Making Sense of Non-Hermitian Hamiltonians

Abstract

The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity guarantees that the energy spectrum is real and that time evolution is unitary (probability-preserving). This paper describes an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose + complex conjugate) is replaced by the physically transparent condition of space-time reflection (PT) symmetry. If H has an unbroken PT symmetry, then the spectrum is real. Examples of PT-symmetric non-Hermitian quantum-mechanical Hamiltonians are H=p^2+ix^3 and H=p^2-x^4. Amazingly, the energy levels of these Hamiltonians are all real and positive! In general, if H has an unbroken PT symmetry, then it has another symmetry represented by a linear operator C. Using C, one can construct a time-independent inner product with a positive-definite norm. Thus, PT-symmetric Hamiltonians describe a new class of complex quantum theories having positive probabilities and unitary time evolution. The Lee Model is an example of a PT-symmetric Hamiltonian. The renormalized Lee-model Hamiltonian has a negative-norm "ghost" state because renormalization causes the Hamiltonian to become non-Hermitian. For the past 50 years there have been many attempts to find a physical interpretation for the ghost, but all such attempts failed. Our interpretation of the ghost is simply that the non-Hermitian Lee Model Hamiltonian is PT-symmetric. The C operator for the Lee Model is calculated exactly and in closed form and the ghost is shown to be a physical state having a positive norm. The ideas of PT symmetry are illustrated by using many quantum-mechanical and quantum-field-theoretic models.

78 pages, 26 figures, invited review article to be published in Rep. Prog. Phys

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• PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics
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• New Quasi-Exactly Solvable Sextic Polynomial Potentials
• P,T,PT, and CPT invariance of Hermitian Hamiltonians
• Semiclassical Analysis of Quasi-Exact Solvability
• Planar Super-Landau Models Revisited
• Analytically Solvable PT-Invariant Periodic Potentials
• C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians
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• Anomalies in PT-Symmetric Quantum Field Theory
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• PT-symmetric non-polynomial oscillators and hyperbolic potential with two known real eigenvalues in a SUSY framework
• Semiclassical analysis of a complex quartic Hamiltonian
• A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons
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• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Observation of PT phase transition in a simple mechanical system
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• PT symmetry and spontaneous symmetry breaking in a microwave billiard
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• Magnetoelectric Effects in Local Light-Matter Interactions
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• PT-Symmetric Oligomers: Analytical Solutions, Linear Stability and Nonlinear Dynamics
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• Kibble-Zurek scaling in the Yang-Lee edge singularity
• Variational Quantum Algorithm for Non-equilibrium Steady States
• Classification of Exceptional Nodal Topologies Protected by $\mathcal{P}\mathcal{T}$ Symmetry
• Dimer with gain and loss: Integrability and $\mathcal{P}\mathcal{T}$-symmetry restoration
• Environmentally-induced exceptional points in elastodynamics
• Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations
• The degenerate band edge laser: a new paradigm for coherent light-matter interaction
• Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report
• Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
• Fate of zero modes in a finite Su-Schrieffer-Heeger Model with $\mathcal{P}\mathcal{T}$ Symmetry
• Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations
• On the integrability of PT-symmetric dimers
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Scale-tailored localization and its observation in non-Hermitian electrical circuits
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Mending the broken PT-regime via an explicit time-dependent Dyson map
• Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Modulation instability in nonlinear complex parity-time (PT) symmetric periodic structures
• Exceptional points in dissipatively coupled spin dynamics
• Discrete PT-symmetric models of scattering
• Optical lattices with exceptional points in the continuum
• Fixed points and emergent topological phenomena in a parity-time-symmetric quantum quench
• Convective and absolute PT symmetry breaking in tight-binding lattices
• Scattering by finite periodic $\mathcal{P}\mathcal{T}$-symmetric structures
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• Solitons and their stability in the nonlocal nonlinear Schroedinger equation with PT-symmetric potentials
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric periodic systems with the quadratic nonlinearity
• On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT-and non-PT-symmetric potentials
• Wave scattering on a domain wall in a chain of PT-symmetric couplers
• Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling
• Non-Hermitian tight-binding network engineering
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Non-Hermitian Hamiltonians of Lie algebraic type
• Origin of maximal symmetry breaking in even PT-symmetric lattices
• An update on PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally-extended supersymmetric partners
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Symmetry and topological classification of Floquet non-Hermitian systems
• Passive $\mathcal{P}\mathcal{T}$-symmetry breaking transitions without exceptional points in dissipative photonic systems
• Bulk and edge-state arcs in non-hermitian coupled-resonator arrays
• Non-Hermitian Dynamic Strings and Anomalous Topological Degeneracy on non-Hermitian Toric-code Model with Parity-time Symmetry
• Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Anyonic-parity-time symmetry in complex-coupled lasers
• Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge
• Scattering theory using smeared non-Hermitian potentials
• PT-symmetry in optics beyond the paraxial approximation
• On integrable wave interactions and Lax pairs on symmetric spaces
• Bloch oscillations in tight-binding lattices with defects
• Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
• Nonlinear quantum dynamics in a PT-symmetric double well
• Emergent phase transition in Cluster Ising model with dissipation
• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling
• Quaternionic quantum mechanics in real Hilbert space
• Quantum Simulation of Dissipative Processes without Reservoir Engineering
• Exact $P_s{T}_d$ Invariant and $P_s{T}_d$ Symmetric Breaking solutions, Symmetry Reductions and Bäcklund Transformations For An AB-KdV System
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Strings from position-dependent noncommutativity
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Inversion symmetric non-Hermitian Chern insulator
• Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence
• Cavity magnon polariton based precision magnetometry
• Non-anti-hermitian quaternionic quantum mechanics
• Exact solution of the Bose Hubbard model with unidirectional hopping
• Ordinary versus PT-symmetric ${\varphi }^3$ quantum field theory
• 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
• Realization and application of parity-time-symmetric oscillators in quantum regime
• Giving up the ghost
• On the N-wave Equations with PT-symmetry
• Perfect transmission scattering as a PT-symmetric spectral problem
• Bohmian quantum trajectories from coherent states
• Eternal life of entropy in non-Hermitian quantum systems
• Wave Instabilities and Unidirectional Light Flow in a Cavity with Rotating Walls
• $\mathcal{P}\mathcal{T}$-symmetric, non-Hermitian quantum many-body physics -- a methodological perspective
• Invisible defects in complex crystals
• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
• Kubo formula for non-Hermitian systems and tachyon optical conductivity
• Partial topological Zak phase and dynamical confinement in non-Hermitian bipartite system
• Jamming anomaly in $\mathcal{P}\mathcal{T}$-symmetric systems
• Topological energy braiding of the non-Bloch bands
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models
• Linear Pseudo-fermions
• Exact quantization of a PT-symmetric (reversible) Liénard-type nonlinear oscillator
• Revisiting the PT-symmetric Trimer: Bifurcations, Ghost States and Associated Dynamics
• Localization, $\mathcal{P}\mathcal{T}$-Symmetry Breaking and Topological Transitions in non-Hermitian Quasicrystals
• Stability Through Asymmetry: Modulationally Stable Nonlinear Supermodes of Asymmetric non-Hermitian Optical Couplers
• Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
• Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator
• Multi-stability and condensation of exciton-polaritons below threshold
• Correlations at PT-symmetric quantum critical point
• Non-Markovian Quantum Exceptional Points
• Irreversibility of the renormalization group flow in non-unitary quantum field theory
• Spontaneous Parity-Time Symmetry Breaking in Moving Media
• One- and two-dimensional solitons in PT-symmetric systems emulating the spin-orbit coupling
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• Occupation-dependent particle separation in one-dimensional non-Hermitian lattices
• From self-adjoint to non self-adjoint harmonic oscillators: physical consequences and mathematical pitfalls
• Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang-Mills and Gravitational Theories
• Spectral Singularities of a General Point Interaction
• Nonclassicality versus entanglement in a noncommutative space
• Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes
• Supersymmetric Valence Bond Solid States
• Photon blockade in non-Hermitian optomechanical systems with nonreciprocal couplings
• Cyclic permutation-time symmetric structure with coupled gain-loss microcavities
• Entanglement in non-equilibrium steady states and many-body localization breakdown in a current driven system
• Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
• Critical behavior of the PT-symmetric $i{\varphi }^3$ quantum field theory
• Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
• Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrodinger equation
• Non-self-adjoint hamiltonians defined by Riesz bases
• Phase transition through the splitting of self-dual spectral singularity in optical potentials
• Universal platform of point-gap topological phases from topological materials
• Non-Bloch quench dynamics
• Cyclotron quantization and mirror-time transition on nonreciprocal lattices
• Manipulating non-reciprocity in a two-dimensional magnetic quantum walk
• Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
• Interpretation of quantum mechanics with indefinite norm
• Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
• Hermitian dynamics in a class of pseudo-Hermitian networks
• Families of particles with different masses in PT-symmetric quantum field theory
• Statistical PT-symmetric lasing in an optical fiber network
• Hermitian versus non-Hermitian representations for minimal length uncertainty relations
• Coherent coupling between multiple ferrimagnetic spheres and a microwave cavity in the quantum-limit
• $\mathcal{P}\mathcal{T}$-symmetric mode-locking
• PT Symmetry as a Generalization of Hermiticity
• Quantum Zeno effect and nonclassicality in a PT symmetric system of coupled cavities
• Stable Atomic Magnetometer in Parity-Time Symmetry Broken Phase
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Quantum catastrophes: a case study
• Coherent structure of Alice-Bob modified Korteweg de-Vries Equation
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model
• Non-Hermitian approach for quantum plasmonics
• Parametric instability of non-Hermitian systems near the exceptional point
• Constructible reality condition of pseudo entropy via pseudo-Hermiticity
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• The topological counterparts of non-Hermitian SSH models
• Non-Hermitian quantum systems and their geometric phases
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Virial theorem and generalized momentum in quaternic quantum mechanics
• Regularized degenerate multi-solitons
• Skin modes in a nonlinear Hatano-Nelson model
• New scattering features of quaternionic point interaction in non-Hermitian quantum mechanics
• Non-Hermitian skin effect edge
• Interaction induced dynamical $\mathcal{P}\mathcal{T}$ symmetry breaking in dissipative Fermi-Hubbard models
• Probability-preserving evolution in a non-Hermitian two-band model
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Directionality Fields generated by a Local Hilbert Transform
• Optimized Steering: Quantum State Engineering and Exceptional Points
• Investigation of non-Hermitian Hamiltonians in the Heisenberg picture
• Revisiting the optical $PT$-symmetric dimer
• Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
• Solvable two dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime
• PT-symmetry breaking in complex nonlinear wave equations and their deformations
• Bound states and photon emission in non-Hermitian nanophotonics
• PT-symmetric models in curved manifolds
• Unitarity corridors to exceptional points
• Quantum battery with non-Hermitian charging
• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential
• $\mathcal{P}\mathcal{T}$ phase control in circular multicore fibers
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• Electronic properties of bilayer graphene catenoid bridge
• Cusp bifurcation in the eigenvalue spectrum of PT-symmetric Bose-Einstein condensates
• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• Hermitian and non-Hermitian formulations of the time evolution of quantum decay
• Unitarity of loop diagrams for the ghost-like $1/(k^2-M_1^2)-1/(k^2-M_2^2)$ propagator
• Neutrino spin oscillations in external fields in curved spacetime
• Spectral projections of the complex cubic oscillator
• Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Optomechanical dynamics in the $\mathcal{P}\mathcal{T}$- and broken-$\mathcal{P}\mathcal{T}$-symmetric regimes
• Horizon as Critical Phenomenon
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Symmetry breaking in dipolar matter-wave solitons in dual-core couplers
• Non-hermitian operator modelling of basic cancer cell dynamics
• Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models
• PT Meets Supersymmetry and Nonlinearity: An Analytically Tractable Case Example
• Non-self-adjoint graphs
• Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance
• Complete Set of Inner Products for a Discrete PT-symmetric Square-well Hamiltonian
• Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation
• A simple approach towards the sign problem using path optimisation
• The problem of coexistence of several non-Hermitian observables in PT-symmetric quantum mechanics
• Exactly solvable time-dependent pseudo-Hermitian $su$(1,1) Hamiltonian models
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
• Giant Emitters in a Structured Bath with Non-Hermitian Skin Effect
• Exceptional points and their coalescence of PT-symmetric interface states in photonic crystals
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields
• Appropriate Inner Product for PT-Symmetric Hamiltonians
• Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry
• Universal Critical Behaviors in Non-Hermitian Phase Transitions
• Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions
• Entanglement, non-Hermiticity, and duality
• Demonstration of a parity-time symmetry breaking phase transition using superconducting and trapped-ion qutrits
• Out-of-time-ordered correlator in non-Hermitian quantum systems
• Coupling-independent, Real-time Wireless Resistive Sensing through Nonlinear PT-symmetry
• PT-symmetry in nonlinear twisted multi-core fibers
• Anderson transition at complex energies in one-dimensional parity-time-symmetric disordered systems
• Null bootstrap for non-Hermitian Hamiltonians
• PT-symmetric chiral metamaterials: Asymmetric effects and PT-phase control
• Non-Hermitian Heisenberg representation
• Conformal bridge between asymptotic freedom and confinement
• Deformed quons and bi-coherent states
• $\eta$-pairing ground states in the non-Hermitian Hubbard model
• $J$-self-adjoint operators with $\mathcal{C}$-symmetries: extension theory approach
• On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators
• Solitons in PT-symmetric ladders of optical waveguides
• The quantum brachistochrone problem for non-Hermitian Hamiltonians
• Tunable nonlinear PT-symmetric defect modes with an atomic cell
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Tight-binding lattices with an oscillating imaginary gauge field
• Anomalous Light Scattering by Topological $\mathcal{P}\mathcal{T}$-symmetric Particle Arrays
• Topological phase in plasma physics
• Confluent Crum-Darboux transformations in Dirac Hamiltonians with $PT$-symmetric Bragg gratings
• Direction reversal of non-Hermitian skin effect via coherent coupling
• Probability Density in the Complex Plane
• Percolation-induced PT symmetry breaking
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• A non self-adjoint model on a two dimensional noncommutative space with unbound metric
• Kelvin-Helmholtz instability is the result of parity-time symmetry breaking
• Inflationary tensor fluctuations, as viewed by Ashtekar variables and their imaginary friends
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Topological optomechanical amplifier with synthetic $\mathcal{P}\mathcal{T}$-symmetry
• Generic examples of PT-symmetric qubit (spin 1/2) Liouvillians
• Wavepacket Self-imaging and Giant Recombinations via Stable Bloch-Zener Oscillations in Photonic Lattices with Local $\mathcal{P}\mathcal{T}$-Symmetry
• Incoherent non-Hermitian skin effect in photonic quantum walks
• The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics
• Quantum dynamics on a lossy non-Hermitian lattice
• Exceptional points as lasing pre-thresholds in open-cavity lasers
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity
• Nonlinear multi-core waveguiding structures with balanced gain and loss
• A brief review of hybrid skin-topological effect
• Topological cascade laser for frequency comb generation in $\mathcal{P}\mathcal{T}$-symmetric structures
• Maximal quantum entanglement at exceptional points via unitary and thermal dynamics
• Topological Microlaser with A non-Hermitian Topological Bulk
• TBA Equations and Quantization Conditions
• Nonlinear Topological Edge States in a non-Hermitian Array of Optical Waveguides Embedded in an Atomic Gas
• Field Theory of Dissipative Systems with Gapped Momentum States
• Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical Applications
• Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics
• PT-symmetric deformations of Calogero models
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Optical conductivity of curved graphene
• Various Scattering Properties of a New PT-symmetric non-Hermitian potential
• Encircling the Liouvillian exceptional points: a brief review
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry
• The Nielsen-Ninomiya theorem, PT-invariant non-Hermiticity and single 8-shaped Dirac cone
• Bound states in the continuum in a two-dimensional PT-symmetric system
• Crypto-unitary forms of quantum evolution operators
• Admissible perturbations and false instabilities in PT-symmetric quantum systems
• Deconfinement to Confinement as PT phase transition
• Imaginary-Scaling versus Indefinite-Metric Quantization of the Pais-Uhlenbeck Oscillator
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• PT-Symmetric Representations of Fermionic Algebras
• Interplay between Fano resonance and $\mathcal{P}\mathcal{T}$ symmetry in non-Hermitian discrete systems
• Universality of Pattern Formation
• Quantum statistical signature of $\mathcal{P}\mathcal{T}$ symmetry breaking
• Supersymmetry, PT-symmetry and Spectral Bifurcation
• Dynamical Majorana Neutrino Masses and Axions II: Inclusion of Axial Background and Anomaly Terms
• Effect of quantum jumps on non-Hermitian system
• Two-qubit entanglement generation through non-Hermitian Hamiltonians induced by repeated measurements on an ancilla
• Compactons versus Solitons
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• PT-symmetric interpretation of unstable effective potentials
• Fractional Schrödinger equation in gravitational optics
• Bragg-induced power oscillations in PT symmetric periodic photonic structures
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Current-voltage characteristics of the N-I-PT-symmetric non-Hermitian superconductor junction as a probe of non-Hermitian formalisms
• Resonance-dominant optomechanical entanglement in open quantum systems
• Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model
• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities
• Near-extremal black holes in Weyl gravity: Quasinormal modes and geodesic instability
• Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians
• Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
• Scattering in the PT-symmetric Coulomb potential
• PT Symmetry in Classical and Quantum Statistical Mechanics
• Mode pairs in $\mathcal{P}\mathcal{T}$-symmetric multimode waveguides
• Wireless Real-Time Capacitance Readout Based on Perturbed Nonlinear Parity-Time Symmetry
• Nonlinear extension of the quantum dynamical semigroup
• Shortcuts to adiabaticity with general two-level non-Hermitian systems
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
• Inverse engineering rigorous adiabatic Hamiltonian for non-Hermitian system
• A third-order exceptional point effect on the dynamics of a single particle in a time-dependent harmonic trap
• The non-Hermitian skin effect: A perspective
• Self acceleration from spectral geometry in dissipative quantum-walk dynamics
• An alternative construction of the positive inner product in non-Hermitian quantum mechanics
• Minimal areas from q-deformed oscillator algebras
• The KdV hierarchy in optics
• Machine learning non-Hermitian topological phases
• Realizing Topological Transition in a Non-Hermitian Quantum Walk with Circuit QED
• Extension of the $CPT$ Theorem to non-Hermitian Hamiltonians and Unstable States
• On nonlocal models of Kulish-Sklyanin type and generalized Fourier transforms
• PT-symmetric spectral singularity and negative frequency resonance
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Non-Hermitian impurities in Dirac systems
• A no-go result for the quantum damped harmonic oscillator
• Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation
• Full counting statistics in the many-body Hatano-Nelson model
• Antilinear deformations of Coxeter groups, an application to Calogero models
• Non-Hermitian Dirac cones with valley-dependent lifetimes
• Interactions of bright and dark solitons with localized $\mathcal{P}\mathcal{T}$-symmetric potentials
• Coupled states of electromagnetic fields with magnetic-dipolar-mode vortices: MDM-vortex polaritons
• High-order series expansion of non-Hermitian quantum spin models
• Non-Hermitian spectral effects in a PT-symmetric waveguide
• Degenerate multi-solitons in the sine-Gordon equation
• Quasinormal modes of black holes in Weyl gravity: Electromagnetic and gravitational perturbations
• Magnified imaging based on non-Hermitian nonlocal cylindrical metasurfaces
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• Determining role of Krein signature for 3D Arnold tongues of oscillatory dynamos
• Non-hermitean hamiltonians with unitary and antiunitary symmetry
• Bulk vortices and half-vortex surface modes in parity-time-symmetric media
• Pseudo-bosons, so far
• Parity-time-symmetric vector rational rogue wave solutions in any n-component nonlinear Schrödinger models
• Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
• Non-Bloch band theory for non-Hermitian continuum systems
• Information and thermodynamic properties of a non-Hermitian particle ensemble
• From Pseudo-bosons to Pseudo-Hermiticity via multiple generalized Bogoliubov transformations
• Embedding, simulation and consistency of $\mathcal{P}\mathcal{T}$ -symmetric quantum Theory
• Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions
• Towards perturbative renormalization of ${\varphi }^2(i\varphi {)}^{\epsilon }$ quantum field theory
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Stochastic $\mathcal{P}\mathcal{T}$-symmetric coupler
• Astrophysical Gravitational Waves in Conformal Gravity
• Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems
• Non-Hermitian quantum mechanics in non-commutative space
• Weak Ergodicity Breaking in Non-Hermitian Many-body Systems
• Spinor solitons and their $\mathcal{P}\mathcal{T}$-symmetric offspring
• Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers
• Ghost Problems from Pauli-Villars to Fourth-Order Quantum Gravity and their Resolution
• Axial gravity: a non-perturbative approach to split anomalies
• Non-Hermitian eigenvalue knots and their isotopic equivalence
• $\mathcal{P}\mathcal{T}$-symmetric coupler with ${\chi }^{(2)}$ nonlinearity
• On the foundations of partially quenched chiral perturbation theory
• Partial inner product spaces, metric operators and generalized hermiticity
• Exactly solvable Wadati potentials in the PT-symmetric Gross-Pitaevskii equation
• Multiply Degenerate Exceptional Points and Quantum Phase Transitions
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Talbot self-imaging in $\mathcal{P}\mathcal{T}$-symmetric complex crystals
• Dynamics of higher-order solitons in regular and PT-symmetric nonlinear couplers
• Statistical mechanics for non-Hermitian quantum systems
• Some remarks on quasi-Hermitian operators
• Near-unit efficiency of chiral state conversion via hybrid-Liouvillian dynamics
• Scattering cross section resonance originating from a spectral singularity
• Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
• Spectral singularities of odd-$PT$-symmetric potential
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials
• Infinitely many inequivalent field theories from one Lagrangian
• Three solvable matrix models of a quantum catastrophe
• Snakes and ghosts in a parity-time-symmetric chain of dimers
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Anti-parity-time symmetry hidden in a damping linear resonator
• Quantum parameter estimation of non-Hermitian systems with optimal measurements
• Shortcuts to adiabaticity in non-Hermitian quantum systems without rotating-wave approximation
• Pseudo supersymmetric partners for the generalized Swanson model
• Behavior of eigenvalues in a region of broken-PT symmetry
• Dynamical Majorana Neutrino Masses and Axions
• Spectral singularity and non-Hermitian PT-symmetric extension of $A_{N-1}$ type Calogero model without confining potential
• Dispersive readout of a weakly coupled qubit via the parity-time-symmetric phase transition
• $\mathcal{P}\mathcal{T}$ symmetric phase transition and single-photon transmission in an optical trimmer system
• Electronic properties of a nanotorus
• Piecewise Adiabatic Following in Non-Hermitian Cycling
• Time-delay and reality conditions for complex solitons
• PT-symmetric lattices with spatially extended gain/loss are generically unstable
• Quantum and Classical Statistical Mechanics of a Class of non-Hermitian Hamiltonians
• Non-Hermitian flatband generator in one dimension
• PT phase transition in a (2+1)-d relativistic system
• Extended topological mode in a one-dimensional non-Hermitian acoustic crystal
• Real spectra for non-Hermitian Dirac equation in 1+1 dimensions with a most general coupling
• Quantum Fisher Information Perspective on Sensing in Anti-PT Symmetric Systems
• Photonic quantum simulations of coupled $PT$-symmetric Hamiltonians
• Solitary waves in Parity-time (PT) symmetric Bragg-grating structure and the existence of Optical Rogue Waves
• PT-symmetry broken by point-group symmetry
• Realization of complex conjugate media using non-PT-symmetric photonic crystals
• From real fields to complex Calogero particles
• Magnon dynamics in parity-time-symmetric dipolarly coupled waveguides and magnonic crystals
• Quantizations from reproducing kernel spaces
• Coupling-induced nonunitary and unitary scattering in anti-PT-symmetric non-Hermitian systems
• Quantum phase transitions in nonhermitian harmonic oscillator
• Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays
• Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: a non-equilibrium potential approach
• Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems
• Symmetry protected exceptional points of interacting fermions
• Light dynamics in nonlinear trimers and twisted multicore fibers
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Basics of Quantum Mechanics, Geometrization and some Applications to Quantum Information
• The Loom for General Fishnet CFTs
• Conserved quantities, exceptional points, and antilinear symmetries in non-Hermitian systems
• Quantum dissipation in a scalar field theory with gapped momentum states
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach
• Passage through exceptional point: Case study
• Scattering of partially coherent radiation by non-Hermitian localized structures having Parity-Time symmetry
• Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models
• Discrete quantum square well of the first kind
• An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples
• Non-Hermiticity-Induced Wave Confinement and Guiding in Loss-Gain-Loss Three-Layer Systems
• Taming Dyson-Schwinger equations with null states
• Observation of two PT transitions in an electric circuit with balanced gain and loss
• Super-exponential diffusion in nonlinear non-Hermitian systems
• New scattering features in non-Hermitian space fractional quantum mechanics
• Solitary waves of a PT-symmetric Nonlinear Dirac equation
• Localized states and skin effect around non-Hermitian impurities in tight-binding models
• Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy
• Does the complex deformation of the Riemann equation exhibit shocks?
• Exact Isospectral Pairs of PT-Symmetric Hamiltonians
• Dynamical stabilization and time in open quantum systems
• Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
• PT-symmetric optical superlattices
• Solitons in a $\mathcal{P}\mathcal{T}$- symmetric ${\chi }^{(2)}$ coupler
• Symmetry-protected localized states at defects in non-Hermitian systems
• Floquet exceptional contours in Lindblad dynamics with time-periodic drive and dissipation
• Signature of PT-symmetric non-Hermitian superconductivity in angle-resolved photoelectron fluctuation spectroscopy
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model
• Non-Hermitian Hamiltonians for Linear and Nonlinear Optical Response: a Model for Plexcitons
• Experimental Observation of Partial Parity-Time Symmetry and Its Phase Transition with a Laser-Driven Cesium Atomic Gas
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• Complex symmetric Hamiltonians and exceptional points of order four and five
• Dynamics of finite dimensional non-hermitian systems with indefinite metric
• Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• Non-Hermitian Floquet invisibility
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• Periodic orbits for classical particles having complex energy
• PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
• Classical Particle in a Complex Elliptic Potential
• Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians
• Many-body Non-Hermitian Skin Effect At Finite Temperatures
• Decay of the Higgs boson to ${\tau }^{-}{\tau }^{+}$ and non-Hermiticity of the Yukawa interaction
• Uncertainty Relation for Non-Hermitian Systems
• Creation and manipulation of bound states in continuum with lasers: Applications to cold atoms and molecules
• Topological properties of non-Hermitian Creutz Ladders
• Use of Equivalent Hermitian Hamiltonian for $PT$-Symmetric Sinusoidal Optical Lattices
• Intertwining operators for non self-adjoint Hamiltonians and bicoherent states
• Bicomplex Hamiltonian systems in Quantum Mechanics
• PT symmetry in relativistic quantum mechanics
• Decays of degeneracies in PT-symmetric ring-shaped lattices
• Nonlinear anti-directional couplers with gain and loss
• Ghost-spin chains, entanglement and $bc$-ghost CFTs
• On the infinite-dimensional QR algorithm
• Acceleration toward polarization singularity inspired by relativistic ExB drift
• Emergence of tunable exceptional points in altermagnet-ferromagnet junctions
• Quantum Algorithms for Open Lattice Field Theory
• Analytically solvable $2\times 2$ $PT$-symmetry dynamics from su(1,1)-symmetry problems
• SUSY transformations with complex factorization constants. Application to spectral singularities
• Spectral analysis, chiral disorder and topological edge states manifestation in open non-Hermitian Su-Schrieffer-Heeger chains
• Nonlocal reductions of the Ablowitz-Ladik equation
• Parity-time-symmetric closed form optical quadrimer waveguides
• $\mathcal{P}T$ symmetry, pattern formation, and finite-density QCD
• Low-power optical bistability in $\mathcal{P}\mathcal{T}$-symmetric chirped Bragg gratings with four-wave mixing
• Lindblad dynamics of Gaussian states and their superpositions in the semiclassical limit
• Order-dependent mappings: strong coupling behaviour from weak coupling expansions in non-Hermitian theories
• Virtual exceptional points in an electromechanical system
• Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction
• 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
• Andreev bound states in junctions formed by conventional and $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian superconductors
• Probing two-body exceptional points in open dissipative systems
• Causality, unitarity, and indefinite metric in Maxwell-Chern-Simons extensions
• Onset of superconductivity in a voltage-biased NSN microbridge
• Metric versus observable operator representation, higher spin models
• Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Chirality sensing employing PT-symmetric and other resonant gain-loss optical systems
• Non-Hermitian noncommutative quantum mechanics
• Novel PT-invariant Solutions For a Large Number of Real Nonlinear Equations
• Coalescence of non-Markovian dissipation, quantum Zeno effect and non-Hermitian physics, in a simple realistic quantum system
• Hidden PT Symmetry and quantization of coupled-oscillators model of QASER
• Exceptional Point of Sixth Order Degeneracy in a Modified Coupled Resonators Optical Waveguide
• Effective protection of quantum coherence by non-Hermitian driving
• Nonlinear currents in a ring-shaped waveguide with balanced gain and dissipation
• Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
• Improving shortcuts to non-Hermitian adiabaticity for fast population transfer in open quantum systems
• Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides
• E2-quasi-exact solvability for non-Hermitian models
• A unidirectional invisible PT-symmetric complex crystal with arbitrary thickness
• Dark soliton of polariton condensates under nonresonant PT-symmetric pumping
• PT phase transition in multidimensional quantum systems
• Competing PT potentials and re-entrant PT symmetric phase for a particle in a box
• Quantum star-graph analogues of PT-symmetric square wells
• Noninteger flux - why it does not work
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• PT-symmetry, indefinite damping and dissipation-induced instabilities
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• Signature of exceptional point phase transition in Hermitian systems
• Non-Hermitian approach of edge states and quantum transport in a magnetic field
• Conformal generation of an exotic rotationally invariant harmonic oscillator
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Quantum inner-product metrics via recurrent solution of Dieudonne equation
• A Unified Theory of Non-Linear Electrodynamics and Gravity
• Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems
• Conformal bridge transformation and PT symmetry
• Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
• 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
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• PT-symmetric quantum graphs
• Tweaking Spectral Topology and Exceptional Points by Nonlinearity in Non-Hermitian Polariton Systems
• Experimentally-realizable $\mathcal{P}\mathcal{T}$ phase transitions in reflectionless quantum scattering
• Non-Hermitian quantum dynamics and entanglement of coupled nonlinear resonators
• 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
• Non-Hermitian Hartman effect
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Stabilization of the coupled pendula chain under parametric PT-symmetric driving force
• Quasinormal mode analysis of chiral power flow from linearly polarized dipole emitters coupled to index-modulated microring resonators close to an exceptional point
• Non linear pseudo-bosons versus hidden Hermiticity
• Overcritical PT-symmetric square well potential in the Dirac equation
• Chaotic diffusion of complex trajectory and its quantum signature
• PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics
• Embedding quantum systems with a non-conserved probability in classical environments
• Spontaneous and explicit parity-time-symmetry breaking in drift wave instabilities
• Robust topological feature against non-Hermiticity in Jaynes-Cummings Model
• Conformal Invariance and the Metrication of the Fundamental Forces
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• Unitary evolution for a two-level quantum system in fractional-time scenario
• Cross-symmetric dipolar-matter-wave solitons in double-well chains
• Quasi-energies, parametric resonances, and stability limits in ac-driven $\mathcal{P}\mathcal{T}$-symmetric systems
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• Field patterns without blow up
• PT-symmetry breaking with divergent potentials: lattice and continuum cases
• Approximate Dirac solutions of complex -symmetric Pöschl-Teller potential in view of spin and pseudospin symmetries
• Edge and bulk dissipative solitons in modulated PT-symmetric waveguide arrays
• The Floquet Baxterisation
• Real-Time Transport in Open Quantum Systems From $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Wheeler-DeWitt equation and the applicability of crypto-Hermitian interaction representation in quantum cosmology
• Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity
• Generalized Ellis-Bronnikov graphene wormhole
• PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation
• Asymptotic Analysis of the Local Potential Approximation to the Wetterich Equation
• Dynamical signatures of point-gap Weyl semimetal
• PT-symmetry breaking in resonant tunneling heterostructures
• Quantum phase transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric transverse-field Ising spin chains
• Dynamical evolutions in non-Hermitian triple-well system with complex potential
• Accessible phases via wave impedance engineering with PT-symmetric metamaterials
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
• Emerging exceptional point with breakdown of skin effect in non-Hermitian systems
• Open quantum systems with loss and gain
• Exact Solutions for Non-Hermitian Dirac-Pauli Equation in an intensive magnetic field
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Anomalous bulk behaviour in the free parafermion $Z(N)$ spin chain
• Time-dependent metric for the two dimensional, non-Hermitian coupled oscillator
• Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• Observables in non-Hermitian systems: A methodological comparison
• Detecting exceptional points through dynamics in non-Hermitian systems
• A black potential for spin less particles
• Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration
• Non-Hermitian multi-particle systems from complex root spaces
• Perturbation theory near degenerate exceptional points
• Spectrum and normal modes of non-hermitian quadratic boson operators
• Inverse dispersion method for calculation of complex photonic band diagram and $\mathcal{P}\mathcal{T}$-symmetry
• Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type
• Position-dependent mass effects on a bilayer graphene catenoid bridge
• Long-time stability of breathers in Hamiltonian $\mathcal{P}\mathcal{T}$-symmetric lattices
• The effect of thermal photons on exceptional points in coupled resonators
• Quantum decay and amplification in a non-Hermitian unstable continuum
• A new solvable complex PT-symmetric potential
• Solvable non-Hermitian discrete square well with closed-form physical inner product
• Physics of PT-Symmetric Quantum Systems at Finite Temperature
• On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Asymptotically vanishing PT-symmetric potentials and negative-mass Schroedinger equations
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Accidental crossings of eigenvalues in one-dimensional complex PT-symmetric Scarf-II potential
• An efficient finite-difference scheme for computation of electron states in free-standing and core-shell quantum wires
• Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids
• Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy
• Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass
• Solitary waves in the Nonlinear Dirac Equation
• Global existence of solutions to coupled $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger equations
• Connecting active and passive $\mathcal{P}\mathcal{T}$-symmetric Floquet modulation models
• Quantum Big Bang without fine-tuning in a toy-model
• $PT$-symmetric graphene under a magnetic field
• Generalized Dimers and their Stokes-variable Dynamics
• Excepional Points from Hamiltonians of hybrid physical systems: Squeezing and anti-Squeezing
• Are observables necessarily Hermitian?
• On nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
• Nonclassical States for Non-Hermitian Hamiltonians with the Oscillator Spectrum
• Principle of minimal singularity for Green's functions
• Bicoherent-State Path Integral Quantization of a non-Hermitian Hamiltonian
• Composite quantum Coriolis forces
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Extending PT symmetry from Heisenberg algebra to E2 algebra
• Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Direct observation of energy band attraction effect in non-Hermitian systems
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• No-signaling principle and Bell inequality in PT-symmetric quantum mechanics
• Phantom without phantom or how the PT symmetry saves us from the Big Rip
• Imaginary Potential Induced Quantum Coherence for Bose-Einstein Condensates
• Non-Hermitian systems of Euclidean Lie algebraic type with real eigenvalue spectra
• Broadband mixing of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-broken phases in photonic heterostructures with a one-dimensional loss/gain bilayer
• Gyrating solitons in a necklace of optical waveguides
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric systems with spin-orbit coupling and critical nonlinearity
• Hybrid form of quantum theory with non-Hermitian Hamiltonians
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Optical Limiter Based on PT-Symmetry Breaking of Reflectionless Modes
• On the K-theoretic classification of dynamically stable systems
• Entangled Quantum State Discrimination using Pseudo-Hermitian System
• Astrophysical Evidence for the Non-Hermitian but $PT$-symmetric Hamiltonian of Conformal Gravity
• Supercritical blowup in coupled parity-time-symmetric nonlinear Schrödinger equations
• Theory of response to perturbations in non-Hermitian systems using five-Hilbert-space reformulation of unitary quantum mechanics
• Static synthetic gauge field control of double optomechanically induced transparency in a closed-contour interaction scheme
• Inflation with Massive Spin-2 Ghosts
• The particle in a box in PT quantum mechanics and an electromagnetic analog
• Helical resonant transport and purified amplification at an exceptional point
• Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics
• Lie transformation method on quantum state evolution of a general time-dependent driven and damped parametric oscillator
• Cosmological perturbations in conformal gravity II
• From Euclidean to Lorentzian Loop Quantum Gravity via a Positive Complexifier
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Gravitational Waves and Degrees of Freedom in Higher Derivative Gravity
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• PT-symmetric sine-Gordon breathers
• Enhancing the sensitivity of nonlinearity sensors through homodyne detection in dissipatively coupled systems
• CPT-Frames for PT-symmetric Hamiltonians
• Appearances of pseudo-bosons from Black-Scholes equation
• Spin Precession of Slow Neutrons in Einstein-Cartan Gravity with Torsion, Chameleon and Magnetic Field
• Hilbert space inner products for PT-symmetric Su-Schrieffer-Heeger models
• Non-Hermitian Hamiltonians and similarity transformations
• Integrable models from PT-symmetric deformations
• Self-Organized Criticality as Witten-type Topological Field Theory with Spontaneously Broken Becchi-Rouet-Stora-Tyutin Symmetry
• Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{P}\mathcal{T}$ symmetry
• Anomalous real spectra of non-Hermitian quantum graphs in strong-coupling regime
• Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry
• Effective non-Hermitian physics for degenerate ground states of a nonHermitian Ising model with $\mathcal{R}\mathcal{T}$ symmetry
• Study of classical mechanical systems with complex potentials
• Symmetry-Protected Topological Phase for Spin-Tensor-Momentum-Coupled Ultracold Atoms
• Holographic fluids: a thermodynamic road to quantum physics
• A possible method for non-Hermitian and non-$PT$-symmetric Hamiltonian systems
• Exceptional points and domains of unitarity for a class of strongly non-Hermitian real-matrix Hamiltonians
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Oscillation death in coupled counter-rotating identical nonlinear oscillators
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators
• Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system
• Spontaneous breaking of permutation symmetry in pseudo-Hermitian quantum mechanics
• N-site-lattice analogues of $V(x)=i{x}^3$
• A complex periodic QES potential and exceptional points
• Identification of observables in quantum toboggans
• The Pauli equation with complex boundary conditions
• Piecewise Adiabatic Following: General Analysis and Exactly Solvable Models
• On the Stability of Coherent States for Pais-Uhlenbeck Oscillator
• Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons
• The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry
• Theory and Numerical Modelling of Parity-Time Symmetric Structures in Photonics: Introduction and Grating Structures in One Dimension
• The connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum finance
• Dynamical control of solitons in a parity-time-symmetric coupler by periodic management
• Position-dependent mass in strong quantum gravitational background fields
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{P}\mathcal{T}$ symmetry
• Winding in Non-Hermitian Systems
• A concise review on pseudo-bosons, pseudo-fermions and their relatives
• Quantum tomography of a third-order exceptional point in a dissipative trapped ion
• Absence of Floquet scattering in oscillating non-Hermitian potential wells
• Singular Value Decomposition and Its Blind Spot for Quantum Chaos in Non-Hermitian Sachdev-Ye-Kitaev Models
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Generalized gauge transformation with $PT$-symmetric non-unitary operator and classical correspondence of non-Hermitian Hamiltonian for a periodically driven system
• Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations
• Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation
• Non-Hermitian quantum rings
• No-signaling principle and quantum brachistochrone problem in $PT$-symmetric fermionic two- and four-dimensional models
• Transition from degeneracy to coalescence: theorem and applications
• Probing de Sitter Space Using CFT States
• Metastable two-component solitons near an exceptional point
• Damping and Pseudo-fermions
• Coherent population oscillations and an effective spin-exchange interaction in a $\mathcal{P}\mathcal{T}$ symmetric polariton mixture
• Nonlinear Parity-Time (PT) symmetric closed-form optical quadrimer waveguides: Attractor perspective
• Non-adiabatic transitions in a non-symmetric optical lattice
• Grating-based microcavity with independent control of resonance energy and linewidth for non-Hermitian polariton system
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Spectral and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric tight-binding chain with gain and loss
• Liouvillian and Hamiltonian exceptional points of atomic vapors: The spectral signatures of quantum jumps
• Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
• On elements of the Lax-Phillips scattering scheme for PT-symmetric operators
• Anomalous mechanisms of the loss of observability in non-Hermitian quantum models
• Spectral Design for Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator
• Anderson localization induced by complex potential
• Rapidly-oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization
• Negative-energy PT-symmetric Hamiltonians
• Higher-order field theories: ${\varphi }^6$, ${\varphi }^8$ and beyond
• Hamiltonian Truncation Crafted for UV-divergent QFTs
• Jordan blocks and the Bethe ansatz I: The eclectic spin chain as a limit
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays
• Classical irregular blocks, Hill's equation and PT-symmetric periodic complex potentials
• Resonances and PT symmetry in quantum curves
• WKB Analysis of PT-Symmetric Sturm-Liouville problems
• Kondo effect in a non-Hermitian, $\mathcal{P}\mathcal{T}$-symmetric Anderson model with Rashba spin-orbit coupling
• Electronic states in a quantum Beltrami surface
• Some ground-state expectation values for the free parafermion Z(N) spin chain
• A generalized family of discrete PT-symmetric square wells
• Non-Hermitian dynamics of a two-spin system with PT symmetry
• WKB Analysis of PT-Symmetric Sturm-Liouville problems. II
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Hierarchy of QM SUSYs on a Bounded Domain
• Variational Approach to studying solitary waves in the nonlinear Schrodinger equation with Complex Potentials
• Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Stability in the higher derivative Abelian gauge field theory
• Taming Hamiltonian systems with balanced loss and gain via Lorentz interaction : General results and a case study with Landau Hamiltonian
• Inhomogeneous modes in the PT-symmetric quantum cosmology
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
• Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Design nearly optimal quantum algorithm for linear differential equations via Lindbladians
• Scattering states of a particle, with position-dependent mass, in a $\mathcal{P}\mathcal{T}$ symmetric heterojunction
• Metric operators for non-Hermitian quadratic su(2) Hamiltonians
• Two-dimensional Schrödinger Hamiltonians with Effective Mass in SUSY Approach
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
• PT-symmetrically deformed shock waves
• Generalized N = 2 Super Landau Models
• Estimating energy levels of a three-level atom in single and multi-parameter metrological schemes
• Switchable Non-Hermitian Skin Effect in Bogoliubov Modes
• Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
• PC-symmetry-protected edge states in interacting driven-dissipative bosonic systems
• Finite-dimensional pseudo-bosons: a non-Hermitian version of the truncated harmonic oscillator
• Sum rule for the pseudo-Rényi entropy
• PT-symmetric quantum systems with positive P
• Quantum Optics of Non-Hermitian Optical Systems: Propagation of Squeezed State of Light through Dispersive non-Hermitian Optical Bilayers
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Symmetry properties of non-Hermitian PT-symmetric quantum field theories
• Origin of branch points in the spectrum of PT-symmetric periodic potentials
• Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems
• Non-Hermitian invisibility in tight-binding lattices
• Scattering of accelerated wave packets
• The cryptohermitian smeared-coordinate representation of wave functions
• Parity-time symmetric systems with memory
• Optimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics
• Waveguide QED with dissipative light-matter couplings
• Pseudo entropy and pseudo-Hermiticity in quantum field theories
• $\mathcal{P}\mathcal{T}$-Symmetry in Hartree-Fock Theory
• Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation
• A first encounter with exceptional points in a quantum model
• Non-Hermitian Model for Asymmetrical Tunneling
• Scattering properties of a PT dipole
• Universal hard-edge statistics of non-Hermitian random matrices
• Solitons in a Hamiltonian $PT$-symmetric coupler
• ${\varphi }^n$ trajectory bootstrap
• Duality between the quantum inverted harmonic oscillator and inverse square potentials
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• From Veneziano to Riemann: A String Theory Statement of the Riemann Hypothesis
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Electric conductivity in non-Hermitian holography
• Squeezed atom laser for Bose-Einstein condensate with minimal length
• Excitation Transmission through a non-Hermitian traversable wormhole
• Nonequilibrium steady states of Bose-Einstein condensates with a local particle loss in double potential barriers
• Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory
• Unbalanced gain and loss in a quantum photonic system
• Real spectra in one-dimensional single-band non-Hermitian Hamiltonians
• PT-symmetric interpretation of double-scaling
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• Systematics of quasi-Hermitian representations of non-Hermitian quantum models
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• PT-Symmetry Breaking Transitions in Polymeric Systems
• Quantum correlations in dissipative gain-loss systems across exceptional points
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
• Quantization of the mean decay time for non-Hermitian quantum systems
• Non-hermitian model for resonant cavities coupled by a chiral mirror
• Stability of new exact solutions of the nonlinear Schrodinger equation in a Poschl-Teller external potential
• Bose-Einstein condensates and the thin-shell limit in anisotropic bubble traps
• Unimodular Hartle-Hawking wave packets and their probability interpretation
• Anomalous Hall effect from a non-Hermitian viewpoint
• Eigenstates and instabilities of chains with embedded defects
• Geometric contribution to adiabatic amplification in non-Hermitian systems
• Accelerating multipartite entanglement generation in non-Hermitian superconducting qubits
• A new non-Hermitian E2-quasi-exactly solvable model
• Quantum, noncommutative and MOND corrections to the entropic law of gravitation
• Nonequilibrium Work Relation from Schroedinger's Unrecognized Probability Theory
• Exceptional Points of Degeneracy with Indirect Bandgap Induced By Mixing Forward and Backward Propagating Waves
• Symmetry classes of dissipative topological insulators with edge dark state
• $\mathcal{P}\mathcal{T}$ symmetry of a square-wave modulated two-level system
• Green Functions for the Wrong-Sign Quartic
• Nonuniqueness of the C operator in PT-symmetric quantum mechanics
• Effects of the third-order dispersion on continuous waves in complex potentials
• Stable solitons in a nearly PT-symmetric ferromagnet with spin-transfer torque
• Non-Hermitian Quantum Quenches in Holography
• Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians
• Perfectly matched layer method for optical modes in dielectric cavities
• PT-symmetric interpretation of the electromagnetic self-force
• Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor
• Krein-unitary Schrieffer-Wolff transformation and band touchings in bosonic Bogoliubov-de Gennes and other Krein-Hermitian Hamiltonians
• Internal nonlocality in generally dilated Hermiticity
• Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model
• Phase Transitions and Virtual Exceptional Points in Quantum Emitters Coupled to Dissipative Baths
• Quantum toboggans: models exhibiting a multisheeted PT symmetry
• Revisit the Poynting vector in PT-symmetric coupled waveguides
• Non self-adjoint Hamiltonians with complex eigenvalues
• Emergence of Exceptional Points in Periodic Metastructures with Hidden PT-symmetric Defects
• Non-Hermitian superconducting diode effect
• Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions
• Particle injection into a chain: decoherence versus relaxation for Hermitian and non-Hermitian dynamics
• Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media
• Anyonic $\mathcal{P}\mathcal{T}$ symmetry, drifting potentials and non-Hermitian delocalization
• Paths of unitary access to exceptional points
• Quasi-Hermitian formulation of quantum mechanics using two conjugate Schrödinger equations
• Wannier-Stark localization in one-dimensional amplitude-chirped lattices
• Retardaion-induced exceptional point
• Theory Including Future Not Excluded -- Formulation of Complex Action Theory II --
• Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
• Guiding structures with multiply connected cross-sections: evolution of propagation in external fields at complex Robin parameters
• Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions
• Non-Hermitian fermions with effective mass
• Topological phase in Kitaev chain with spatially separated pairing processes
• Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Broken Hermiticity phase transition in Bose-Hubbard model
• Non-Hermitian Numerical Renormalization Group: Solution of the non-Hermitian Kondo model
• Abstract ladder operators and their applications
• Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model
• A unifying asymptotic approach for nonadiabatic transitions near pairs of real or complex turning points
• Reconfiguration of quantum states in $\mathcal{P}T$-symmetric quasi-one dimensional lattices
• Matrix representation of the time operator
• Particles versus fields in PT-symmetrically deformed integrable systems
• Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras
• Born-Padé approach to electromagnetic scattering in complex one-dimensional inhomogeneous slabs
• Quantum star-graph analogues of PT-symmetric square wells. II: Spectra
• Controlling properties of a hybrid Cooper pair box interacting with a nanomechanical resonator in the presence of Kerr nonlinearities and losses
• Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings
• $\mathcal{P}\mathcal{T}$-symmetric currents of a Bose-Einstein condensate in a triple well
• Equilibrium states in open quantum systems
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• Quantum mechanical settings inspired by RLC circuits
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Generalized Bogoliubov transformations versus $\mathcal{D}$% -pseudo-bosons
• Level Crossings in Complex Two-Dimensional Potentials
• PT symmetric lattices with a local degree of freedom
• Comment on `Supersymmetry, PT-symmetry and spectral bifurcation'
• Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices
• Non-Relativistic Anti-Snyder Model and Some Applications
• Higher-order gap ratios of singular values in open quantum systems
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits
• Galois conjugates of String-net Model
• On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials
• Non-Hermitian Generalization of Rayleigh-Schrödinger Perturbation Theory
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• Supersymmetric Analysis of the Dirac-Weyl Operator within PT Symmetry
• Quantum Groups as Global Symmetries
• Exceptional points and quantum correlations in precise measurements
• Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase
• Rigged Hilbert Space Approach for Non-Hermite Systems with Positive Definite Metric
• Complex entanglement entropy for complex conformal field theory
• Universal spectral behavior of $x^2(ix{)}^{\epsilon }$ potentials
• Nonlinear supersymmetry as a hidden symmetry
• SUSY shields the scaling symmetry of conformal quantum mechanics
• Gravitational waves from inspiralling compact binaries in conformal gravity
• On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation
• Dynamics of mode entanglement in a system of cavities coupled with a chiral mirror
• An introductory review on resource theories of generalized nonclassical light
• Universal scaling at a pre-thermal dark state
• Spin-Vorticity Coupling for Massive Vector Mesons
• Quantum knots
• Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{P}\mathcal{T}$- and supersymmetric potential
• Jordan blocks and the Bethe ansatz II: The eclectic spin chain beyond $K=1$
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Gain-compensated cavities for the dynamic control of light-matter interactions
• Emergent Non-Hermitian Edge Polarisation in an Hermitian Tight-binding Model
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Correlations at higher-order exceptional points in non-Hermitian models
• Operator correlations in a quenched non-Hermitian Luttinger liquid
• Non-stationary non-Hermitian "wrong-sign'' quantum oscillators and their meaningful physical interpretation
• Robust unidirectional phantom helix states in the XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Prevalence of multistability and nonstationarity in driven chemical networks
• Symmetry breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials
• Imaginary-Temperature Zeros for Quantum Phase Transitions
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
• PT symmetry and large-N models
• Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
• Dynamics of non-Hermitian Floquet Wannier-Stark system
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Localization due to topological stochastic disorder in active networks
• Loss revives bistable state near the exceptional point in a non-Hermitian microwave photonic meta-molecule
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation
• Unitarity through PT symmetry in Quantum Quadratic Gravity
• Hermitian - non-Hermitian interfaces in quantum theory
• Non-Hermitian inverted Harmonic Oscillator-Type Hamiltonians Generated from Supersymmetry with Reflections
• PHOENIX -- Paderborn highly optimized and energy efficient solver for two-dimensional nonlinear Schrödinger equations with integrated extensions
• Demonstration of a Tunable Non-Hermitian Nonlinear Microwave Dimer
• Heisenberg and Heisenberg-Like Representations via Hilbert Space Bundle Geometry in the Non-Hermitian Regime
• Néel vector controlled exceptional contours in $p$-wave magnet-ferromagnet junctions
• Global solution of the cubic oscillator
• A PT-symmetric dual-core system with the sine-Gordon nonlinearity and derivative coupling
• Quantization of Big Bang in crypto-Hermitian Heisenberg picture
• Enhancement of signal-to-noise ratio at a high-order exceptional point of coherent perfect absorption
• Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
• Instantaneous modulations in time-varying complex optical potentials
• Unconventional quantum criticality in a non-Hermitian extended Kitaev chain
• Non-Hermitian Floquet-Free Analytically Solvable Time Dependant Systems
• Non-Hermitian guided modes and exceptional points using loss-free negative-index materials
• Area distribution of two-dimensional random walks and non Hermitian Hofstadter quantum mechanics
• Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via $\mathcal{P}\mathcal{T}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Supersymmetric approach to exact solutions of $(1+1)$-dimensional time-independent Klein-Gordon equation : Application to a position-dependent mass and a $\mathcal{P}\mathcal{T}$-symmetric vector potential
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip
• 2*2 random matrix ensembles with reduced symmetry: From Hermitian to PT-symmetric matrices
• Gibbs states defined by biorthogonal sequences
• PT-symmetric model with an interplay between kinematical and dynamical non-localities
• Topological field theory of dynamical systems
• Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials
• PT invariant complex E(8) root spaces
• Original study of the $g{\varphi }^2(i\varphi {)}^{\epsilon }$ theory. Analysis of all orders in $\epsilon$ and resummations
• Non-Hermitian theory of valley excitons in two-dimensional semiconductors
• Manipulating Spectral Windings and Skin Modes through Nonconservative Couplings
• Manifestation of Superposition and Coherence in $\mathcal{P}\mathcal{T}$-symmetry through the $\eta$-inner Product
• Krein signature for instability of $\mathcal{P}\mathcal{T}$-symmetric states
• Scattering of Spin-$\frac{1}{2}$ Particles from a $\mathcal{P}\mathcal{T}$-symmetric Complex Potential
• Resonant-amplified and invisible Bragg scattering based on spin coalescing modes
• Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
• Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling
• Double-Scaling Limit of the O(N)-Symmetric Anharmonic Oscillator
• Conformal anomaly in non-hermitian quantum mechanics
• Anomalous Dimensions and the Renormalizability of the Four-Fermion Interaction
• Scattering off PT-symmetric upside-down potentials
• Imaginary spin-orbital coupling in parity-time symmetric systems with momentum-dependent gain and loss
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• A 'Dysonization' Scheme for Identifying Particles and Quasi-Particles Using Non-Hermitian Quantum Mechanics
• CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework
• Conformal bridge in a cosmic string background
• Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
• Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario
• PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring
• Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics
• Complex tridiagonal quantum Hamiltonians and matrix continued fractions
• Non-Hermitian wave packet approximation for coupled two-level systems in weak and intense fields
• A generalized Swanson Hamiltonian in a second-derivative pseudo-supersymmetric framework
• Lopsided optical diffraction in loop electromagnetically induced grating
• Solitonic fixed point attractors in the complex Ginzburg-Landau equation for associative memories
• Entanglement control of two-level atoms in dissipative cavities
• Entanglement Efficiencies in PT-Symmetric Quantum Mechanics
• Composite Quantum Phases in Non-Hermitian Systems
• Testing the Wave-Particle Duality of Gravitational Wave Using the Spin-Orbital-Hall Effect of Structured Light
• Cumulants of time-integrated observables of closed quantum systems and PT-symmetry, with an application to the quantum Ising chain
• Three-Dimensional Solutions of Supersymmetrical Intertwining Relations and Pairs of Isospectral Hamiltonians
• Multicomplex solitons
• Stability boundaries of a Mathieu equation having PT symmetry
• Correlated Nonreciprocity around Conjugate Exceptional Points
• Superoscillatory PT-symmetric potentials
• Ring-Frustrated Non-Hermitian $XY$ Model
• New version of pseudo-hermiticity in the two-sided deformation of Heisenberg algebra
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Stability of exact solutions of the nonlinear Schroedinger equation in an external potential having supersymmetry and parity-time symmetry
• Quantum chaos in PT symmetric quantum systems
• Non-Hermitian Boundary in a Surface Selective Reconstructed Magnetic Weyl Semimetal
• A new method for driven-dissipative problems: Keldysh-Heisenberg equations
• Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Markov constant and quantum instabilities
• Deformations of Yang-Mills theory
• Supercurrent from the imaginary part of the Andreev levels in non-Hermitian Josephson junctions
• Quantum geometrical effects in non-Hermitian systems
• On the Pauli group on 2-qubits in dynamical systems with pseudofermions
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• PT-Symmetric Model of Immune Response
• Arnold's potentials and quantum catastrophes II
• Factorized Hilbert-space metrics and non-commutative quasi-Hermitian observables
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Conserved quantities in non-Hermitian systems via vectorization method
• Scattering in a varying mass PT symmetric double heterojunction
• Non-Hermitian physics and engineering in silicon photonics
• Pseudo-Hermitian and PT -symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase
• Vector Models in PT Quantum Mechanics
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• Random non-Hermitian action theory for stochastic quantum dynamics: from canonical to path integral quantization
• Slow approach to adiabaticity in many-body non-Hermitian systems: the Hatano-Nelson Model
• Structure of conformal gravity in the presence of a scale breaking scalar field
• Response of exact solutions of the nonlinear Schrodinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry
• Classical Trajectories of the Continuum States of the $\mathcal{P}\mathcal{T}$ symmetric Scarf II potential
• Perpetual emulation threshold of PT-symmetric Hamiltonians
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Shock wave generation and propagation in dissipative and nonlocal nonlinear Rydberg media
• Resonant scattering of two-dimensional honeycomb PT dipole structure
• Gain engineering and atom lasing in a topological edge state in synthetic dimensions
• Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians
• Extended Wannier-Stark ladder and particle-pair Bloch oscillations in dimerized non-Hermitian systems
• Axial momentum for the relativistic Majorana particle
• Nonparaxial electromagnetic Bragg scattering in periodic media with PT symmetry
• Nonlinear n-Pseudo Fermions
• Adjusting exceptional points using saturable nonlinearities
• Schrieffer-Wolff transformation for non-Hermitian systems: application for $\mathcal{P}\mathcal{T}$-symmetric circuit QED
• Jordan blocks and the Bethe ansatz III: Class 5 model and its symmetries
• Singular spinors as expansion coefficients of local spin-half fermionic and bosonic fields: On the two-fold Wigner degeneracy
• Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space
• Non-Hermitian tearing by dissipation
• Gap solitons and symmetry breaking in parity-time symmetric microring CROWs
• $\mathcal{P}\mathcal{T}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities
• Metric Operator For The Non-Hermitian Hamiltonian Model and Pseudo-Supersymmetry
• Order-invariant two-photon quantum correlations in PT-symmetric interferometers
• Semi-localization transition driven by a single asymmetrical tunneling
• Quantum control and the challenge of non-Hermitian model-building
• $\mathcal{P}\mathcal{T}$-symmetry phase transition in a Bose-Hubbard model with localized gain and loss
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• Mixedness timescale in non-Hermitian quantum systems
• Hidden symmetries in non-self-adjoint graphs
• Supersymmetry of $\mathcal{P}\mathcal{T}$- symmetric tridiagonal Hamiltonians
• Energy-independent complex single $P$-waves $NN$ potential from Marchenko equation
• CPT-symmetric discrete square well
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Some spectral equivalences between Schrodinger operators
• Justification of the Asymptotic Coupled Mode Approximation of Out-of-Plane Gap Solitons in Maxwell Equations
• Boundaries and profiles in the Wigner formalism
• A Bound on the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential
• Lax-Phillips scattering theory for PT-symmetric ρ-perturbed operators
• Uncertainty relations: curiosities and inconsistencies
• Exact Christoffel-Darboux Expansions: A New, Multidimensional, Algebraic, Eigenenergy Bounding Method
• Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems
• Intrinsic exceptional point -- a challenge in quantum theory
• Topological spin textures in electronic non-Hermitian systems
• Witnessing criticality in non-Hermitian systems via entropic uncertainty relation
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• $T\bar{T}$ deformation on non-Hermitian two coupled SYK model
• Mathematical and physical meaning of the crossings of energy levels in $\mathcal{P}\mathcal{T}-$symmetric systems
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
• PT-Symmetry Quantum Electrodynamics--PTQED
• Exact solution for the time dependent non-Hermitian generalized Swanson oscillator
• Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos
• Dynamical symmetry algebra of two superintegrable two-dimensional systems
• Fermionic duality: General symmetry of open systems with strong dissipation and memory
• Chiral state conversion in a levitated micromechanical oscillator with in situ control of parameter loops
• Topological and fractal defect states in non-Hermitian lattices
• Conditional observability versus self-duality in a schematic model
• Reciprocity in parity violating non-Hermitian systems
• Quantum Instability
• Interference of non-Hermiticity with Hermiticity at exceptional points
• EP restoration and fast-light edge states in photonic crystal waveguide with glide and time reversal symmetry
• Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models
• High-fidelity multipartite entanglement creation in non-Hermitian qubits
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• $\mathcal{P}\mathcal{T}$-symmetric strings
• Resonant instabilities mediated by drag and electrostatic interactions in laboratory and astrophysical dusty plasmas
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter
• Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
• Monopoles in non-Hermitian systems
• Multi-well log-anharmonic oscillators
• Ad hoc physical Hilbert spaces in Quantum Mechanics
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Laser induced $\mathcal{P}\mathcal{T}$-symmetry breaking in the fluctuations of electronic fluids
• Dual opposing quadrature-PT symmetry
• Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions
• Perturbative expansion of irreversible works in symmetric and asymmetric processes
• Extracting the internal nonlocality from the dilated Hermiticity
• PT-symmetric and antisymmetric nonlinear states in a split potential box
• Deconfined quantum criticality and generalised exclusion statistics in a non-hermitian BCS model
• Features, paradoxes and amendments of perturbative non-Hermitian quantum mechanics
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• Contact interactions and Kronig-Penney Models in Hermitian and PT-symmetric Quantum Mechanics
• Sublattice signatures of transitions in a $\mathcal{P}\mathcal{T}$-symmetric dimer lattice
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Non-Hermitian interaction of a discrete state with a continuum
• Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. II. Three-Dimensional Model
• Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• A solvable non-unitary fermionic long-range model with extended symmetry
• Observation of Perfect Absorption in Hyperfine Levels of Molecular Spins with Hermitian Subspaces
• Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model
• Random non-Hermitian Hamiltonian framework for symmetry breaking dynamics
• Manipulating spectral transitions and photonic transmission in a non-Hermitian optical system through nanoparticle perturbations
• Dynamic transition of the density-matrix topology under parity-time symmetry
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• Transport characteristics of a $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian system: Effect of environmental interaction
• The large-g observability of the low-lying energies in the strongly singular potentials $V(x)=x^2+g^2/x^6$ after their PT-symmetric regularization
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Robustness of tripartite entangled states in passive PT-symmetric qubits
• New Concept of Solvability in Quantum Mechanics
• Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraint
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• Solvable spectral problems from 2d CFT and N=2 gauge theories
• Bosonic Holes in Quadratic Bosonic Systems
• Exploring Metamaterial Lasers through Non-Hermitian Scattering Formalism
• Symmetry induced enhancement in finite-time thermodynamic trade-off relations
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Comment on: `Numerical estimates of the spectrum for anharmonic PT symmetric potentials' [Phys. Scr. \textbf{85} (2012) 065005]
• Using mixed many-body particle states to generate exact $\mathcal{P}\mathcal{T}$-symmetry in a time-dependent four-well system
• Continuous time crystals as a PT symmetric state and the emergence of critical exceptional points
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Supersymmetric $\eta$ operators
• Planarizable Supersymmetric Quantum Toboggans
• Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: I. Inherited and genuine singularities
• Quantum-to-semiclassical Husimi dynamics of non-Hermitian localization transitions
• Spectral inversion of an indefinite Sturm-Liouville problem due to Richardson
• Resonances and continued-fraction Green's functions in non-Hermitian Bose-Hubbard-like quantum models
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators
• Non-Hermitian gravitational effects on Bose-Einstein condensate
• Connections Between Complex PT-Invariant Solutions and Complex Periodic Solutions of Several Nonlinear Equations
• A Hermitian bypass to the non-Hermitian quantum theory
• The Large-N Limit of PT-Symmetric O(N) Models
• Comment on 'The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'
• Does Cosmology require Hermiticity in Quantum Mechanics?
• Spectral zeta functions of a 1D Schrödinger problem
• Three alternative model-building strategies using quasi-Hermitian time-dependent observables
• Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems
• Projective Geometry and $\mathcal{P}\mathcal{T}$-Symmetric Dirac Hamiltonian
• Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity
• Scattering Dynamics and Boundary States of a Non-Hermitian Dirac Equation
• Does Gravity Render Probability Quasilocal?
• Hofstadter's Cocoon
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Computation and Verification of Spectra for Non-Hermitian Systems
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Homodyne Measurement of a Non-Hermitian Qubit Undergoing Fluorescence
• Minimal Proper-time in Quantum Field Theory
• Path-integral Bosonization of $d=2$ PT symmetric models
• Localized vibrational modes in waveguide quantum optomechanics with spontaneously broken PT symmetry
• Nonlocality of Observables in Quasi-Hermitian Quantum Theory
• Soliton dynamics and stability in the ABS spinor model with a PT-symmetric periodic potential
• Isospectral Hermitian counterpart of complex non Hermitian Hamiltonian $p^2-g{x}^4+a/x^2$
• A non-trivial PT-symmetric continuum Hamiltonian and its Eigenstates and Eigenvalues
• An investigation of $\mathcal{P}\mathcal{T}$-symmetry breaking in tight-binding chains
• Phase transitions in quasi-Hermitian quantum models at exceptional points of order four
• $\mathcal{P}\mathcal{T}$-Symmetric Generalized Extended Momentum Operator
• Entanglement of pseudo-Hermitian random states
• Non-Hermitian magnetic moment
• Experimental Realization of Non-Abelian Permutations in a Three-State Non-Hermitian System
• Semi-analytical solutions for eigenvalue problems of chains and periodic graphs
• Dynamical non-Hermitian systems: Fingerprints and pure dephasing induced protection effect
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Non-Gaussian Phase Transition and Cascade of Instabilities in the Dissipative Quantum Rabi Model
• Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
• Oscillators with imaginary coupling: spectral functions in quantum mechanics and quantum field theory
• Exceptional spectrum and dynamic magnetization
• Construction of potentials with multiple spectral singularities
• Momentum relation and classical limit in the future-not-included complex action theory
• Power-law scaling of asymmetries in viscous flow with PT-symmetric inflow and outflow
• Some Consequences of the Grunewald-O'Halloran Conjecture for Pseudoquonic Operators
• Conformal cosmology with a positive effective gravitational constant
• Quantum mechanics using two auxiliary inner products
• Exploring Spectral Singularities in Dirac Semimetals: The Role of Non-Hermitian Physics and Dichroism
• Extremely broken generalized $\mathcal{P}\mathcal{T}$ symmetry
• Resilience of $\mathcal{P}\mathcal{T}$ symmetry against stochasticity in a gain-loss balanced oscillator
• Interference effects and modified Born rule in the presence of torsion
• Application of Jordan Decomposition to Non-Hermitian Lattice Models with Spectrally-Isolated Lower Dimensional States
• Recurrence method in Non-Hermitian Systems
• A Testable Theory for The Emergence of the Classical World
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Smoking Gun Signatures of Quasilocal Probability in Black Hole Ringdowns
• Non-Hermitian Effects in the Su-Schrieffer-Heeger model: Exploring Substrate Coupling and Decoupling Dynamics
• Non-Hermitian physics and topological phenomena in convective thermal metamaterials
• Regularization of energy-dependent pointlike interactions in 1D quantum mechanics
• Piecewise linear potentials for false vacuum decay and negative modes
• Comment on "Numerical estimates of the spectrum for anharmonic PT symmetric potentials" by Bowen et al
• Superradiant Quantum Phase Transition in Open Systems: System-Bath Interaction at the Critical Point
• Scattering by infinitely rising one-dimensional potentials
• Complex Inflaton Potentials with Nonminimal Coupling: Robust Inflation and Geometric Reheating
• Anisotropy and asymptotic degeneracy of the physical-Hilbert-space inner-product metrics in an exactly solvable crypto-unitary quantum model
• Non-Hermitian Gravitational Wave Scattering
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model
• Probing Planck scale effects on absolute mass limit in neutrino flavor evolution
• $\mathcal{P}\mathcal{T}-$Symmetric Two-Level Open Quantum Systems: Information Theoretic Facets
• Coulomb potential and the paradoxes of PT-symmetrization
• Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry
• Time-dependent exchange creates the time-frustrated state of matter
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
• Electronic states in a bilayer graphene quantum ripple
• The Control of the Oscillation Threshold with Asymmetric Gain in Operational Amplifiers
• Emergence of Hermitian topology from non-Hermitian knots
• Nonreciprocal Coupling Induced Non-Hermitian Entanglement in Optomechanical Systems
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Mutual compatibility/incompatibility of quasi-Hermitian quantum observables
• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology
• On the $\mathcal{P}\mathcal{T}$-symmetric parametric amplifier
• Non-Hermitian superintegrable systems
• Exceptional point in self-consistent Markovian master equations
• Floquet spin textures in optically pumped non-Hermitian surface states
• The non-Hermitian landscape of autoionization
• Asymptotic non-Hermitian degeneracy phenomenon and its exactly solvable simulation
• Continuum Landau surface states in a non-Hermitian Weyl semimetal
• The $\mathcal{P}\mathcal{T}$-symmetry-breaking transition in a chain of trapped interacting ions
• The initial value problem for gravitational waves in conformal gravity
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states
• Functional renormalization group for non-Hermitian and $\mathcal{P}\mathcal{T}$-symmetric systems
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description
• Physical constraints on effective non-Hermitian systems
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Mesoscopic Möbius ladder lattices as non-Hermitian model systems
• Balancing gain and loss in symmetrised multi-well potentials
• Hexagonal Warping Control of Exceptional Points in Topological Insulator--Ferromagnetic Heterojunctions
• Non-Hermitian Bose-Hubbard-like quantum models
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• To quantify the difference of $\eta$-inner products in $\mathcal{P}\mathcal{T}$-symmetric theory
• Triple exceptional point with unitary paths of unfolding in a three-site fermionic Swanson-like model
• A unifying E2-quasi-exactly solvable model
• Investigation of the Effect of Quantum Measurement on Parity-Time Symmetry
• Emergence and localization of exceptional points in an exactly solvable toy model
• Stability via symmetry breaking in interacting driven systems
• Free Particle to Complex KdV breathers through Isospectral Deformation
• Cryptohermitian Hamiltonians on graphs. II. Hermitizations
• Preparation of Many-body Ground States by Time Evolution with Variational Microscopic Magnetic Fields and Incomplete Interactions
• Stochastic unravelings for Heisenberg picture and trace-nonpreserving dynamics