Enhancement of photon creation through the pseudo-Hermitian dynamical Casimir effect
• Non-Hermitian spectral changes in the scattering of partially coherent radiation by periodic structures
• Noninteger flux - why it does not work
• Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?
• Overcritical PT-symmetric square well potential in the Dirac equation
• Bulk-edge correspondence and stability of multiple edge states of a $\mathcal{P}\mathcal{T}$ symmetric non-Hermitian system by using non-unitary quantum walks
• Thermodynamics of Pseudo-Hermitian Systems in Equilibrium
• Finite-temperature quantum criticality in a complex-parameter plane
• Resonant generation of $p$-wave Cooper pair in non-Hermitian Kitaev chain at exceptional point
• $\mathcal{P}\mathcal{T}$ symmetric evolution, coherence and violation of Leggett-Garg inequalities
• Chaotic diffusion of complex trajectory and its quantum signature
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• Unitary evolution for a two-level quantum system in fractional-time scenario
• Coherent states of non-Hermitian quantum systems
• The Floquet Baxterisation
• Quantum Work Relations and Response Theory in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Systems
• $\ell$-oscillators from second-order invariant PDEs of the centrally extended Conformal Galilei Algebras
• Real-Time Transport in Open Quantum Systems From $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
• Spontaneous and explicit parity-time-symmetry breaking in drift wave instabilities
• Complete particle-pair annihilation as a dynamical signature of the spectral singularity
• Transfer-matrix formulation of the scattering of electromagnetic waves and broadband invisibility in three dimensions
• IR/UV mixing from local similarity maps of scalar non-Hermitian field theories
• Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
• Non-Hermitian multi-particle systems from complex root spaces
• The effect of thermal photons on exceptional points in coupled resonators
• The Quantum Effective Mass Hamilton-Jacobi Problem
• Generalized Grassmannian Coherent States For Pseudo-Hermitian $n$ Level Systems
• Quantum deleting and cloning in a pseudo-unitary system
• Linear representation of energy-dependent Hamiltonians
• Spectrum and normal modes of non-hermitian quadratic boson operators
• PT-symmetric regularizations in supersymmetric quantum mechanics
• Direct observation of energy band attraction effect in non-Hermitian systems
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity
• Quantum Models of Consciousness from a Quantum Information Science Perspective
• Gravitational Effects in g Factor Measurements and High-Precision Spectroscopy: Limits of Einstein's Equivalence Principle
• Cosmological perturbations in conformal gravity II
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• Solvable dilation model of $\mathcal{P}\mathcal{T}$-symmetric systems
• Proposal of a quantum version of active particles via a nonunitary quantum walk
• Bosonic pair creation and the Schiff-Snyder-Weinberg effect
• Non-Hermitian Hamiltonians and similarity transformations
• Topological field theory of dynamical systems. II
• Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement
• Formation of Exceptional Points in pseudo-Hermitian Systems
• A possible method for non-Hermitian and non-$PT$-symmetric Hamiltonian systems
• Extended Jaynes-Cummings models and (quasi)-exact solvability
• Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation
• Quantum mold casting for topological insulating and edge states
• Transfer matrix for long-range potentials
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Non-Hermitian $\mathcal{P}\mathcal{T}$-Symmetric Dirac-Pauli Hamiltonians with Real Energy Eigenvalues in the Magnetic Field
• Exact propagators for complex SUSY partners of real potentials
• PT-Symmetric Quantum Electrodynamics and Unitarity
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• A Novel SUSY Energy Bound States Treatment of the Klein-Gordon Equation with PT-Supersymmetric and q-Deformed Hulthen Potential
• Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
• The cryptohermitian smeared-coordinate representation of wave functions
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Tachyonic Field Theory and Neutrino Mass Running
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Neutrino Helicity Reversal and Fundamental Symmetries
• Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty
• Multitude of exceptional points in van der Waals magnets
• Waveguide QED with dissipative light-matter couplings
• Mixed states driven by Non-Hermitian Hamiltonians of a nuclear spin ensemble
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• Symmetry classes of dissipative topological insulators with edge dark state
• Anyonic $\mathcal{P}\mathcal{T}$ symmetry, drifting potentials and non-Hermitian delocalization
• Dynamical formulation of low-energy scattering in one dimension
• Non-Hermitian Quantum Quenches in Holography
• Internal nonlocality in generally dilated Hermiticity
• Dynamical Theory of Scattering, Exact Unidirectional Invisibility, and Truncated $\mathfrak{z}{e}^{-2i{k}_{0}x}$ potential
• Towards the theory of types III and IV non-Hermitian Weyl fermions
• Operator size growth in Lindbladian SYK
• Electric conductivity in non-Hermitian holography
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems
• Emergent $\mathcal{P}\mathcal{T}$-symmetry breaking of collective modes with topological critical phenomena
• Equivalent Hermitian operator from supersymmetric quantum mechanics
• Krein-unitary Schrieffer-Wolff transformation and band touchings in bosonic Bogoliubov-de Gennes and other Krein-Hermitian Hamiltonians
• Entropy and entanglement in a bipartite quasi-Hermitian system and its Hermitian counterparts
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices
• Dynamical Signatures of Liouvillian Flat Band
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits
• $\mathcal{P}\mathcal{T}$-symmetric currents of a Bose-Einstein condensate in a triple well
• Non-Relativistic Anti-Snyder Model and Some Applications
• Exact solutions for time-dependent complex symmetric potential well
• Supersymmetric Analysis of the Dirac-Weyl Operator within PT Symmetry
• Which Metrics Are Consistent with a Given Pseudo-Hermitian Matrix?
• Topological phase in Kitaev chain with spatially separated pairing processes
• An Algebraic PT-Symmetric Quantum Theory with a Maximal Mass
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
• Pseudo-Hermitian continuous-time quantum walks
• Non-Hermitian Hamiltonian versus E=0 localized states
• $\mathcal{P}\mathcal{T}$-symmetric quantum Rabi model: Solutions and exceptional points
• On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule
• On the one-dimensional reggeon model: eigenvalues of the Hamiltonian and the propagator
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• Linear level repulsions near exceptional points of non-Hermitian systems
• Exceptional points and pseudo-Hermiticity in real potential scattering
• Dynamics of non-Hermitian Floquet Wannier-Stark system
• Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction
• Essential implications of similarities in non-Hermitian systems
• Invariant PDEs of Conformal Galilei Algebra as deformations: cryptohermiticity and contractions
• Exponential quantum advantages for practical non-Hermitian eigenproblems
• Instantaneous modulations in time-varying complex optical potentials
• Metric-scalar gravity with torsion and the measurability of the non-minimal coupling
• Unitarity through PT symmetry in Quantum Quadratic Gravity
• Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip
• New families of non-parity-time-symmetric complex potentials with all-real spectra
• Quantum knots
• Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials
• Pseudo-Hermiticity, PT-symmetry, and the Metric Operator
• Enhancement of signal-to-noise ratio at a high-order exceptional point of coherent perfect absorption
• PT symmetry as a necessary and sufficient condition for unitary time evolution
• Pseudo-Hermiticity and Electromagnetic Wave Propagation: The case of anisotropic and lossy media
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules
• PT-symmetry and Schrödinger operators. The double well case
• A generalized Swanson Hamiltonian in a second-derivative pseudo-supersymmetric framework
• Non-Hermitian systems with a real spectrum and selective skin effect
• Tunable tachyon mass in the PT-broken massive Thirring model
• Discrete spectrum of thin PT-symmetric waveguide
• Supersymmetric quantum mechanics and the Riemann hypothesis
• Infinite-dimensional representations of the rotation group and Dirac's monopole problem
• Scattering of Spin-$\frac{1}{2}$ Particles from a $\mathcal{P}\mathcal{T}$-symmetric Complex Potential
• Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
• Manifestation of Superposition and Coherence in $\mathcal{P}\mathcal{T}$-symmetry through the $\eta$-inner Product
• Metric Operator For The Non-Hermitian Hamiltonian Model and Pseudo-Supersymmetry
• Non-Hermitian tearing by dissipation
• Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Emerging (2+1)D electrodynamics and topological instanton in pseudo-Hermitian two-level systems
• A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian Quantum Mechanics : $\gamma$-deformed $su(2)$ generators, Partial $\mathcal{P}\mathcal{T}$-symmetry and Higgs algebra
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Composition of Transfer Matrices for Potentials with Overlapping Support
• Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space
• Initial states of qubit-boson models leading to conserved quantities
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• Adjusting exceptional points using saturable nonlinearities
• Electron Self-energy in Pseudo-Hermitian Quantum Electrodynamics with a Maximal Mass M
• Canonical Expansion of PT-Symmetric Operators and Perturbation Theory
• Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetry
• Spherical-separablility of non-Hermitian Hamiltonians and pseudo-PT-symmetry
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Monopoles in non-Hermitian systems
• Asymptotic Exceptional Steady States in Dissipative Dynamics
• Eigenvalues collision for PT-symmetric waveguide
• Pseudo-Hermiticity and Electromagnetic Wave Propagation in Dispersive Media
• Conditional observability versus self-duality in a schematic model
• Quantum implementation of non-unitary operations with biorthogonal representations
• Lorentz Quantum Computer
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Extracting the internal nonlocality from the dilated Hermiticity
• Emergent non-Hermitian conservation laws at exceptional points
• Supersymmetric $\eta$ operators
• Anti-$\mathcal{P}\mathcal{T}$-symmetric Qubit: Decoherence and Entanglement Entropy
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
• An update on coherent scattering from complex non-PT-symmetric Scarf II potential with new analytic forms
• Nonlocality of Observables in Quasi-Hermitian Quantum Theory
• General Approach to Error Detection of Bosonic Codes via Phase Estimation
• A Hermitian bypass to the non-Hermitian quantum theory
• $\mathcal{P}\mathcal{T}$-Symmetric Generalized Extended Momentum Operator
• Entanglement of pseudo-Hermitian random states
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Some Remarks on Quantum Brachistochrone
• Quantum backreaction effect in optical solitons
• Consistent treatment of quantum systems with a time-dependent Hilbert space
• Path-integral Bosonization of $d=2$ PT symmetric models
• Third-order exceptional surface in a pseudo-Hermitian superconducting circuit
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes
• Planarizable Supersymmetric Quantum Toboggans
• On the construction of pseudo-Hermitian Hamiltonians by means of similarity transformations
• Balancing gain and loss in symmetrised multi-well potentials
• Swanson Hamiltonian: non-PT-symmetry phase
• Reduced dynamics in quasi-Hermitian systems
• Anisotropic oscillator with pseudo-hermiticity and its noncommutative extension
• Identification of the metric for diagonalizable (anti-)pseudo-Hermitian Hamilton operators represented by two-dimensional matrices
• Regularization of energy-dependent pointlike interactions in 1D quantum mechanics
• Instantons and transseries of the Mathieu potential deformed by a $\mathcal{P}\mathcal{T}$-symmetry parameter
• Neutrino Pair Cerenkov Radiation for Tachyonic Neutrinos
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model
• Quantization of pseudo-hermitian systems
• $\mathcal{P}\mathcal{T}-$Symmetric Two-Level Open Quantum Systems: Information Theoretic Facets
• Physical constraints on effective non-Hermitian systems
• Non-real Eigenvalues for PT-Symmetric Double Wells
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system
• $\mathcal{P}\mathcal{T}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics
• Topological Field Theory and Stochastic Dynamics
• PT-symmetry and Integrability
• Bound state eigenvalues from transmission coefficients