Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian

Abstract

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudo-supersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler-DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum.

Revised version, to appear in J. Math. Phys

References in corpus (4)

• Supersymmetry and the spontaneous breakdown of PT symmetry
• Quantum Complex Henon-Heiles Potentials
• Conservation of pseudo-norm in PT symmetric quantum mechanics
• The Interpretation of Quantum-Mechanical Models with Non-Hermitian Hamiltonians and Real Spectra

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• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
• Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• The potential (iz)^m generates real eigenvalues only, under symmetric rapid decay conditions
• Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Chiral state transfer under dephasing
• Long-range entangled zero-mode state in a non-Hermitian lattice
• Weak Ergodicity Breaking in Non-Hermitian Many-body Systems
• Extension of selected configuration interaction for transcorrelated methods
• Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
• Spin-half bosons with mass dimension three half: Evading the spin-statistics theorem
• Third order spectral branch points in Krein space related setups: PT-symmetric matrix toy model, MHD alpha^2-dynamo, and extended Squire equation
• Pseudo supersymmetric partners for the generalized Swanson model
• Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator
• Propagation of Electromagnetic Waves in Linear Media and Pseudo-Hermiticity
• Spiked potentials and quantum toboggans
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials
• Dispersive readout of a weakly coupled qubit via the parity-time-symmetric phase transition
• Wave-kinetic approach to zonal-flow dynamics: recent advances
• Exact solutions for time-dependent non-Hermitian oscillators: classical and quantum pictures
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Universal subdiffusive behavior at band edges from transfer matrix exceptional points
• turboMagnon -- A code for the simulation of spin-wave spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory
• Realization of complex conjugate media using non-PT-symmetric photonic crystals
• Shortcuts to adiabaticity in non-Hermitian quantum systems without rotating-wave approximation
• $\mathcal{P}\mathcal{T}$ symmetric phase transition and single-photon transmission in an optical trimmer system
• Quantum and Classical Statistical Mechanics of a Class of non-Hermitian Hamiltonians
• Real spectra for non-Hermitian Dirac equation in 1+1 dimensions with a most general coupling
• CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C
• Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
• Creation and annihilation operators and coherent states for the PT-symmetric oscillator
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Restoring number conservation in quadratic bosonic Hamiltonians with dualities
• Conserved quantities, exceptional points, and antilinear symmetries in non-Hermitian systems
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Nonlinear Holomorphic Supersymmetry on Riemann Surfaces
• Non-Hermitian Holography
• Scattering of partially coherent radiation by non-Hermitian localized structures having Parity-Time symmetry
• On the Pseudo-Hermiticity of a Class of PT-Symmetric Hamiltonians in One Dimension
• Discrete quantum square well of the first kind
• Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries
• Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems
• Quantum centrality testing on directed graphs via PT-symmetric quantum walks
• Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models
• Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry
• QT-Symmetry and Weak Pseudo-Hermiticity
• Signature of PT-symmetric non-Hermitian superconductivity in angle-resolved photoelectron fluctuation spectroscopy
• PT-symmetric optical superlattices
• Dynamics of finite dimensional non-hermitian systems with indefinite metric
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• Dissipative time crystals originating from parity-time symmetry
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• On the Role of the Normalization Factors ${\kappa }_n$ and of the Pseudo-Metric $\mathcal{P}\ne {\mathcal{P}}^{†}$ in Crypto-Hermitian Quantum Models
• Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• Classical oscillator with position-dependent mass in a complex domain
• Floquet exceptional contours in Lindblad dynamics with time-periodic drive and dissipation
• Remarks on PT-pseudo-norm in PT-symmetric quantum mechanics
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• $S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians
• Exactly solvable models with PT-symmetry and with an asymmetric coupling of channels
• Alternative descriptions and bipartite compound quantum systems
• Scaling laws for non-Hermitian skin effect with long-range couplings
• On-demand Parity-Time symmetry in a lone oscillator through complex, synthetic gauge fields
• Nonlocal reductions of the Ablowitz-Ladik equation
• Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution
• Analytically solvable $2\times 2$ $PT$-symmetry dynamics from su(1,1)-symmetry problems
• Use of Equivalent Hermitian Hamiltonian for $PT$-Symmetric Sinusoidal Optical Lattices
• PT-Invariant Periodic Potentials with a Finite Number of Band Gaps
• Nonlinear parity-time-symmetric transition in finite-size optical couplers
• Structure, Time Propagation and Dissipative Terms for Resonances
• Scattering theory for stationary materials with $\mathcal{P}\mathcal{T}$ symmetry
• Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup
• Can degenerate bound states occur in one dimensional quantum mechanics?
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• The Gram Matrix of a PT-symmetric Quantum System
• Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction
• Andreev bound states in junctions formed by conventional and $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian superconductors
• Quantum state discrimination in a PT-symmetric system
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Non-Hermitian noncommutative quantum mechanics
• Ising chain with topological degeneracy induced by dissipation
• Scrambling and operator entanglement in local non-Hermitian quantum systems
• Overcritical PT-symmetric square well potential in the Dirac equation
• Conformal generation of an exotic rotationally invariant harmonic oscillator
• Improving shortcuts to non-Hermitian adiabaticity for fast population transfer in open quantum systems
• Gain-Loss Coupled Systems
• $\mathcal{D}$-deformed harmonic oscillators
• Non-Hermitian quantum dynamics and entanglement of coupled nonlinear resonators
• Dual oscillators and Quantum Pendulums: spectrum and correlators
• PT-symmetric quantum graphs
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials
• Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model
• Supersymmetric Biorthogonal Quantum Systems
• 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
• Quasinormal mode analysis of chiral power flow from linearly polarized dipole emitters coupled to index-modulated microring resonators close to an exceptional point
• Signature of exceptional point phase transition in Hermitian systems
• Non-Hermitian spectral changes in the scattering of partially coherent radiation by periodic structures
• Enhancement of photon creation through the pseudo-Hermitian dynamical Casimir effect
• Thermodynamics of Pseudo-Hermitian Systems in Equilibrium
• Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?
• PT-symmetric supersymmetry in a solvable short-range model
• Conformal bridge transformation and PT symmetry
• Dissipative dynamics in open XXZ Richardson-Gaudin models
• Strengthened PT-symmetry with P $\ne$ P${}^{†}$
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• Quantum transport in non-Hermitian impurity array
• Unitary evolution for a two-level quantum system in fractional-time scenario
• Investigation of PT-symmetric Hamiltonian systems from an alternative point of view
• Quantum Work Relations and Response Theory in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Systems
• The MHD alpha^2-dynamo, Z_2-graded pseudo-Hermiticity, level crossings and exceptional points of branching type
• Embedding quantum systems with a non-conserved probability in classical environments
• Complex oscillator and Painlevé IV equation
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• The spectrum of a Harmonic Oscillator Operator Perturbed by Point Interactions
• The Floquet Baxterisation
• Wide-range-tunable Dirac-cone band structure in a chiral-time-symmetric non-Hermitian system
• Spontaneous and explicit parity-time-symmetry breaking in drift wave instabilities
• $\ell$-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
• Resonant generation of $p$-wave Cooper pair in non-Hermitian Kitaev chain at exceptional point
• Coherent states of non-Hermitian quantum systems
• On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics
• Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations
• IR/UV mixing from local similarity maps of scalar non-Hermitian field theories
• Quantum deleting and cloning in a pseudo-unitary system
• Connecting active and passive $\mathcal{P}\mathcal{T}$-symmetric Floquet modulation models
• Transfer-matrix formulation of the scattering of electromagnetic waves and broadband invisibility in three dimensions
• Observables in non-Hermitian systems: A methodological comparison
• Parity-time symmetry under magnetic flux
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Complete particle-pair annihilation as a dynamical signature of the spectral singularity
• The effect of thermal photons on exceptional points in coupled resonators
• Unitary Scattering Protected by Pseudo-Hermiticity
• Quantum Big Bang without fine-tuning in a toy-model
• Generalized Grassmannian Coherent States For Pseudo-Hermitian $n$ Level Systems
• The Quantum Effective Mass Hamilton-Jacobi Problem
• On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)
• Stretching An Anisotropic DNA
• p-Adic Schrödinger-Type Operator with Point Interactions
• A universal form of complex potentials with spectral singularities
• Spectrum and normal modes of non-hermitian quadratic boson operators
• A new solvable complex PT-symmetric potential
• Nonlinear supersymmetry: from classical to quantum mechanics
• Gauging non-Hermitian Hamiltonians
• Linear representation of energy-dependent Hamiltonians
• Cosmological perturbations in conformal gravity II
• On the K-theoretic classification of dynamically stable systems
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Quantum Models of Consciousness from a Quantum Information Science Perspective
• From Euclidean to Lorentzian Loop Quantum Gravity via a Positive Complexifier
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Direct observation of energy band attraction effect in non-Hermitian systems
• Gravitational Effects in g Factor Measurements and High-Precision Spectroscopy: Limits of Einstein's Equivalence Principle
• On nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
• Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity
• Quadratic pseudosupersymmetry in two-level systems
• Lorentz invariant photon number density
• Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
• Bosonic pair creation and the Schiff-Snyder-Weinberg effect
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Quantum Systems and Alternative Unitary Descriptions
• Spontaneous breaking of permutation symmetry in pseudo-Hermitian quantum mechanics
• Formation of Exceptional Points in pseudo-Hermitian Systems
• Position-dependent mass in strong quantum gravitational background fields
• Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement
• A possible method for non-Hermitian and non-$PT$-symmetric Hamiltonian systems
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• A Perturbative Treatment Of A Generalized PT-Symmetric Quartic Anharmonic Oscillator
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Non-Hermitian Hamiltonians and similarity transformations
• Extended Jaynes-Cummings models and (quasi)-exact solvability
• Proposal of a quantum version of active particles via a nonunitary quantum walk
• Identification of observables in quantum toboggans
• Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature
• Majorana quanta, string scattering, curved spacetimes and the Riemann Hypothesis
• Solvable dilation model of $\mathcal{P}\mathcal{T}$-symmetric systems
• The phase diagram and vortex properties of PT-symmetric non-Hermitian two-component superfluid
• Structure formation in turbulence as instability of effective quantum plasma
• Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation
• Topological field theory of dynamical systems. II
• Self-Organized Criticality as Witten-type Topological Field Theory with Spontaneously Broken Becchi-Rouet-Stora-Tyutin Symmetry
• Non-Hermitian $\mathcal{P}\mathcal{T}$-Symmetric Dirac-Pauli Hamiltonians with Real Energy Eigenvalues in the Magnetic Field
• Lorentz Symmetric Quantum Field Theory for Symplectic Fermions
• Quantum mold casting for topological insulating and edge states
• Small-$\epsilon$ behavior of the Non-Hermitian PT-Symmetric Hamiltonian $H=p^2+x^2(ix{)}^{\epsilon }$
• Coalescing Majorana edge modes in non-Hermitian PT-symmetric Kitaev chain
• Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation
• WKB Analysis of PT-Symmetric Sturm-Liouville problems. II
• Effective Field calculations of the Energy Spectrum of the $\mathcal{P}\mathcal{T}$-Symmetric ($-x^4$) Potential
• Pseudo-Hermitian coherent states under the generalized quantum condition with position-dependent mass
• On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators
• Exact propagators for complex SUSY partners of real potentials
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Wave Function of the Universe and Its Meaning
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Exceptional point in a coupled Swanson system
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• $\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry
• PT-Symmetric Quantum Electrodynamics and Unitarity
• Quantum Metrology with Higher-order Exceptional Points in Atom-cavity Magnonics
• Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays
• Probing de Sitter Space Using CFT States
• Transfer matrix for long-range potentials
• Non-Hermitian quantum rings
• Comparing Hermitian and Non-Hermitian Quantum Electrodynamics
• Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain
• Exact quantization conditions and full transseries structures for $\mathcal{P}\mathcal{T}$ symmetric anharmonic oscillators
• Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Tachyonic Field Theory and Neutrino Mass Running
• Pseudo-Hermitian Random Matrix Models: General Formalism
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Parity-time symmetric systems with memory
• A Novel SUSY Energy Bound States Treatment of the Klein-Gordon Equation with PT-Supersymmetric and q-Deformed Hulthen Potential
• On Wigner Degeneracy in Elko theory: Hermiticity and Dark Matter
• Origin of branch points in the spectrum of PT-symmetric periodic potentials
• Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM
• Kappa-deformed Dirac oscillator in an external magnetic field
• Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
• The cryptohermitian smeared-coordinate representation of wave functions
• Switchable Non-Hermitian Skin Effect in Bogoliubov Modes
• Multitude of exceptional points in van der Waals magnets
• Mixed states driven by Non-Hermitian Hamiltonians of a nuclear spin ensemble
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Waveguide QED with dissipative light-matter couplings
• Scattering states of a particle, with position-dependent mass, in a $\mathcal{P}\mathcal{T}$ symmetric heterojunction
• Neutrino Helicity Reversal and Fundamental Symmetries
• Dynamical formulation of low-energy scattering in one dimension
• Effects of the third-order dispersion on continuous waves in complex potentials
• Symmetry classes of dissipative topological insulators with edge dark state
• Nonuniqueness of the C operator in PT-symmetric quantum mechanics
• Anyonic $\mathcal{P}\mathcal{T}$ symmetry, drifting potentials and non-Hermitian delocalization
• Internal nonlocality in generally dilated Hermiticity
• Aspects of the ODE/IM correspondence
• Operator size growth in Lindbladian SYK
• Equivalent Hamiltonian for Lee Model
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Entropy and entanglement in a bipartite quasi-Hermitian system and its Hermitian counterparts
• Quantum simulation of dissipation for Maxwell equations in dispersive media
• Emergent $\mathcal{P}\mathcal{T}$-symmetry breaking of collective modes with topological critical phenomena
• Particle injection into a chain: decoherence versus relaxation for Hermitian and non-Hermitian dynamics
• Non-Hermiticity in quantum nonlinear optics through symplectic transformations
• Electric conductivity in non-Hermitian holography
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Real spectra in one-dimensional single-band non-Hermitian Hamiltonians
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• Krein-unitary Schrieffer-Wolff transformation and band touchings in bosonic Bogoliubov-de Gennes and other Krein-Hermitian Hamiltonians
• Non-Hermitian Quantum Quenches in Holography
• Dynamical Theory of Scattering, Exact Unidirectional Invisibility, and Truncated $\mathfrak{z}{e}^{-2i{k}_{0}x}$ potential
• Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator
• Green Functions for the Wrong-Sign Quartic
• Pseudo-conservative dynamics of coupled polariton condensates
• Squeezed atom laser for Bose-Einstein condensate with minimal length
• Quantum toboggans: models exhibiting a multisheeted PT symmetry
• Dynamics of Disordered Mechanical Systems with Large Connectivity, Free Probability Theory, and Quasi-Hermitian Random Matrices
• Nonequilibrium Work Relation from Schroedinger's Unrecognized Probability Theory
• Non-Hermitian Model for Asymmetrical Tunneling
• Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems
• Dynamics in non-Hermitian systems with nonreciprocal coupling
• Supersymmetric Analysis of the Dirac-Weyl Operator within PT Symmetry
• On the one-dimensional reggeon model: eigenvalues of the Hamiltonian and the propagator
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Interplay between nonclassicality and $\mathcal{P}\mathcal{T}$ symmetry in an effective two level system with open system effects
• $\mathcal{P}\mathcal{T}$-symmetric quantum Rabi model: Solutions and exceptional points
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• Parsing skin effect in a non-Hermitian spinless BHZ-like model
• Non-Hermitian Quantum Fermi Accelerator
• Non-Bloch band theory for time-modulated discrete mechanical systems
• An Algebraic PT-Symmetric Quantum Theory with a Maximal Mass
• Non-Relativistic Anti-Snyder Model and Some Applications
• $\mathcal{P}\mathcal{T}$-symmetric currents of a Bose-Einstein condensate in a triple well
• Equivalence and Hermiticity of Dirac Hamiltonians in the Kerr gravitational field
• Pseudo-hermitian random matrix theory: a review
• Exact solutions for time-dependent complex symmetric potential well
• Pseudo-Hermitian continuous-time quantum walks
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits
• Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices
• On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule
• Eigenvalue problems for the complex PT-symmetric potential V(x)= igx
• Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• sh(2/2) Superalgebra eigenstates and generalized supercoherent and supersqueezed states
• Topological phase in Kitaev chain with spatially separated pairing processes
• Which Metrics Are Consistent with a Given Pseudo-Hermitian Matrix?
• Two-level systems: exact solutions and underlying pseudo-supersymmetry
• Non-Hermitian Hamiltonian versus E=0 localized states
• A model of a 2d non-Fermi liquid with SO(5) symmetry, AF order, and a d-wave SC gap
• Nonlinear transition between PT-symmetric and PT-broken modes in coupled fiber lasers
• Enhancement of signal-to-noise ratio at a high-order exceptional point of coherent perfect absorption
• Dynamics of mode entanglement in a system of cavities coupled with a chiral mirror
• Extended unitarity and absence of skin effect in periodically driven systems
• Locality, Correlations, Information, and non-Hermitian Quantum Systems
• An introductory review on resource theories of generalized nonclassical light
• Parity-Time Symmetry and Exceptional points: A Tutorial
• Dynamics of non-Hermitian Floquet Wannier-Stark system
• Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
• Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials
• Pseudo-Hermiticity, PT-symmetry, and the Metric Operator
• Non-hermitian time evolution: from static to parametric instability
• Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip
• Topological field theory of dynamical systems
• Unitarity through PT symmetry in Quantum Quadratic Gravity
• Schrödinger type eigenvalue problems with polynomial potentials: Asymptotics of eigenvalues
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• Phase transitions as a manifestation of spontaneous unitarity violation
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Linear level repulsions near exceptional points of non-Hermitian systems
• Unusual isospectral factorizations of shape invariant Hamiltonians with Scarf II potential
• Balanced gain and loss in spatially extended non-$\mathcal{P}\mathcal{T}$-symmetric multi-well potentials
• Sums over geometries and improvements on the mean field approximation
• Instantaneous modulations in time-varying complex optical potentials
• Exponential quantum advantages for practical non-Hermitian eigenproblems
• Non-Hermiticity: a new paradigm for model building in particle physics
• Quantum knots
• New families of non-parity-time-symmetric complex potentials with all-real spectra
• Physics of crypto-Hermitian and/or cryptosupersymmetric field theories
• Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
• Correlations at higher-order exceptional points in non-Hermitian models
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• Invariant PDEs of Conformal Galilei Algebra as deformations: cryptohermiticity and contractions
• Exceptional points and pseudo-Hermiticity in real potential scattering
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation
• Essential implications of similarities in non-Hermitian systems
• Scattering of Spin-$\frac{1}{2}$ Particles from a $\mathcal{P}\mathcal{T}$-symmetric Complex Potential
• Pseudo-symmetric random matrices: semi-Poisson and sub-Wigner statistics
• The Analytic Continuation of the Lippmann-Schwinger Eigenfunctions, and Antiunitary Symmetries
• Manifestation of Superposition and Coherence in $\mathcal{P}\mathcal{T}$-symmetry through the $\eta$-inner Product
• PT symmetry as a necessary and sufficient condition for unitary time evolution
• Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
• Pseudo-Hermiticity and Electromagnetic Wave Propagation: The case of anisotropic and lossy media
• Einstein's equations and the pseudo-entropy of pseudo-Riemannian information manifolds
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry
• Heat transport through an open coupled scalar field theory hosting stability-to-instability transition
• Coherent and squeezed states of quantum Heisenberg algebras
• PT-symmetry and Schrödinger operators. The double well case
• A generalized Swanson Hamiltonian in a second-derivative pseudo-supersymmetric framework
• New version of pseudo-hermiticity in the two-sided deformation of Heisenberg algebra
• Infinite-dimensional representations of the rotation group and Dirac's monopole problem
• Supersymmetric quantum mechanics and the Riemann hypothesis
• Three-Dimensional Solutions of Supersymmetrical Intertwining Relations and Pairs of Isospectral Hamiltonians
• Crypto-Harmonic Oscillator in Higher Dimensions: Classical and Quantum Aspects
• Parallel numerical method for nonlocal-in-time Schrödinger equation
• Discrete spectrum of thin PT-symmetric waveguide
• Space-time symmetry and nonreciprocal parametric resonance in mechanical systems
• Conformal bridge in a cosmic string background
• Tunable tachyon mass in the PT-broken massive Thirring model
• Quantum mechanical equivalence of the metrics of a centrally symmetric gravitational field
• Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
• The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism
• Quasi-exact minus-quartic oscillators in strong-core regime
• Recognizing critical lines via entanglement in non-Hermitian systems
• Stability of time-periodic $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonians with different periodicities
• Schrodinger Operators with Non-Symmetric Zero-Range Potentials
• Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space
• Initial states of qubit-boson models leading to conserved quantities
• The Lefschetz thimble and the sign problem
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Emerging (2+1)D electrodynamics and topological instanton in pseudo-Hermitian two-level systems
• New Deformed Heisenberg Algebra from the $\mu$-Deformed Model of Dark Matter
• Supersymmetric Theory of Stochastic ABC Model: A Numerical Study
• Factorized Hilbert-space metrics and non-commutative quasi-Hermitian observables
• Non-Hermitian tearing by dissipation
• Robustness of entanglement in a non-Hermitian cavity-optomechanical system even away from exceptional points
• Conserved quantities in non-Hermitian systems via vectorization method
• Acoustic response in a a one-dimensional layered pseudo-Hermitian metamaterial containing defects
• Local preservation of no-signaling in multiparty PT-symmetric evolutions
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Hermitian and non-Hermitian topology in active matter
• Quantized Area of the Schwarzschild Black Hole: A non-Hermitian Perspective
• Supersymmetry of $\mathcal{P}\mathcal{T}$- symmetric tridiagonal Hamiltonians
• Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase
• Representation Dependence of Superficial Degree of Divergences in Quantum Field Theory
• Exceptional points in perturbed dielectric spheres: A resonant-state expansion study
• Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space
• Metric Operator For The Non-Hermitian Hamiltonian Model and Pseudo-Supersymmetry
• Gaussian-random Ensembles of Pseudo-Hermitian Matrices
• Canonical Expansion of PT-Symmetric Operators and Perturbation Theory
• Schrieffer-Wolff transformation for non-Hermitian systems: application for $\mathcal{P}\mathcal{T}$-symmetric circuit QED
• Adjusting exceptional points using saturable nonlinearities
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Oblique scattering from non-Hermitian optical waveguides
• Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetry
• Spherical-separablility of non-Hermitian Hamiltonians and pseudo-PT-symmetry
• Some spectral equivalences between Schrodinger operators
• Artificial Hawking radiation, weak pseudo-Hermiticity and Weyl semimetal blackhole analogy
• Hofstadter-Toda spectral duality and quantum groups
• Quantization of Second Order Fermions
• $\mathcal{P}\mathcal{T}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities
• Composition of Transfer Matrices for Potentials with Overlapping Support
• Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model
• Topologically protected two-fluid edge states
• Quantum implementation of non-unitary operations with biorthogonal representations
• Building ground states of Hubbard model by time-ordered bound-pair injection
• Lorentz Quantum Computer
• Quantum geometric tensors from sub-bundle geometry
• Natural polynomials for Kerr quasi-normal modes
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Asymptotic Exceptional Steady States in Dissipative Dynamics
• Pseudo-Hermiticity and Electromagnetic Wave Propagation in Dispersive Media
• Dynamical symmetry algebra of two superintegrable two-dimensional systems
• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. II. Three-Dimensional Model
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• Monopoles in non-Hermitian systems
• Quantum Instability
• Extracting the internal nonlocality from the dilated Hermiticity
• Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics
• Linked $\mathcal{P}\mathcal{T}$-symmetry to Supersymmetry in a class of non-Hermitian Hamiltonians
• Improved coherence time of a non-Hermitian qubit in a $\mathcal{P}\mathcal{T}$-symmetric Environment
• Conditional observability versus self-duality in a schematic model
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Understanding Partial PT symmetry as weighted composition conjugation in Reproducing Kernel Hilbert Space :An application to non-hermitian Bose-Hubbard type Hamiltonian in Fock space
• Meissner effect in non-Hermitian superconductors
• Eigenvalues collision for PT-symmetric waveguide
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Some Remarks on Quantum Brachistochrone
• Real spectra and phase transition of skin effect in nonreciprocal systems
• How to deal with the arrow of time in quantum field theory
• Continuous time crystals as a PT symmetric state and the emergence of critical exceptional points
• Euler Polynomials and Identities for Non-Commutative Operators
• Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
• Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes
• The stability and energy exchange mechanism of divergent states with real energy
• Cylindrical first order superintegrability with complex magnetic fields
• Anti-$\mathcal{P}\mathcal{T}$-symmetric Qubit: Decoherence and Entanglement Entropy
• Oscillators with imaginary coupling: spectral functions in quantum mechanics and quantum field theory
• Edge states and persistent current in a PT-symmetric extended Su-Schrieffer-Heeger model with generic boundary conditions
• Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators
• Pseudo-PT symmetric Dirac equation : effect of a new mean spin angular momentum operator on Gilbert damping
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity
• Decomposition of a system in pseudo-Hermitian quantum mechanics
• Exceptional spectrum and dynamic magnetization
• A note on hidden classes in spinor classification
• Pseudo-Hermitian systems, involutive symmetries and pseudofermions
• Enhanced quantum phase estimation with $q$-deformed nonideal nonclassical light
• $\mathcal{P}\mathcal{T}$-Symmetric Generalized Extended Momentum Operator
• Two-step Shape Invariance in the Framework of N-fold Supersymmetry
• Path-integral Bosonization of $d=2$ PT symmetric models
• Second-order pseudo-Hermitian spin-$1/2$ bosons
• Supersymmetric $\eta$ operators
• Consistent treatment of quantum systems with a time-dependent Hilbert space
• Detecting quantum chaos via pseudo-entropy
• Isospectral Hermitian counterpart of complex non Hermitian Hamiltonian $p^2-g{x}^4+a/x^2$
• Third-order exceptional surface in a pseudo-Hermitian superconducting circuit
• Enhancement of sensitivity near exceptional points in dissipative qubit-resonator systems
• Insight of the Green's function as a defect state in a boundary value problem
• Wigner multiplets in QFT: from Wigner degeneracy to Elko fields
• Dynamical non-Hermitian systems: Fingerprints and pure dephasing induced protection effect
• Disorder and non-Hermiticity in Kitaev spin liquids with a Majorana Fermi surface
• Exact solution of Schrödinger equation for the complex Morse potential to investigate physical systems with position-dependent complex mass
• Planarizable Supersymmetric Quantum Toboggans
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• PT-symmetry enabled stable modes in multi-core fiber
• Entanglement of pseudo-Hermitian random states
• Synchronization in PT-symmetric optomechanical resonators
• A Hermitian bypass to the non-Hermitian quantum theory
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• Geometric phase for Dirac Hamiltonian under gravitational fields in the non-relativistic regime
• Quantum backreaction effect in optical solitons
• Clustering of steady-state correlations in open systems with long-range interactions
• Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics
• The Hyperbolic Bloch Equations of General Relativity
• Balancing gain and loss in symmetrised multi-well potentials
• The ODE/IM correspondence and PT-symmetric quantum mechanics
• Solvers for the Hermitian and the pseudo-Hermitian Bethe-Salpeter equation in the Yambo code: Implementation and Performance
• Dynamic manifestation of exception points in a non-Hermitian continuous model with an imaginary periodic potential
• Algebraic construction of associated functions of nondiagonalizable models with anharmonic oscillator complex interaction
• Anharmonic oscillators in the complex plane, $\mathcal{P}\mathcal{T}$-symmetry, and real eigenvalues
• On pseudo-Hermitian operators with generalized $\mathcal{C}$-symmetries
• Phase-Space Topology and Spectral Flow in Screened Magnetized Plasmas
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
• Complex Inflaton Potentials with Nonminimal Coupling: Robust Inflation and Geometric Reheating
• Physical constraints on effective non-Hermitian systems
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system
• PT symmetry and the evolution speed in open quantum systems
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Quantum Simulation of Two-Level $PT$-Symmetric Systems Using Hermitian Hamiltonians
• Neutrino Pair Cerenkov Radiation for Tachyonic Neutrinos
• On non-existence of continuous families of stationary nonlinear modes for a class of complex potentials
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Covariant formulation of the Berry connection in non-Hermitian systems
• Deconfined quantum criticality with internal supersymmetry
• Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics
• Parity-Time Symmetric Spin-1/2 Richardson-Gaudin Models
• Development of an approximate method for quantum optical models and their pseudo-Hermicity
• $\mathcal{P}\mathcal{T}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics
• 1D Spontaneous Symmetry Breaking in thermal equilibrium via Non-Hermitian Construction
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Dissipation-induced bound states as a two-level system
• $\mathcal{P}\mathcal{T}$-like phase transitions from square roots of supersymmetric Hamiltonians
• Quantization of pseudo-hermitian systems
• Rabi oscillations at the exceptional point in anti-parity-time symmetric diffusive systems
• Dirac-like Hamiltonians associated to Schrödinger factorizations
• Functional renormalization group for non-Hermitian and $\mathcal{P}\mathcal{T}$-symmetric systems
• A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems
• Vacuum Stability of the wrong sign $(-{\varphi }^6)$ Scalar Field Theory
• A weak pseudo-Hermitian two band model, artificial Hawking radiation and tunneling
• Anisotropic oscillator with pseudo-hermiticity and its noncommutative extension
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models
• Characteristic influence of exceptional points in quantum dynamics
• Edge-wave phase-shifts versus normal-mode phase-tilts in an Eady problem with a sloping boundary
• Bound state eigenvalues from transmission coefficients
• Application of Jordan Decomposition to Non-Hermitian Lattice Models with Spectrally-Isolated Lower Dimensional States
• Non-real Eigenvalues for PT-Symmetric Double Wells
• $\mathcal{P}\mathcal{T}-$Symmetric Two-Level Open Quantum Systems: Information Theoretic Facets
• Reduced dynamics in quasi-Hermitian systems
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
• Singular Mapping for a $PT$-Symmetric Sinusoidal Optical Lattice at the Symmetry-Breaking Threshold
• Conformal Laplace superintegrable systems in 2D: polynomial invariant subspaces
• Probing Planck scale effects on absolute mass limit in neutrino flavor evolution
• Non-Hermitian superintegrable systems
• Foundational aspects of spinor structures and exotic spinors
• Bosonic Spin-1 SOPHY
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description
• A rigorous Hermitian proof about the G-dynamics and analogy with Berry-Keating's Hamiltonian
• On the construction of pseudo-Hermitian Hamiltonians by means of similarity transformations
• Nonreciprocal electrical transport in linear systems with balanced gain and loss in the bulk
• Three-level Λ-type atomic systems with a Pseudo-Hermitian PT-symmetric Hamiltonian
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model