Complex Extension of Quantum Mechanics

Abstract

It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new Hamiltonians that one can construct to explain experimental data. One might expect that a quantum theory based on a non-Hermitian Hamiltonian would violate unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed physical symmetry C of the Hamiltonian. Using C, an inner product is constructed whose associated norm is positive definite. This construction is completely general and works for any PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalisation of it.

4 Pages, Version to appear in PRL

References in corpus (2)

• Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics
• Two-Point Green's Function in PT-Symmetric Theories

Cited by in corpus (911)

• Making Sense of Non-Hermitian Hamiltonians
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• PT-symmetric laser-absorber
• Pseudo-Hermitian Representation of Quantum Mechanics
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Non-Hermitian Topology and Exceptional-Point Geometries
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Biorthogonal Quantum Mechanics
• Introduction to PT-Symmetric Quantum Theory
• Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures
• Observation of parity-time symmetry breaking in a single spin system
• Coherent perfect absorbers: linear control of light with light
• Faster than Hermitian Quantum Mechanics
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Non-Hermitian topological phenomena: A review
• Must a Hamiltonian be Hermitian?
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Nonlinear switching and solitons in PT-symmetric photonic systems
• New topological invariants in non-Hermitian systems
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Observation of PT phase transition in a simple mechanical system
• Experimental realization of a Weyl exceptional ring
• Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices
• Observation of higher-order non-Hermitian skin effect
• Non-Hermitian Many-Body Localization
• Stability analysis for solitons in PT-symmetric optical lattices
• PT-Symmetric Electronics
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Nonlinear suppression of time-reversals in PT-symmetric optical couplers
• Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
• Optical solitons in $\mathcal{P}\mathcal{T}$-symmetric nonlinear couplers with gain and loss
• Observation of Defect States in PT-Symmetric Optical Lattices
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• Optical realization of relativistic non-Hermitian quantum mechanics
• Spectral singularities and Bragg scattering in complex crystals
• Simulating dynamic quantum phase transitions in photonic quantum walks
• Antisymmetric PT-photonic structures with balanced positive and negative index materials
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Signatures of three coalescing eigenfunctions
• Observation of critical phenomena in parity-time-symmetric quantum dynamics
• Mixed-state evolution in the presence of gain and loss
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• PT-Symmetric Talbot Effects
• Quadratic Gravity
• Parity-time-symmetric topological superconductor
• Observation of PT-symmetric quantum interference
• Quantum noise and self-sustained radiation of PT-symmetric systems
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Mechanical PT symmetry in coupled optomechanical systems
• Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• Continuous and discrete Schrodinger systems with PT-symmetric nonlinearities
• Local PT symmetry violates the no-signaling principle
• On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts
• Holographic Description of AdS Cosmologies
• Observation of Fast Evolution in Parity-Time-Symmetric System
• PT-Symmetric Wave Chaos
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Pseudo Parity-Time Symmetry in Optical Systems
• Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems
• Pseudospectra in non-Hermitian quantum mechanics
• Dual PT-Symmetric Quantum Field Theories
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Fermion doubling theorems in 2D non-Hermitian systems for Fermi points and exceptional points
• Nonlinear reversal of PT symmetric phase transition in a system of coupled semiconductor micro-ring resonators
• Robust and fragile PT-symmetric phases in a tight-binding chain
• Exceptional contours and band structure design in parity-time symmetric photonic crystals
• Nonlocal bright spatial solitons in defocusing Kerr media supported by PT symmetric potentials
• Experimental demonstration of an anisotropic exceptional point
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model
• Non-Hermitian Hamiltonians and no-go theorems in quantum information
• Constant-intensity waves and their modulation instability in non-Hermitian potentials
• Topological classification of non-Hermitian systems with reflection symmetry
• First-order intertwining operators and position-dependent mass Schrodinger equations in d dimensions
• Supersymmetry-generated complex optical potentials with real spectra
• Time-dependent version of cryptohermitian quantum theory
• On the metric operator for the imaginary cubic oscillator
• Hamiltonian for the zeros of the Riemann zeta function
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Bypassing the bandwidth theorem with PT symmetry
• Defect states emerging from a non-Hermitian flat band of photonic zero modes
• Time evolution of non-Hermitian Hamiltonian systems
• Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems
• Bragg solitons in nonlinear PT-symmetric periodic potentials
• Optical mesh lattices with PT-symmetry
• Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal
• Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
• Time Dependent $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Virtual Parity-Time Symmetry
• Solitons in a chain of PT-invariant dimers
• Solitons supported by complex PT symmetric Gaussian potentials
• Parity-Time Symmetry in Non-Hermitian Complex Optical Media
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• Exceptional Point Dynamics in Photonic Honeycomb Lattices with PT Symmetry
• Rational Solitons in the Parity-Time-Symmetric Nonlocal Nonlinear Schrödinger Model
• PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues
• Exceptional points in topological edge spectrum of PT symmetric domain walls
• Enhanced sensing of weak anharmonicities through coherences in dissipatively coupled anti-PT symmetric systems
• Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential
• Nonlinear modal interactions in parity-time ($\mathcal{P}\mathcal{T}$) symmetric lasers
• Projective Hilbert space structures at exceptional points
• Stimulation of the fluctuation superconductivity by the PT-symmetry
• Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
• Exceptional magnetic sensitivity of PT-symmetric cavity magnon polaritons
• Non-hermitian quantum thermodynamics
• Defective Edge States and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Ghost Busting: PT-Symmetric Interpretation of the Lee Model
• Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
• Three-Hilbert-Space Formulation of Quantum Mechanics
• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• Increase of entanglement by local PT -symmetric operations
• Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Structure of Lefschetz thimbles in simple fermionic systems
• Conceptual Problems in Scattering from Localized non-Hermitian Potentials
• Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
• Chiral state-conversion without encircling an exceptional point
• Unidirectional zero sonic reflection in passive $\mathcal{P}\mathcal{T}$ symmetric Willis media
• Breaking of PT-symmetry in bounded and unbounded scattering systems
• Quantum sensing with a single-qubit pseudo-Hermitian system
• Observation of $\mathcal{P}\mathcal{T}$-symmetric quantum coherence in a single ion system
• Topological classification of defects in non-Hermitian systems
• Topological classification of non-Hermitian bands
• On the Quantum Resolution of Cosmological Singularities using AdS/CFT
• The C Operator in PT-Symmetric Quantum Theories
• Electric circuits for non-Hermitian Chern insulators
• PT-symmetric photonic quantum systems with gain and loss do not exist
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Explicit definition of $\mathcal{P}\mathcal{T}$ symmetry for non-unitary quantum walks with gain and loss
• Physics counterpart of the PT non-hermitian tight-binding chain
• One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
• Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects
• Wave propagation through disordered media without backscattering and intensity variations
• Optical waveguide arrays: quantum effects and PT symmetry breaking
• Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice
• $\mathcal{P}\mathcal{T}$-Symmetry-Induced Wave Confinement and Guiding in Epsilon-Near-Zero Metamaterials
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Topological phases in Kitaev chain with imbalanced pairing
• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Consistency of PT-symmetric quantum mechanics
• Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry
• PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics
• Causality and phase transitions in PT-symmetrical optical systems
• Reflectionless Potentials and PT Symmetry
• Jarzynski equality in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics
• Parity-time symmetry in a flat band system
• Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures
• Magnetic suppression of non-Hermitian skin effects
• Parity-time symmetry in optical microcavity systems
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Measuring Non-Hermitian Operators via Weak Values
• Quantum Geometric Tensor in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
• Simulating Exceptional Non-Hermitian Metals with Single-Photon Interferometry
• Analytic Results for a PT-symmetric Optical Structure
• Completeness and Orthonormality in PT-symmetric Quantum Systems
• Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
• PT spectroscopy of the Rabi problem
• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• Geometric Phase in PT-Symmetric Quantum Mechanics
• Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation
• Stabilizing Non-Hermitian Systems by Periodic Driving
• On complexified mechanics and coquaternions
• Classical limit of non-Hermitian quantum dynamics - a generalised canonical structure
• Transport and spectral features in non-Hermitian open systems
• Achieving arbitrary polarization control using complex birefringent meta-materials
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Speeding up entanglement generation by proximity to higher-order exceptional points
• Hunting for the non-Hermitian exceptional points with fidelity susceptibility
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• Direct Measurement of Topological Properties of an Exceptional Parabola
• Complex Correspondence Principle
• Degrees and signatures of broken PT-symmetry in (non-uniform) lattices
• Classical Trajectories for Complex Hamiltonians
• Hermitian zero modes protected by nonnormality: Application of pseudospectra
• Fermionic coherent states for pseudo-Hermitian two-level systems
• Experimental demonstration of asymmetric diffraction based on a passive parity-time-symmetric acoustic grating
• General solution of scalar field cosmology with a (piecewise) exponential potential
• $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian Dirac semimetals
• Chiral metamaterials with PT symmetry and beyond
• On the invariant method for the time-dependent non-Hermitian Hamiltonians
• Eigenvalue structure of a Bose-Einstein condensate in a PT-symmetric double well
• Steering magnonic dynamics and permeability at exceptional points in a parity-time symmetric waveguide
• Quasinormal modes and Purcell factors of coupled loss-gain resonators and index-modulated ring resonators near exceptional points
• Dimensional Transmutation in Gravity and Cosmology
• $PT$-symmetric invisible defects and confluent Darboux-Crum transformations
• Complexified Dynamical Systems
• Gegenbauer-solvable quantum chain model
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians
• Non-Hermitian Floquet Topological Matter -- A Review
• Magnon Accumulation in Chirally Coupled Magnets
• Two (2 + 1)-dimensional integrable nonlocal nonlinear Schrodinger equations: Breather, rational and semi-rational solutions
• PT-Symmetric Quantum Electrodynamics
• Experimental observation of information flow in the anti-$\mathcal{P}\mathcal{T}$-symmetric system
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Enhanced energy transfer in a Dicke quantum battery
• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories
• Parity-time symmetric coupled asymmetric dimers
• Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism
• Anisotropic exceptional points of arbitrary order
• Delayed sudden death of entanglement at exceptional points
• Interactions of Hermitian and non-Hermitian Hamiltonians
• PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
• $\mathcal{P}\mathcal{T}$-symmetric slowing-down of decoherence
• Perfect State Transfer in PT-symmetric Non-Hermitian Networks
• Designing non-Hermitian real spectra through electrostatics
• Time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics in generic non-Hermitian systems
• Nonlinear PT-symmetric plaquettes
• Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
• Dynamical nonlinear higher-order non-Hermitian skin effects and topological trap-skin phase
• Exceptional entanglement phenomena: non-Hermiticity meeting non-classicality
• Semiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics
• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• Construction of a unique metric in quasi-Hermitian quantum mechanics: non-existence of the charge operator in a 2 x 2 matrix model
• Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report
• Uniqueness and Self-Conjugacy of Dirac Hamiltonians in arbitrary Gravitational Fields
• Energy Observable for a Quantum System with a Dynamical Hilbert Space and a Global Geometric Extension of Quantum Theory
• On the pseudo-Hermitian nondiagonalizable Hamiltonians
• Solution of the problem of uniqueness and hermiticity of hamiltonians for Dirac particles in gravitational fields
• Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories
• Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry
• Modulation instability in nonlinear complex parity-time (PT) symmetric periodic structures
• Reciprocal and unidirectional scattering of parity-time symmetric structures
• Discrete PT-symmetric models of scattering
• Calculation of the Hidden Symmetry Operator for a $\cP\cT$-Symmetric Square Well
• Steering between Level Repulsion and Attraction: Broad tunability of Two-Port Driven Cavity Magnon-Polaritons
• Fixed points and emergent topological phenomena in a parity-time-symmetric quantum quench
• Bound State Wave Functions through the Quantum Hamilton - Jacobi Formalism
• Scattering in $\mathcal{P}\mathcal{T}$ and $\mathcal{R}\mathcal{T}$ Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension
• Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
• PT-symmetric deformations of integrable models
• Origin of maximal symmetry breaking in even PT-symmetric lattices
• Wave scattering on a domain wall in a chain of PT-symmetric couplers
• Non-Hermitian Hamiltonians of Lie algebraic type
• Asymmetric transmission through a flux-controlled non-Hermitian scattering center
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
• Passive $\mathcal{P}\mathcal{T}$-symmetry breaking transitions without exceptional points in dissipative photonic systems
• Krein space related perturbation theory for MHD alpha-2-dynamos and resonant unfolding of diabolical points
• Anyonic-parity-time symmetry in complex-coupled lasers
• Spontaneously Breaking Non-Abelian Gauge Symmetry in Non-Hermitian Field Theories
• Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay
• Non-Hermitian Dynamic Strings and Anomalous Topological Degeneracy on non-Hermitian Toric-code Model with Parity-time Symmetry
• Flux Continuity and Probability Conservation in Complexified Bohmian Mechanics
• Low-dimensional optical chirality in complex potentials
• Contrasting Spectral Signatures and Sensitivities of CPA-Lasing in a $\mathcal{P}\mathcal{T}$-Symmetric Periodic Structure
• Emergent phase transition in Cluster Ising model with dissipation
• The C Operator in PT-Symmetric Quantum Field Theory Transforms as a Lorentz Scalar
• Connections between the Open-boundary Spectrum and Generalized Brillouin Zone in Non-Hermitian Systems
• Chiral coupling of magnons in waveguides
• Beyond the WKB approximation in PT-symmetric quantum mechanics
• Application of Pseudo-Hermitian Quantum Mechanics to a PT-Symmetric Hamiltonian with a Continuum of Scattering States
• A return to observability near exceptional points in a schematic PT-symmetric model
• Dimensionality reduction of many-body problem using coupled-cluster sub-system flow equations: classical and quantum computing perspective
• Spontaneous Breaking of Classical PT Symmetry
• A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields
• Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Realization and application of parity-time-symmetric oscillators in quantum regime
• PT/Non-PT Symmetric and Non-Hermitian Poschl-Teller-Like Solvable Potentials via Nikiforov-Uvarov Method
• Giving up the ghost
• Observation of slowly decaying eigenmodes without exceptional points in Floquet, dissipative, synthetic circuits
• $\mathcal{P}\mathcal{T}$-symmetric, non-Hermitian quantum many-body physics -- a methodological perspective
• Dynamical topological invariant for non-Hermitian Rice-Mele model
• Deformed quantum mechanics and q-Hermitian operators
• Conserved quantities in parity-time symmetric systems
• Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories
• Non-Hermitian Hamiltonian for a Modulated Jaynes-Cummings Model with PT Symmetry
• Self-hybridization within non-Hermitian plasmonic systems
• Semiclassical Analysis of Spectral Singularities and Their Applications in Optics
• Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
• Nonlocal gap solitons in parity-time symmetric optical lattices
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• One- and two-dimensional solitons in PT-symmetric systems emulating the spin-orbit coupling
• Experimental simulation of the Parity-Time-symmetric dynamics using photonics qubits
• Spectral Singularities of a General Point Interaction
• PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability
• PT symmetry of a conditionally exactly solvable potential
• Scattering properties of PT-symmetric layered periodic structures
• Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point
• Hermitian dynamics in a class of pseudo-Hermitian networks
• Families of particles with different masses in PT-symmetric quantum field theory
• Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system
• The disappearing $Q$ operator
• Conditional observability
• Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
• PT-symmetric quantum state discrimination
• Interpretation of quantum mechanics with indefinite norm
• Fragile PT-symmetry in a solvable model
• Flat bands and PT-symmetry in quasi-one-dimensional lattices
• Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree
• Solvability and PT-symmetry in a double-well model with point interactions
• PT Symmetry as a Generalization of Hermiticity
• Which Green Functions Does the Path Integral for Quasi-Hermitian Hamiltonians Represent?
• Hermitian scattering behavior for the non-Hermitian scattering center
• Skin modes in a nonlinear Hatano-Nelson model
• Isospectral Hamiltonians from Moyal products
• A physical interpretation for the non-Hermitian Hamiltonian
• Is the CPT-norm always positive?
• PT-Symmetric Quantum Mechanics: A Precise and Consistent Formulation
• New Quasi-Exactly Solvable Sextic Polynomial Potentials
• Moyal products -- a new perspective on quasi-hermitian quantum mechanics
• All Hermitian Hamiltonians Have Parity
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• Coupled-channel version of PT-symmetric square well
• Parametric instability of non-Hermitian systems near the exceptional point
• Real spectra in non-Hermitian topological insulators
• Quantum information dynamics in a high-dimensional parity-time-symmetric system
• Non-Hermitian quantum systems and their geometric phases
• Wave emission and absorption at spectral singularities
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Probability-preserving evolution in a non-Hermitian two-band model
• Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics
• Non-Hermitian skin effect edge
• PT-Symmetric Non-Hermitian Quantum Field Theories with Supersymmetry
• PT-symmetric models in curved manifolds
• P,T,PT, and CPT invariance of Hermitian Hamiltonians
• Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential
• Manipulating non-Hermitian skin effect via electric fields
• Quantum Phase Transition in a Quantum Ising Chain at Nonzero Temperatures
• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• Quantum Mechanics of Proca Fields
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Bragg gap solitons in $\mathcal{P}\mathcal{T}$ symmetric lattices with competing nonlinearity
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• Real Description of Classical Hamiltonian Dynamics Generated by a Complex Potential
• Magnon Trap by Chiral Spin Pumping
• Imaginary couplings in non-Hermitian coupled-mode theory: Effects on exceptional points of optical resonators
• Generalized Swanson models and their solutions
• Complete Set of Inner Products for a Discrete PT-symmetric Square-well Hamiltonian
• Exactly solvable time-dependent pseudo-Hermitian $su$(1,1) Hamiltonian models
• Non-Hermitian interferometer: Unidirectional amplification without distortion
• The problem of coexistence of several non-Hermitian observables in PT-symmetric quantum mechanics
• On the 'toy model" in the Reggeon field theory
• Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation
• From Generalized Dirac Equations to a Candidate for Dark Energy
• Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
• Nonunique C operator in PT Quantum Mechanics
• C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians
• The Hilbert-Space Structure of Non-Hermitian Theories with Real Spectra
• PT-symmetric chiral metamaterials: Asymmetric effects and PT-phase control
• Entanglement, non-Hermiticity, and duality
• Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime
• The quantum brachistochrone problem for non-Hermitian Hamiltonians
• Null bootstrap for non-Hermitian Hamiltonians
• Stable States with Non-Zero Entropy under Broken $\mathcal{P}\mathcal{T}$-Symmetry
• On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators
• Numerical calculation of the complex berry phase in non-Hermitian systems
• $J$-self-adjoint operators with $\mathcal{C}$-symmetries: extension theory approach
• Probability Density in the Complex Plane
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Acoustic Multifunctional Logic Gates and Amplifier based on Passive Parity-Time Symmetry
• The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics
• Tight-binding lattices with an oscillating imaginary gauge field
• Optical Reciprocity Induced Symmetry of the Scattering Eigenstates in Non-$\mathcal{P}\mathcal{T}$-Symmetric Heterostructures
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Kelvin-Helmholtz instability is the result of parity-time symmetry breaking
• Pseudo-Hermitian approach to energy-dependent Klein-Gordon models
• Quantum dynamics on a lossy non-Hermitian lattice
• From PT-symmetric quantum mechanics to conformal field theory
• Non-inertial quantum clock frames lead to non-Hermitian dynamics
• Transport properties in a Non-Hermitian triple-quantum-dot structure
• $\mathcal{P}\mathcal{T}$ symmetry breaking in waveguide arrays with competing loss/gain pairs
• An analysis of the zero energy states in graphene
• Computing Spectra -- On the Solvability Complexity Index Hierarchy and Towers of Algorithms
• Non-Hermitian Hamiltonians with a Real Spectrum and Their Physical Applications
• Generation of Bell, W and GHZ states via exceptional points in non-Hermitian quantum spin systems
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Maximal quantum entanglement at exceptional points via unitary and thermal dynamics
• PT-Symmetric Quantum Theory Defined in a Krein Space
• Information retrieval and eigenstates coalescence in a non-Hermitian quantum system with anti-$\mathcal{P}\mathcal{T}$ symmetry
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation
• PT-symmetric deformations of Calogero models
• Experiments in PT-symmetric quantum mechanics
• Simple harmonic oscillation in non-Hermitian SSH chain at exceptional point
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry
• Linking scalar elastodynamics and non-Hermitian quantum mechanics
• Matching method and exact solvability of discrete PT-symmetric square wells
• Lattice gluodynamics at negative g^2
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• Pseudo-Hermitian Quantum Dynamics of Tachyonic Spin-1/2 Particles
• Stationary modes and integrals of motion in nonlinear lattices with PT-symmetric linear part
• Scattering properties of PT-symmetric objects
• Interplay between Fano resonance and $\mathcal{P}\mathcal{T}$ symmetry in non-Hermitian discrete systems
• Shape-preserving beam transmission through non-Hermitian disordered lattices
• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians
• Bragg-induced power oscillations in PT symmetric periodic photonic structures
• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
• Wireless Real-Time Capacitance Readout Based on Perturbed Nonlinear Parity-Time Symmetry
• Light neutrino masses from a non-Hermitian Yukawa theory
• Scattering-free pulse propagation through invisible non-Hermitian disorder
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Experimental observation of the Yang-Lee quantum criticality in open systems
• Coupled states of electromagnetic fields with magnetic-dipolar-mode vortices: MDM-vortex polaritons
• Interactions of bright and dark solitons with localized $\mathcal{P}\mathcal{T}$-symmetric potentials
• Magnified imaging based on non-Hermitian nonlocal cylindrical metasurfaces
• Non-linear dynamics of the non-Hermitian Su-Schrieffer-Heeger model
• $\mathcal{P}\mathcal{T}$-Symmetric Coherent Perfect Absorber with Graphene
• General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
• Bulk vortices and half-vortex surface modes in parity-time-symmetric media
• Controlling decoherence via $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian open quantum systems
• Anomalous Parity-Time Symmetry Transition away from an Exceptional Point
• Weak Ergodicity Breaking in Non-Hermitian Many-body Systems
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Non-Hermitian quantum mechanics in non-commutative space
• Long-range entangled zero-mode state in a non-Hermitian lattice
• Statistical mechanics for non-Hermitian quantum systems
• Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
• Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers
• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• Third order spectral branch points in Krein space related setups: PT-symmetric matrix toy model, MHD alpha^2-dynamo, and extended Squire equation
• Pseudo supersymmetric partners for the generalized Swanson model
• Spiked potentials and quantum toboggans
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Photonic quantum simulations of coupled $PT$-symmetric Hamiltonians
• Quantum parameter estimation of non-Hermitian systems with optimal measurements
• Realization of complex conjugate media using non-PT-symmetric photonic crystals
• Chebyshev-polynomial expansion of the localization length of Hermitian and non-Hermitian random chains
• Solitary waves in Parity-time (PT) symmetric Bragg-grating structure and the existence of Optical Rogue Waves
• Geometric phase and phase diagram for non-Hermitian quantum XY model
• Real spectra for non-Hermitian Dirac equation in 1+1 dimensions with a most general coupling
• Kurt Symanzik - a stable fixed point beyond triviality
• CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions
• Eigenvalue dynamics in the presence of non-uniform gain and loss
• Super-exponential diffusion in nonlinear non-Hermitian systems
• An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples
• Quantum toboggans
• Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians
• Non-Hermiticity-Induced Wave Confinement and Guiding in Loss-Gain-Loss Three-Layer Systems
• Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems
• Level density and level-spacing distributions of random, self-adjoint, non-Hermitian matrices
• Localized modes in dissipative lattice media: An overview
• Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries
• Magnon dynamics in parity-time-symmetric dipolarly coupled waveguides and magnonic crystals
• Conserved quantities, exceptional points, and antilinear symmetries in non-Hermitian systems
• Scattering of partially coherent radiation by non-Hermitian localized structures having Parity-Time symmetry
• Mapping between Hamiltonians with attractive and repulsive potentials on a lattice
• On the Role of the Normalization Factors ${\kappa }_n$ and of the Pseudo-Metric $\mathcal{P}\ne {\mathcal{P}}^{†}$ in Crypto-Hermitian Quantum Models
• Pseudo-Hermitian random matrix theory
• Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians
• Charge Conjugation Invariance of the Vacuum and the Cosmological Constant Problem
• Generalised quantum speed limit for arbitrary time-continuous evolution
• Systematic pathway to $\mathcal{P}\mathcal{T}$ symmetry breaking in scattering systems
• PT-symmetric optical superlattices
• Exact Isospectral Pairs of PT-Symmetric Hamiltonians
• Classical Particle in a Complex Elliptic Potential
• Dynamics of finite dimensional non-hermitian systems with indefinite metric
• Does the complex deformation of the Riemann equation exhibit shocks?
• Repeatability of measurements: Equivalence of hermitian and non-hermitian observables
• Quantum simulation of a general anti-PT-symmetric Hamiltonian with a trapped ion qubit
• PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
• Floquet exceptional contours in Lindblad dynamics with time-periodic drive and dissipation
• Exactly solvable models with PT-symmetry and with an asymmetric coupling of channels
• Exceptional point induced lasing dynamics in a non-Hermitian system
• Alternative descriptions and bipartite compound quantum systems
• Uncertainty Relation for Non-Hermitian Systems
• Analytically solvable $2\times 2$ $PT$-symmetry dynamics from su(1,1)-symmetry problems
• Bicomplex Hamiltonian systems in Quantum Mechanics
• Scattering theory for stationary materials with $\mathcal{P}\mathcal{T}$ symmetry
• Nonlinear anti-directional couplers with gain and loss
• Chern number in Ising models with spatially modulated real and complex fields
• Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution
• Flow of time during energy measurements and the resulting time-energy uncertainty relations
• Nonlinear wave dynamics near phase transition in $\mathcal{P}\mathcal{T}$-symmetric localized potentials
• Many-body Non-Hermitian Skin Effect At Finite Temperatures
• Structure, Time Propagation and Dissipative Terms for Resonances
• On-demand Parity-Time symmetry in a lone oscillator through complex, synthetic gauge fields
• Irreducible second order SUSY transformations between real and complex potentials
• PT symmetry in relativistic quantum mechanics
• Nonlinear parity-time-symmetric transition in finite-size optical couplers
• Acceleration toward polarization singularity inspired by relativistic ExB drift
• Complex Adiabatic Connection: a Hidden Non-Hermitian Path from Ground to Excited States
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Ising chain with topological degeneracy induced by dissipation
• Complex Path Integrals and the Space of Theories
• 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
• Scrambling and operator entanglement in local non-Hermitian quantum systems
• Parity-time-symmetric closed form optical quadrimer waveguides
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Smooth Singularities Exposed: Chimeras of the Differential Spacetime Manifold
• Random matrix ensembles for $PT$-symmetric systems
• Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction
• The Gram Matrix of a PT-symmetric Quantum System
• Conformal bridge transformation and PT symmetry
• Competing PT potentials and re-entrant PT symmetric phase for a particle in a box
• PT-symmetric quantum graphs
• Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces
• Quasinormal mode analysis of chiral power flow from linearly polarized dipole emitters coupled to index-modulated microring resonators close to an exceptional point
• Shadow-free multimers as extreme-performance meta-atoms
• Coherent perfect absorption and laser modes in a cylindrical structure of conjugate metamaterials
• PT-symmetric supersymmetry in a solvable short-range model
• Complex Solitary Waves and Soliton Trains in KdV and mKdV Equations
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials
• Non-Hermitian spectral changes in the scattering of partially coherent radiation by periodic structures
• Hermitian Hamiltonian equivalent to a given non-Hermitian one. Manifestation of spectral singularity
• Quantum inner-product metrics via recurrent solution of Dieudonne equation
• Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
• Dual oscillators and Quantum Pendulums: spectrum and correlators
• Detecting topological exceptional points in a parity-time symmetric system with cold atoms
• Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
• Thermodynamics of Pseudo-Hermitian Systems in Equilibrium
• Entanglement in Non-Hermitian Quantum Theory
• Analysis of unidirectional non-paraxial invisibility of purely reflective PT-symmetric volume gratings
• Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system
• PT phase transition in multidimensional quantum systems
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation
• Finite-temperature quantum criticality in a complex-parameter plane
• PT-supersymmetric partner of a short-range square well
• Quantum transport in non-Hermitian impurity array
• Balanced gain and loss in Bose-Einstein condensates without PT symmetry
• Spontaneous and explicit parity-time-symmetry breaking in drift wave instabilities
• Accessible phases via wave impedance engineering with PT-symmetric metamaterials
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• Algebraic maximum violation of the Leggett-Garg inequality in a two-level system under PT symmetric dynamics
• Chaotic diffusion of complex trajectory and its quantum signature
• Optical Modes in PT-Symmetric Double-Channel Waveguides
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• Investigation of PT-symmetric Hamiltonian systems from an alternative point of view
• The MHD alpha^2-dynamo, Z_2-graded pseudo-Hermiticity, level crossings and exceptional points of branching type
• Determination of the domain of the admissible matrix elements in the four-dimensional PT-symmetric anharmonic model
• Compact Localized States in Engineered Flat-Band $\mathcal{P}\mathcal{T}$ Metamaterials
• Stability and collisions of quantum droplets in PT -symmetric dual-core couplers
• Resonant generation of $p$-wave Cooper pair in non-Hermitian Kitaev chain at exceptional point
• Real-Time Transport in Open Quantum Systems From $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States
• Dynamical evolutions in non-Hermitian triple-well system with complex potential
• Coherent states of non-Hermitian quantum systems
• Emerging exceptional point with breakdown of skin effect in non-Hermitian systems
• PT-symmetry breaking with divergent potentials: lattice and continuum cases
• Random cyclic matrices
• Many-body phase transitions in a non-Hermitian Ising chain
• Approximate Dirac solutions of complex -symmetric Pöschl-Teller potential in view of spin and pseudospin symmetries
• General theory of regular biorthogonal pairs and its physical applications
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Strengthened PT-symmetry with P $\ne$ P${}^{†}$
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• IR/UV mixing from local similarity maps of scalar non-Hermitian field theories
• Phase space representation of non-Hermitian system with $\mathcal{P}\mathcal{T}$-symmetry
• PT-symmetric regularizations in supersymmetric quantum mechanics
• Physics of PT-Symmetric Quantum Systems at Finite Temperature
• Complete particle-pair annihilation as a dynamical signature of the spectral singularity
• Conserved Correlation in PT -symmetric Systems: Scattering and Bound States
• Gauging non-Hermitian Hamiltonians
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Parity-time symmetry under magnetic flux
• Connecting active and passive $\mathcal{P}\mathcal{T}$-symmetric Floquet modulation models
• Quantum deleting and cloning in a pseudo-unitary system
• On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)
• Transport and localization of waves in ladder-shaped lattices with locally $\mathcal{P}\mathcal{T}$-symmetric potentials
• Observing a Changing Hilbert-Space Inner Product
• Linear representation of energy-dependent Hamiltonians
• Quantum Big Bang without fine-tuning in a toy-model
• One-Way Optical Transition based on Causality in Momentum Space
• CPT-Frames for PT-symmetric Hamiltonians
• Are observables necessarily Hermitian?
• Enhancing the sensitivity of nonlinearity sensors through homodyne detection in dissipatively coupled systems
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity
• Phantom without phantom or how the PT symmetry saves us from the Big Rip
• Quasinormal modes and self-adjoint extensions of the Schroedinger operator
• Entangled Quantum State Discrimination using Pseudo-Hermitian System
• Bistable soliton switching dynamics in a $\mathcal{P}\mathcal{T}$-symmetric coupler with saturable nonlinearity
• Stationary states in the many-particle description of Bose-Einstein condensates with balanced gain and loss
• No-signaling principle and Bell inequality in PT-symmetric quantum mechanics
• Resonant interaction of ${\varphi }^4$ kink with spatially periodic $\mathcal{P}\mathcal{T}$-symmetric perturbation
• Pseudo-reality and pseudo-adjointness of Hamiltonians
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group Theory
• Extending PT symmetry from Heisenberg algebra to E2 algebra
• Quadratic pseudosupersymmetry in two-level systems
• On the K-theoretic classification of dynamically stable systems
• Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations
• N-site-lattice analogues of $V(x)=i{x}^3$
• Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
• Effective non-Hermitian physics for degenerate ground states of a nonHermitian Ising model with $\mathcal{R}\mathcal{T}$ symmetry
• A possible method for non-Hermitian and non-$PT$-symmetric Hamiltonian systems
• Identification of observables in quantum toboggans
• Constructing the scattering matrix for optical microcavities as a nonlocal boundary value problem
• Piecewise Adiabatic Following: General Analysis and Exactly Solvable Models
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Theory and Numerical Modelling of Parity-Time Symmetric Structures in Photonics: Introduction and Grating Structures in One Dimension
• Spontaneous breaking of permutation symmetry in pseudo-Hermitian quantum mechanics
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
• Generalized gauge transformation with $PT$-symmetric non-unitary operator and classical correspondence of non-Hermitian Hamiltonian for a periodically driven system
• A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators
• The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry
• A Perturbative Treatment Of A Generalized PT-Symmetric Quartic Anharmonic Oscillator
• Extended Jaynes-Cummings models and (quasi)-exact solvability
• Dynamical control of solitons in a parity-time-symmetric coupler by periodic management
• Parity-Time Symmetry Breaking beyond One Dimension: The Role of Degeneracy
• WKB Analysis of PT-Symmetric Sturm-Liouville problems. II
• Simulating non-Hermitian dynamics of a multi-spin quantum system and an emergent central spin model
• $\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry
• Nonlinear Parity-Time (PT) symmetric closed-form optical quadrimer waveguides: Attractor perspective
• Negative-energy PT-symmetric Hamiltonians
• On elements of the Lax-Phillips scattering scheme for PT-symmetric operators
• Hybridization of topological surface states with a flat band
• Gain assisted controllable fast light generation in cavity magnomechanics
• Comprehensive understanding of parity-time transitions in $\mathcal{P}\mathcal{T}$ symmetric photonic crystals with an antiunitary group theory
• On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators
• Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Non-adiabatic transitions in a non-symmetric optical lattice
• On the Physics of the Minimal Length: The Question of Gauge Invariance
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• Temporal correlation beyond quantum bounds in non-hermitian dynamics
• Coherent population oscillations and an effective spin-exchange interaction in a $\mathcal{P}\mathcal{T}$ symmetric polariton mixture
• Bounded dynamics of finite PT-symmetric magnetoinductive arrays
• PT-Symmetric Quantum Electrodynamics and Unitarity
• Anomalous second-order skin modes in Floquet non-Hermitian systems
• Modulational instability in $\mathcal{P}\mathcal{T}$-symmetric Bragg grating structures with saturable nonlinearity
• Quantum mold casting for topological insulating and edge states
• Fate of non-Hermitian free fermions with Wannier-Stark ladder
• Small-$\epsilon$ behavior of the Non-Hermitian PT-Symmetric Hamiltonian $H=p^2+x^2(ix{)}^{\epsilon }$
• Renormalisation group flows connecting a $4-\epsilon$ dimensional Hermitian field theory to a $\mathcal{P}\mathcal{T}$-symmetric theory for a fermion coupled to an axion
• Effects of non-uniform distributions of gain and loss in photonic crystals
• What is the resonant state in open quantum systems?
• Symmetry properties of non-Hermitian PT-symmetric quantum field theories
• $\mathcal{P}\mathcal{T}$-Symmetry in Hartree-Fock Theory
• Non-Markovian anti-parity-time symmetric systems: theory and experiment
• Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems
• Spin Josephson effects of spin-orbit-coupled Bose-Einstein condensates in a non-Hermitian double well
• A Novel SUSY Energy Bound States Treatment of the Klein-Gordon Equation with PT-Supersymmetric and q-Deformed Hulthen Potential
• Real energies and Berry phases in all PT-regimes in time-dependent non-Hermitian theories
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems
• Parity-time symmetric systems with memory
• Metric operators for non-Hermitian quadratic su(2) Hamiltonians
• Semiclassical analysis of a complex quartic Hamiltonian
• Tachyonic Field Theory and Neutrino Mass Running
• Exact quantization conditions and full transseries structures for $\mathcal{P}\mathcal{T}$ symmetric anharmonic oscillators
• Origin of branch points in the spectrum of PT-symmetric periodic potentials
• PT-symmetric quantum systems with positive P
• Emergence of Exceptional Points in Periodic Metastructures with Hidden PT-symmetric Defects
• Effects of the third-order dispersion on continuous waves in complex potentials
• $\mathcal{P}\mathcal{T}$ symmetry of a square-wave modulated two-level system
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Nonuniqueness of the C operator in PT-symmetric quantum mechanics
• PT-Symmetry Breaking Transitions in Polymeric Systems
• PT-symmetric gain and loss in a rotating Bose-Einstein condensate
• On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm
• Aspects of the ODE/IM correspondence
• General PT-Symmetric Matrices
• Green Functions for the Wrong-Sign Quartic
• Equivalent Hamiltonian for Lee Model
• Controlled self-similar matter waves in PT-symmetric waveguide
• Accelerating multipartite entanglement generation in non-Hermitian superconducting qubits
• Non-Hermitian description of the dynamics of inter-chain pair tunnelling
• Self-organized PT-symmetry of exciton-polariton condensate in a double-well potential
• Non-Hermiticity in quantum nonlinear optics through symplectic transformations
• Pseudo-conservative dynamics of coupled polariton condensates
• Scattering of the asymmetric ${\varphi }^6$ kinks from a $\mathcal{P}\mathcal{T}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons
• Lower bound of minimal time evolution in quantum mechanics
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
• Recursive Calculation of Effective Potential and Variational Resummation
• Wannier-Stark localization in one-dimensional amplitude-chirped lattices
• Parity-time-symmetric coupled microring lasers operating around an exceptional point
• Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks
• Non-Hermitian Numerical Renormalization Group: Solution of the non-Hermitian Kondo model
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• An Algebraic PT-Symmetric Quantum Theory with a Maximal Mass
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Supersymmetric Analysis of the Dirac-Weyl Operator within PT Symmetry
• Equivalence and Hermiticity of Dirac Hamiltonians in the Kerr gravitational field
• Parsing skin effect in a non-Hermitian spinless BHZ-like model
• Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• PT Symmetry and Hermithean Hamiltonian in the Local Supercritical Pomeron Model
• Asymptotic Behavior of the \Beta Function in the Φ^4 Theory: A Scheme Without Complex Parameters
• Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_1\otimes d_2$ Dimensional System
• Non-Hermitian fermions with effective mass
• Dynamical evolution of an effective two-level system with PT symmetry
• PT symmetric lattices with a local degree of freedom
• Topological phase in Kitaev chain with spatially separated pairing processes
• Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model
• Rigged Hilbert Space Approach for Non-Hermite Systems with Positive Definite Metric
• Generalized Nonanalytic Expansions, PT-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators
• Universal spectral behavior of $x^2(ix{)}^{\epsilon }$ potentials
• Theory Including Future Not Excluded -- Formulation of Complex Action Theory II --
• Two-way enhancement of sensitivity by tailoring higher-order exceptional points
• Towards non-Hermitian quantum statistical thermodynamics
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• Generalized continuity equations from two-field Schrödinger Lagrangians
• Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices
• Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase
• Controlling properties of a hybrid Cooper pair box interacting with a nanomechanical resonator in the presence of Kerr nonlinearities and losses
• An introductory review on resource theories of generalized nonclassical light
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
• Fractionality and $\mathcal{P}\mathcal{T}$- symmetry in a square lattice
• Non self-adjoint operators with real spectra and extensions of quantum mechanics
• A PT-symmetric dual-core system with the sine-Gordon nonlinearity and derivative coupling
• On J-Self-Adjoint Operators with Stable C-Symmetry
• A controllable anti-P-pseudo-Hermitian mechanical system and its application
• Instantaneous modulations in time-varying complex optical potentials
• Universal scaling at a pre-thermal dark state
• Non-Hermiticity: a new paradigm for model building in particle physics
• Parity-Time Symmetry and Exceptional points: A Tutorial
• Essential implications of similarities in non-Hermitian systems
• Bohmian trajectories for Kerr-Newman particles in complex space-time
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• Complex Langevin Dynamics and Supersymmetric Quantum Mechanics
• Quantum knots
• Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip
• An ansatz for the eigenstates in PT-symmetric quantum mechanics
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Pseudo-Hermiticity, PT-symmetry, and the Metric Operator
• Locality, Correlations, Information, and non-Hermitian Quantum Systems
• Recognizing critical lines via entanglement in non-Hermitian systems
• Electrical tunability due to coalescence of exceptional points in parity-time symmetric waveguides
• Composite Quantum Phases in Non-Hermitian Systems
• Bound-states for generalized trigonometric and hyperbolic Pöschl-Teller potentials
• Dirac Hamiltonian with Imaginary Mass and Induced Helicity-Dependence by Indefinite Metric
• Quantum mechanical equivalence of the metrics of a centrally symmetric gravitational field
• Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
• Entanglement Efficiencies in PT-Symmetric Quantum Mechanics
• Conformal anomaly in non-hermitian quantum mechanics
• Demonstration of a two-dimensional PT-symmetric crystal: Bulk dynamics, topology, and edge states
• Double-sided unidirectional reflectivity
• Superoscillatory PT-symmetric potentials
• Infinite-dimensional representations of the rotation group and Dirac's monopole problem
• PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring
• PT symmetry as a necessary and sufficient condition for unitary time evolution
• Controllable non-Hermitian qubit-qubit Coupling in Superconducting quantum Circuit
• Imaginary spin-orbital coupling in parity-time symmetric systems with momentum-dependent gain and loss
• Hamiltonian and Linear-Space Structure for Damped Oscillators: II. Critical Points
• Cumulants of time-integrated observables of closed quantum systems and PT-symmetry, with an application to the quantum Ising chain
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Bicomplex Lucas and Horadam Numbers
• Quantum thermodynamics aspects with a thermal reservoir based on $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Stability boundaries of a Mathieu equation having PT symmetry
• Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics
• Local preservation of no-signaling in multiparty PT-symmetric evolutions
• Supersymmetry of $\mathcal{P}\mathcal{T}$- symmetric tridiagonal Hamiltonians
• A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian Quantum Mechanics : $\gamma$-deformed $su(2)$ generators, Partial $\mathcal{P}\mathcal{T}$-symmetry and Higgs algebra
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• Removal of instabilities of the higher derivative theories in the light of antilinearity
• Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator
• Treating Ostrogradski instability for Gallilean invariant Chern Simon's model via \mathcal{PT} symmetry
• Nonparaxial electromagnetic Bragg scattering in periodic media with PT symmetry
• Perpetual emulation threshold of PT-symmetric Hamiltonians
• Stability of time-periodic $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonians with different periodicities
• Making the PT symmetry unbreakable
• $\mathcal{P}\mathcal{T}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities
• Chiral-reversing vortex radiation from a single emitter by eigenstates phase locking
• Fractionality and PT-symmetry in an electrical transmission line
• Non-Hermitian tearing by dissipation
• PT symmetry and supersymmetry
• PT-symmetric transport in non-PT-symmetric bi-layer optical arrays
• Extended Wannier-Stark ladder and particle-pair Bloch oscillations in dimerized non-Hermitian systems
• The Lefschetz thimble and the sign problem
• Implementation and topological characterization of Weyl exceptional rings in quantum-mechanical systems
• Robustness of entanglement in a non-Hermitian cavity-optomechanical system even away from exceptional points
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Factorized Hilbert-space metrics and non-commutative quasi-Hermitian observables
• Three-Dimensional Shape Invariant Non-Separable Model With Equidistant Spectrum
• Asymmetric optical amplifier based on parity-time symmetry
• A real expectation value of the time-dependent non-Hermitian Hamiltonians
• Conserved quantities in non-Hermitian systems via vectorization method
• Disorder effects in tunable waveguide arrays with parity-symmetric tunneling
• Bound states of PT-symmetric separable potentials
• Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity
• Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space
• Metric Operator For The Non-Hermitian Hamiltonian Model and Pseudo-Supersymmetry
• Comment on ``New ansatz for metric operator calculation in pseudo-Hermitian field theory''
• CPT-symmetric discrete square well
• Some spectral equivalences between Schrodinger operators
• Gaussian-random Ensembles of Pseudo-Hermitian Matrices
• PT-Symmetric Quantum Field Theory
• Geometry of PT-symmetric quantum mechanics
• PT-symmetric and antisymmetric nonlinear states in a split potential box
• Interplay of fractionality and $\mathcal{P}\mathcal{T}$- symmetry on a 1D lattice
• Instanton calculus without equations of motion: semiclassics from monodromies of a Riemann surface
• PT-/non-PT-Symmetric and non-Hermitian Hellmann Potential: Approximate Bound and Scattering States with Any $\ell$-Values
• Understanding Partial PT symmetry as weighted composition conjugation in Reproducing Kernel Hilbert Space :An application to non-hermitian Bose-Hubbard type Hamiltonian in Fock space
• $\mathcal{P}\mathcal{T}$-Symmetric Quantum Discrimination of Three States
• Negative Gilbert damping in cavity optomagnonics
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Lüders bounds of Leggett-Garg inequalities, $\mathcal{P}\mathcal{T}$- symmetric evolution and arrow-of-time
• Exceptional points in SSH-like models with hopping amplitude gradient
• Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics
• Physical Meaning of Hermiticity and Shortcomings of the Composite (Hermitian + non-Hermitian) Quantum Theory of Gunther and Samsonov
• Characterizing the Yang-Lee zeros of the classical Ising model through dynamic quantum phase transitions
• Monopoles in non-Hermitian systems
• Quantum counterpart of spontaneously broken classical PT symmetry
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• Quantum Instability
• Laser induced $\mathcal{P}\mathcal{T}$-symmetry breaking in the fluctuations of electronic fluids
• Witnessing criticality in non-Hermitian systems via entropic uncertainty relation
• Fall-to-the-centre as a $\mathcal{P}\mathcal{T}$ symmetry breaking transition
• Faster than Hermitian Time Evolution
• Closed timelike curves in PT-symmetric wormholes
• Mechanical cosmology: simulating scalar fluctuations in expanding Universes using synthetic mechanical lattices
• $\mathcal{P}\mathcal{T}$-symmetric mapping of three states and its implementation on a cloud quantum processor
• Parallel dynamics between non-Hermitian and Hermitian systems
• Exact solution for the time dependent non-Hermitian generalized Swanson oscillator
• Beam Dynamics in a Double-Channel Waveguide with Gain and Loss
• Bosonic Holes in Quadratic Bosonic Systems
• Stronger sum uncertainty relations for non-Hermitian operators
• Topology and $\mathcal{P}\mathcal{T}$ Symmetry in a Non-Hermitian Su-Schrieffer-Heeger Chain with Periodic Hopping Modulation
• Protecting coherence in the non-Hermitian two-level system
• Consistent treatment of quantum systems with a time-dependent Hilbert space
• On the non-relativistic limit of charge conjugation in QED
• The Unruh effect for higher derivative field theory
• PT-symmetry enabled stable modes in multi-core fiber
• A Hermitian bypass to the non-Hermitian quantum theory
• Field extension of real values of physical observables in classical theory can help attain quantum results
• Fixed lines in a non-Hermitian Kitaev chain with spatially balanced pairing processes
• Finding room for antilinear terms in the Hamiltonian
• Planarizable Supersymmetric Quantum Toboggans
• Enhancement of sensitivity near exceptional points in dissipative qubit-resonator systems
• Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Unitarization of Pseudo-Unitary Quantum Circuits in the S-matrix Framework
• Entanglement generation across exceptional points in two-qubit open quantum system -- the role of initial states
• Quasi-exactly solvable cases of the N-dimensional symmetric quartic anharmonic oscillator
• A non-trivial PT-symmetric continuum Hamiltonian and its Eigenstates and Eigenvalues
• Emulating exceptional-point encirclements using imperfect (leaky) photonic components
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Computation and Verification of Spectra for Non-Hermitian Systems
• An investigation of $\mathcal{P}\mathcal{T}$-symmetry breaking in tight-binding chains
• Entanglement of pseudo-Hermitian random states
• Fermionic model with a non-Hermitian Hamiltonian
• Soliton dynamics and stability in the ABS spinor model with a PT-symmetric periodic potential
• Geometric phase for Dirac Hamiltonian under gravitational fields in the non-relativistic regime
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• Nonlocality of Observables in Quasi-Hermitian Quantum Theory
• Observation of plasmonic exceptional points
• Time evolution and adiabatic approximation in $PT$-symmetric quantum mechanics
• Quantum violations of Lüders bound Leggett-Garg inequalities for quantum channel
• Pseudo-PT symmetric Dirac equation : effect of a new mean spin angular momentum operator on Gilbert damping
• Oscillators with imaginary coupling: spectral functions in quantum mechanics and quantum field theory
• On the $\mathcal{P}\mathcal{T}$-symmetric parametric amplifier
• Rabi oscillations at the exceptional point in anti-parity-time symmetric diffusive systems
• Eigenvalue and Eigenfunction for the $PT$-symmetric Potential $V=-(ix{)}^N$
• Free Particle to Complex KdV breathers through Isospectral Deformation
• PT-symmetric quantum models living in an auxiliary Pontryagin space
• Characteristic influence of exceptional points in quantum dynamics
• PT symmetry and the evolution speed in open quantum systems
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Shannon Entropy and Diffusion Coeffcient in Parity-Time Symmetric Quantum Walks
• Invisibility and PT Symmetry: A Simple Geometrical Viewpoint
• Effects of complex parameters on classical trajectories of Hamiltonian systems
• Can PT-Symmetric Quantum Mechanics be a Viable Alternative Quantum Theory?
• Vortex ring beams in nonlinear $\mathcal{P}\mathcal{T}$-symmetric systems
• Three-level Λ-type atomic systems with a Pseudo-Hermitian PT-symmetric Hamiltonian
• Mutual compatibility/incompatibility of quasi-Hermitian quantum observables
• On pseudo-Hermitian operators with generalized $\mathcal{C}$-symmetries
• The Klein-Gordon Equation of Generalized Hulthen Potential in Complex Quantum Mechanics
• Uncertainty Relation for Pseudo-Hermitian Quantum Systems
• The soliton nature of the super-Klein tunneling effect
• Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics
• Parity-Time Symmetric Spin-1/2 Richardson-Gaudin Models
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model
• $\mathcal{P}\mathcal{T}-$Symmetric Two-Level Open Quantum Systems: Information Theoretic Facets
• Emergence of Hermitian topology from non-Hermitian knots
• Quantum Quintom Cosmology
• A Weyl Creation Algebra Approach to the Riemann Hypothesis
• Discrete solitons dynamics in $\mathcal{P}\mathcal{T}$-symmetric oligomers with complex-valued couplings
• Hilbert space representation for quasi-Hermitian position-deformed Heisenberg algebra and Path integral formulation
• Localization with non-Hermitian off-diagonal disorder
• Complexity Issues in Computing Spectra, Pseudospectra and Resolvents
• Identification of the metric for diagonalizable (anti-)pseudo-Hermitian Hamilton operators represented by two-dimensional matrices
• Defect solitons in defective PT potentials with real part of dual-frequency lattices
• Computing eigenfunctions and eigenvalues of boundary value problems with the orthogonal spectral renormalization method
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system
• Unidirectional weak visibility in band gap and singular scattering in conduction band of one-dimensional parity-time symmetric photonic crystal
• Stability band structure for periodic states in periodic potentials
• Instantons and transseries of the Mathieu potential deformed by a $\mathcal{P}\mathcal{T}$-symmetry parameter
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry
• A mathematical formalism of non-Hermitian quantum mechanics and observable-geometric phases
• Investigation of the Effect of Quantum Measurement on Parity-Time Symmetry
• A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems
• Balancing gain and loss in symmetrised multi-well potentials
• Topology with broken parity-time symmetry
• Cryptohermitian Hamiltonians on graphs. II. Hermitizations
• Operator based approach to PT-symmetric problems on a wedge-shaped contour
• $\mathcal{P}\mathcal{T}$-Symmetric Quantum State Discrimination for Attack on BB84 Quantum Key Distribution