Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
From MaRDI portal
Publication:4492556
DOI10.1103/PhysRevLett.80.5243zbMath0947.81018arXivphysics/9712001WikidataQ56212699 ScholiaQ56212699MaRDI QIDQ4492556
Stefan Boettcher, Carl M. Bender
Publication date: 16 July 2000
Published in: Physical Review Letters (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/physics/9712001
Related Items
Non-Hermitian Hamiltonians and similarity transformations ⋮ The emergence of eigenvalues of a \(\mathcal{PT}\)-symmetric operator in a thin strip ⋮ \(\mathcal{RT}\)-symmetric Laplace operators on star graphs: real spectrum and self-adjointness ⋮ Information geometry of complex Hamiltonians and exceptional points ⋮ \(N\)-soliton solution for an integrable nonlocal discrete focusing nonlinear Schrödinger equation ⋮ Spatiotemporal localized modes in \(\mathcal{PT}\)-symmetric optical media ⋮ Complete particle-pair annihilation as a dynamical signature of the spectral singularity ⋮ Complex oscillator and Painlevé IV equation ⋮ Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system ⋮ Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system ⋮ Equation of motion and general solution for the one-dimensional complex cell response in the signal-tuned approach ⋮ Nonlocal general vector nonlinear Schrödinger equations: integrability, \(\mathcal{PT}\) symmetribility, and solutions ⋮ Darboux transformation and analytic solutions of the discrete \(\mathcal{PT}\)-symmetric nonlocal nonlinear Schrödinger equation ⋮ Dynamics of generalized PT-symmetric dimers with time-periodic gain-loss ⋮ Spatiotemporal soliton structures in \((3+1)\)-dimensional \(\mathcal{PT}\)-symmetric nonlinear couplers with gain and loss ⋮ Control and management of the combined Peregrine soliton and Akhmediev breathers in \({\mathcal{PT}}\)-symmetric coupled waveguides ⋮ Transparency of the complex PT-symmetric potentials for coherent injection ⋮ An analysis of the zero energy states in graphene ⋮ Spatiotemporal localized solitons in cubic and power-law competing nonlinear media with different diffractions and \(\mathcal {PT}\)-symmetric potentials ⋮ Supersymmetric quantum mechanics and solvable models ⋮ Pseudo Hermitian interactions in the Dirac equation ⋮ Probability density in the complex plane ⋮ Convergent quantum normal forms, \(\mathcal PT\)-symmetry and reality of the spectrum ⋮ Y-system and deformed thermodynamic Bethe Ansatz ⋮ \textit{PT} phase transition in higher-dimensional quantum systems ⋮ On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities ⋮ Eigenvalue problems for the complex PT-symmetric potential \(V(x)=igx\) ⋮ Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems ⋮ \(N\)-site-lattice analogues of \(V(x) = \text ix^3\) ⋮ Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters ⋮ A note on the \(\mathcal PT\) invariant periodic potential \(V(x) = 4\cos^2x + 4iV_0\sin2x\) ⋮ Minimum uncertainty wavelets in non-relativistic super-symmetric quantum mechanics ⋮ Comment on `Supersymmetry, PT-symmetry and spectral bifurcation' ⋮ A non-Hermitian circular billiard ⋮ Eigensystem of an \(L ^{2}\)-perturbed harmonic oscillator is an unconditional basis ⋮ On the Dirac equation with PT-symmetric potentials in the presence of position-dependent mass ⋮ Self-isospectral tri-supersymmetry in \(\mathcal P \mathcal T\)-symmetric quantum systems with pure imaginary periodicity ⋮ Quantum knots ⋮ Anharmonic oscillators in the complex plane, \(\mathcal{PT}\)-symmetry, and real eigenvalues ⋮ A generalized non-Hermitian oscillator Hamiltonian, \(\mathcal N\)-fold supersymmetry and position-dependent mass models ⋮ Entanglement efficiencies in \(\mathcal{PT}\)-symmetric quantum mechanics ⋮ On the normalization constant of \(PT\)-symmetric and real Rosen-Morse I potentials ⋮ \(\mathcal P\mathcal T\)-symmetric quantum electrodynamics ⋮ Universal properties of conformal quantum many-body systems ⋮ Three solvable matrix models of a quantum catastrophe ⋮ Vacuum stability of the wrong sign \((-\phi^6)\) scalar field theory ⋮ Asymptotically vanishing -symmetric potentials and negative-mass Schrödinger equations ⋮ Classical oscillator with position-dependent mass in a complex domain ⋮ Non-Hermitian non-PT-symmetric Dirac Hamiltonians with real energy eigenvalues ⋮ Spectral projections of the complex cubic oscillator ⋮ The optical properties of two-dimensional Scarff parity-time symmetric potentials ⋮ An existence criterion for the \(\mathcal{PT}\)-symmetric phase transition ⋮ Nonunique \(C\) operator \(PT\) in quantum mechanics ⋮ Which Green functions does the path integral for quasi-Hermitian Hamiltonians represent? ⋮ Real spectra for the non-Hermitian Dirac equation in 1+1 dimensions with the most general coupling ⋮ Nonlinear symmetries of perfectly invisible \textit{PT}-regularized conformal and superconformal mechanics systems ⋮ TBA equations and resurgent quantum mechanics ⋮ Algebraic methods for least squares problem in split quaternionic mechanics ⋮ Unidirectional reflectionlessness in a non-Hermitian quantum system of surface plasmon coupled to two plasmonic cavities ⋮ Integrable \(\mathcal{PT}\)-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model ⋮ Bright solitons in a \(\mathcal{P} \mathcal{T}\)-symmetric chain of dimers ⋮ \(\mathcal{PT}\) symmetric nonlinear optical lattice: analytical solutions ⋮ On the quantisation of complex higher derivative theories and avoiding the Ostrogradsky ghost ⋮ Adiabatic approximation for the evolution generated by an \(A\)-uniformly pseudo-Hermitian Hamiltonian ⋮ Two generalized Wigner-Yanase skew information and their uncertainty relations ⋮ Path integral for an effective two level atom in a Kerr-like medium and Stark shift with a pseudo Hermitian Hamiltonian ⋮ The Coulomb potential and the paradoxes of PT symmetrization ⋮ Investigation of non-Hermitian Hamiltonians in the Heisenberg picture ⋮ Phase transitions in Wick-rotated~ \(\mathcal{PT}\)-symmetric optics ⋮ Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions ⋮ PT phase transition in a \((2+1)\)-d relativistic system ⋮ Scattering by infinitely rising one-dimensional potentials ⋮ Three PT-symmetric Hamiltonians with completely different spectra ⋮ Bound states in the continuum generated by supersymmetric quantum mechanics and phase rigidity of the corresponding wavefunctions ⋮ The crypto-Hermitian smeared-coordinate representation of wave functions ⋮ Deconstructing non-dissipative non-Dirac-Hermitian relativistic quantum systems ⋮ Nonlinear localized modes in \(\mathcal{PT}\)-symmetric optical media with competing gain and loss ⋮ Decays of degeneracies in \(\mathcal PT\)-symmetric ring-shaped lattices ⋮ Non-Hermitian Hamiltonians with unitary and antiunitary symmetries ⋮ Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra ⋮ Extending \(\mathcal{P}\mathcal{T}\) symmetry from Heisenberg algebra to E2 Algebra ⋮ Green functions for the wrong-sign quartic ⋮ \(\mathcal{PT}\) invariant complex \(E_{8}\) root spaces ⋮ Path integrals for pseudo-Hermitian Hamiltonians ⋮ \(\mathcal{CPT}\)-symmetric discrete square well ⋮ \(\mathcal{PT}\)-symmetry in (generalized) effect algebras ⋮ Asymptotic properties of solvable \({\mathcal{PT}}\)-symmetric potentials ⋮ On Bell-like inequalities and pseudo-Hermitian operators ⋮ \({\mathcal{PT}}\) symmetry vs. hermiticity ⋮ Constructing exactly solvable pseudo-Hermitian many-particle quantum systems by isospectral deformation ⋮ Spectrum of the metric operator of a simple \(\mathcal{PT}\)-symmetric model ⋮ \({\mathcal{PT}}\)-symmetric periodic optical potentials ⋮ \({\mathcal{PT}}\) symmetry in statistical mechanics and the sign problem ⋮ Cryptohermitian Hamiltonians on graphs. II: Hermitizations ⋮ Two-point Green's function in PT-symmetric theories ⋮ Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration ⋮ Quantum toboggans with two branch points ⋮ Overcritical \(\mathcal PT\)-symmetric square well potential in the Dirac equation ⋮ Multi-instantons and exact results. IV: Path integral formalism ⋮ Truncations of a class of pseudo-Hermitian tridiagonal matrices ⋮ Superconducting metamaterials ⋮ Finite-dimensional pseudo-bosons: a non-Hermitian version of the truncated harmonic oscillator ⋮ Embedding, simulation and consistency of \(\mathcal{PT}\)-symmetric quantum theory ⋮ Hermitian-non-Hermitian interfaces in quantum theory ⋮ Two-dimensional solitons in cubic-saturable media with \(\mathcal{PT}\)-symmetric lattices ⋮ Regularized degenerate multi-solitons ⋮ Photonic scattering on a trimer with \(PT\)-symmetry ⋮ Rational solutions for the nonlocal sixth-order nonlinear Schrödinger equation ⋮ Two patterns of \(\mathcal{PT}\)-symmetry breakdown in a non-numerical six-state simulation ⋮ Families of rational solutions of the \(y\)-nonlocal Davey-Stewartson II equation ⋮ Breather, lump and \(X\) soliton solutions to nonlocal KP equation ⋮ Observables, disassembled ⋮ Dirichlet spectra of the paradigm model of complex PT-symmetric potential: \(V(x)=-(ix)^N\) ⋮ Solitons in \(\mathcal{PT}\)-symmetric SRR dimers chain with alternating electric and magnetic coupling ⋮ Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility ⋮ Stable solitons in the 1D and 2D generalized nonlinear Schrödinger equations with the periodic effective mass and \(\mathcal{PT}\)-symmetric potentials ⋮ Asymmetric optical mode conversion and transmission by breaking PT-symmetry on silicon photonic circuits ⋮ On the theory of \(\mathcal{PT}\)-symmetric operators ⋮ Modulational instability in a \(P T\)-symmetric vector nonlinear Schrödinger system ⋮ Mending the broken PT-regime via an explicit time-dependent Dyson map ⋮ One- and two-dimensional bright solitons in inhomogeneous defocusing nonlinearities with an antisymmetric periodic gain and loss ⋮ Butterfly-shaped and dromion-like optical waves in a tapered graded-index waveguide with variable group-velocity dispersion ⋮ Enhancing parameter estimation precision by non-Hermitian operator process ⋮ Are observables necessarily Hermitian? ⋮ Quantum entropy of non-Hermitian entangled systems ⋮ \({\mathcal PT}\)-symmetry, indefinite damping and dissipation-induced instabilities ⋮ \( \mathcal{P}\mathcal{T} \) deformation of angular Calogero models ⋮ Eigenvalue dynamics of a \(\mathcal{PT}\)-symmetric Sturm-Liouville operator and criteria for similarity to a self-adjoint or a normal operator ⋮ Perfectly invisible \( \mathcal{P}\mathcal{T} \)-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry ⋮ \(PT\) symmetry, conformal symmetry, and the metrication of electromagnetism ⋮ A simple approach towards the sign problem using path optimisation ⋮ Nonlocal reductions of the Ablowitz-Ladik equation ⋮ Nonlocal reductions of the multicomponent nonlinear Schrödinger equation on symmetric spaces ⋮ Schrödinger operators with complex potential but real spectrum ⋮ Extended two-parameter squeezed states ⋮ Variational ansatz for PT-symmetric quantum mechanics ⋮ Negative-energy levels of the Dirac equation in \(N\) dimensions ⋮ Algebraic techniques for Schrödinger equations in split quaternionic mechanics ⋮ Rational and semi-rational solutions of the \(y\)-nonlocal Davey-Stewartson I equation ⋮ Complex periodic potentials with real band spectra. ⋮ Darboux transformation and explicit solutions for \(2 + 1\)-dimensional nonlocal Schrödinger equation ⋮ Conventional Bell basis in \textit{PT}-symmetric quantum theory ⋮ Uncertainty relations with the generalized Wigner-Yanase-Dyson skew information ⋮ Enhancing and protecting quantum correlations of a two-qubit entangled system via non-Hermitian operation ⋮ Riemann-Hilbert problems and soliton solutions of nonlocal real reverse-spacetime mKdV equations ⋮ Stability band structure for periodic states in periodic potentials ⋮ Two \((2+1)\)-dimensional integrable nonlocal nonlinear Schrödinger equations: breather, rational and semi-rational solutions ⋮ Implications of losing hermiticity in quantum mechanics ⋮ Dynamics of PT-asymmetric multi-peak solitons with complex potentials ⋮ On a nonlocal modified Korteweg-de Vries equation: integrability, Darboux transformation and soliton solutions ⋮ Localized modes of the (n+1)-dimensional Schrödinger equation with power-law nonlinearities in \(\mathcal{PT}\)-symmetric potentials ⋮ Solitons and dynamics for a general integrable nonlocal coupled nonlinear Schrödinger equation ⋮ Pseudo \(\mathcal{PT}\)-symmetry in time periodic non-Hermitian Hamiltonians systems ⋮ The fractional dimensional spatiotemporal accessible solitons supported by PT-symmetric complex potential ⋮ Search of exact invariants for \(\mathcal{PT}\) and non-\(\mathcal{PT}\)-symmetric complex Hamiltonian systems ⋮ Broken and unbroken solutions and dynamic behaviors for the mixed local-nonlocal Schrödinger equation ⋮ Saigo-Maeda operators involving the Appell function, real spectra from symmetric quantum Hamiltonians and violation of the second law of thermodynamics for quantum damped oscillators ⋮ Hermitizable, isospectral complex second-order differential operators ⋮ Scattering from a \(PT\) symmetric standing wave ⋮ Necessity of \(\mathcal{PT}\) symmetry for soliton families in one-dimensional complex potentials ⋮ An inclusive SUSY approach to position dependent mass systems ⋮ Pure soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation ⋮ A completeness theorem for the system of eigenfunctions of the complex Schrödinger operator with potential \(q(x)=cx^\alpha \) ⋮ New scattering features in non-Hermitian space fractional quantum mechanics ⋮ General soliton solutions to a nonlocal long-wave-short-wave resonance interaction equation with nonzero boundary condition ⋮ General soliton solutions to a \((2+1)\)-dimensional nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions ⋮ Algebraic quantum theory with maximal frequency ⋮ The stationary optomechanical entanglement between an optical cavity field and a cubic anharmonic oscillator ⋮ Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices ⋮ Delocalization of a non-Hermitian quantum walk on random media in one dimension ⋮ Numerical simulations of parity-time symmetric nonlinear Schrödinger equations in critical case ⋮ The soliton solutions and long-time asymptotic analysis for an integrable variable coefficient nonlocal nonlinear Schrödinger equation ⋮ Complex invariants for some time-independent and time-dependent classical systems ⋮ Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. I: two-dimensional model ⋮ Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. II: Three-dimensional model ⋮ Pseudo-Hermitian random matrix models: general formalism ⋮ On the properties of phononic eigenvalue problems ⋮ Darboux transformation to the nonlocal complex short pulse equation ⋮ Asymptotic stage of modulation instability for the nonlocal nonlinear Schrödinger equation ⋮ Riemann-Hilbert problems and inverse scattering of nonlocal real reverse-spacetime matrix AKNS hierarchies ⋮ Higher-dimensional soliton generation, stability and excitations of the \(\mathcal{PT}\)-symmetric nonlinear Schrödinger equations ⋮ Localization of the light in two-dimensional PT-symmetric optical lattice ⋮ Higher-order dynamic localization in sinusoidal modulated optical lattices with \(\mathcal{PT}\)-symmetry ⋮ Long time asymptotics for the nonlocal mKdV equation with finite density initial data ⋮ Bootstrapping PT symmetric quantum mechanics ⋮ Conjugations on \(L^2(\mathbb{T}^N)\) and invariant subspaces ⋮ Real eigenspectra in non-Hermitian multidimensional Hamiltonians ⋮ PT-symmetry in mutually coupled semiconductor lasers with a non-zero time delay ⋮ Time-dependent \(\mathcal{C}\)-operators as Lewis-Riesenfeld invariants in non-Hermitian theories ⋮ Wigner-Yanase skew information and uncertainty relations for quaternionic mixed states ⋮ Conjugations preserving Toeplitz kernels ⋮ Complex optical potentials and pseudo-Hermitian Hamiltonians ⋮ Diagonalization of complex symmetric matrices: generalized Householder reflections, iterative deflation and implicit shifts ⋮ Second order SUSY transformations with `complex energies' ⋮ Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information ⋮ Algebraic techniques for eigenvalues and eigenvectors of a split quaternion matrix in split quaternionic mechanics ⋮ Dynamics of 1D and 3D quantum droplets in parity-time-symmetric harmonic-Gaussian potentials with two competing nonlinearities ⋮ Exotic vector freak waves in the nonlocal nonlinear Schrödinger equation ⋮ Two-dimensional SUSY-pseudo-Hermiticity without separation of variables ⋮ P-, T-, PT-, and CPT-invariance of Hermitian Hamiltonians ⋮ Pseudo-Hermiticity, weak pseudo-Hermiticity and \(\eta \)-orthogonality condition ⋮ Anomalous mechanisms of the loss of observability in non-Hermitian quantum models ⋮ Entanglement of multipartite fermionic coherent states for pseudo-Hermitian Hamiltonians ⋮ Ghosts in higher derivative Maxwell-Chern-Simon's theory and \(\mathcal{PT}\)-symmetry ⋮ Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learning ⋮ Spectral analysis, chiral disorder and topological edge states manifestation in open non-Hermitian Su-Schrieffer-Heeger chains ⋮ Characterization of dynamical measurement's uncertainty in a two-qubit system coupled with bosonic reservoirs ⋮ A pseudo-Hermitian \(\beta\)-Hermite family of matrices ⋮ Complex Langevin dynamics and supersymmetric quantum mechanics ⋮ Rational solutions of a weakly coupled nonlocal nonlinear Schrödinger equation ⋮ The resistive state in a superconducting wire: Bifurcation from the normal state ⋮ Scattering in \(\mathcal{PT}\)-symmetric quantum mechanics ⋮ A note on pseudo-Hermitian systems with point interactions and quantum separability ⋮ Isospectral Hamiltonians from Moyal products ⋮ On an equivalent Hermitian Hamiltonian for the wrong-sign quartic potential ⋮ Krein-space formulation of \(\mathcal{PT}\) symmetry, \(\mathcal{CPT}\)-inner products, and pseudo-Hermiticity ⋮ Comparative analysis of real and \(\mathcal{PT}\)-symmetric scarf potentials ⋮ Non-Hermitian \(d\)-dimensional Hamiltonians with position-dependent mass and their \(\eta\)-pseudo-Hermiticity generators ⋮ On a few new quantization recipes using \(\mathcal{PT}\)-symmetry ⋮ A positive-definite scalar product for free Proca particle ⋮ On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm ⋮ The effective potential for the PT-symmetric and non-Hermitian \((-g\phi^4)\) field theoretic model ⋮ Parity anomaly in a \(\mathcal{PT}\)-symmetric quartic Hamiltonian ⋮ Two-level systems: exact solutions and underlying pseudo-supersymmetry ⋮ A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons ⋮ Bound-state solutions of the Klein-Gordon equation for the generalized \(PT\)-symmetric hulthén potential ⋮ On the metric operator for a nonsolvable non-Hermitian model ⋮ A new solvable complex PT-symmetric potential ⋮ Ad hoc physical Hilbert spaces in quantum mechanics ⋮ Multiply degenerate exceptional points and quantum phase transitions ⋮ Open quantum systems with loss and gain ⋮ Localization of the states of a \(PT\)-symmetric double well ⋮ Non-Hermitian \(\mathcal{PT}\)-symmetric Dirac-Pauli Hamiltonians with real energy eigenvalues in the magnetic field ⋮ Reciprocity in parity violating non-Hermitian systems ⋮ Singular mapping for a \(PT\)-symmetric sinusoidal optical lattice at the symmetry-breaking threshold ⋮ Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type ⋮ Supersymmetric model of a Bose-Einstein condensate in a \(\mathcal{PT}\)-symmetric double-delta trap ⋮ Finite element calculations of \(\mathcal{PT}\)-symmetric Bose-Einstein condensates ⋮ \(\mathcal D\)-deformed harmonic oscillators ⋮ On the pseudospectrum of the harmonic oscillator with imaginary cubic potential ⋮ Hilbert space inner products for \(\mathcal{PT}\)-symmetric Su-Schrieffer-Heeger models ⋮ PT-symmetry in one-dimensional quantum periodic potentials ⋮ RG-Whitham dynamics and complex Hamiltonian systems ⋮ Stable 2D localized modes in anisotropic media with harmonic and \(\mathcal{PT}\)-symmetric potentials ⋮ From non-Hermitian oscillator-like operators to Freud polynomials and some uences ⋮ Properties of non-Hermitian quantum field theories. ⋮ Differential realizations of polynomial algebras in finite-dimensional spaces of monomials. ⋮ \(\mathcal{PT}\)-symmetric quantum toboggans ⋮ Modeling quantum harmonic oscillator in complex domain ⋮ The generalized \(PT\) -symmetric sinh-gordon potential solvable within quantum Hamilton-Jacobi formalism ⋮ First-order intertwining operators with position dependent mass and \(\eta\)-weak-pseudo-hermiticity generators ⋮ \((1+1)\)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: Effectively \(\mathcal{PT}\)-symmetric ⋮ Energy-levels crossing and radial Dirac equation: Supersymmetry and quasi-parity spectral signatures ⋮ PT-symmetric solutions of Schrödinger equation with position-dependent mass via point canonical transformation ⋮ On the generation of non-Hermitian Hamiltonians with real spectra by a modified Darboux transform ⋮ Exponential type complex and non-Hermitian potentials within quantum Hamilton-Jacobi formalism ⋮ Irreducible second order SUSY transformations between real and complex potentials ⋮ Coherent states of non-Hermitian quantum systems ⋮ Bound state solutions of the Schrödinger equation for a \(\mathcal{PT}\)-symmetric potential with Dirac delta functions ⋮ An ansatz for the eigenstates in \(\mathcal{PT}\)-symmetric quantum mechanics ⋮ Real description of classical Hamiltonian dynamics generated by a complex potential ⋮ Multi-instantons and exact results. III: Unification of even and odd anharmonic oscillators ⋮ Parity-time \((\mathcal{PT})\) invariance and pseudo-Hermitian Hamiltonian of a nonlinear oscillator ⋮ Exact solutions of the Klein-Gordon equation for the Scarf-type potential via Nikiforov-Uvarov method ⋮ Asymptotics of eigenvalues of non-self-adjoint Schrödinger operators on a half-line ⋮ Non-Hermitian quantum mechanics in non-commutative space ⋮ \(PT\) symmetry and Hermitian Hamiltonian in the local supercritical pomeron model ⋮ Conditional observability ⋮ Non-perturbative calculations for the effective potential of the PT symmetric and non-Hermitian (\(-g\varphi ^{4}\)) field theoretical model ⋮ Non-Hermitian Hamiltonians and the Painlevé IV equation with real parameters ⋮ Pseudo-hermiticity of an exactly solvable two-dimensional model ⋮ Two-dimensional systems that arise from the Noether classification of Lagrangians on the line ⋮ Invariants of two-dimensional systems via complex Lagrangians with applications ⋮ Discrete symmetries and generalized fields of dyons ⋮ Conditions of spectrum localization for operators not close to self-adjoint operators ⋮ Kaluza-Klein towers in warped spaces with metric singularities ⋮ Field extension of real values of physical observables in classical theory can help attain quantum results ⋮ The Coulomb-harmonic oscillator correspondence in \(\mathcal {PT}\) symmetric quantum mechanics ⋮ A PT-invariant potential with complex QES eigenvalues ⋮ PT-symmetric sextic potentials ⋮ Real discrete spectrum in the complex non-PT-symmetric Scarf II potential ⋮ A new non-Hermitian \(E_2\)-quasi-exactly solvable model ⋮ \(\eta \)-weak-pseudo-hermiticity generators and radially symmetric Hamiltonians ⋮ Lower bound of minimal time evolution in quantum mechanics ⋮ Relativistic confinement of neutral fermions with partially exactly solvable and exactly solvable PT-symmetric potentials in the presence of position-dependent mass ⋮ Spherical-separability of non-Hermitian Hamiltonians and pseudo-\(\mathcal{PT}\)-symmetry ⋮ Considerable sets of linear operators in Hilbert spaces as operator generalized effect algebras ⋮ On spectral properties of the discrete Schrödinger operator with pure imaginary finite potential ⋮ Exact solution for Morse oscillator in \(\mathcal P\mathcal T\)-symmetric quantum mechanics ⋮ On harmonic oscillators described by non-Hermitian operators and generalized Heisenberg relations ⋮ Existence of different intermediate Hamiltonians in type A \({\mathcal N}\)-fold supersymmetry ⋮ Conditionally exactly solvable potentials: A supersymmetric construction method ⋮ Resonances and PT symmetry in quantum curves ⋮ \(\text{sl}(2, \mathbb C)\) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues ⋮ Breather and lump solutions for nonlocal Davey-Stewartson II equation ⋮ Chaotic dynamics and optical power saturation in parity-time (\textit{PT}) symmetric double-ring resonator ⋮ Envelope solitons in a nonlinear string with mirror nonlocality ⋮ Degenerate soliton solutions and their dynamics in the nonlocal Manakov system: I symmetry preserving and symmetry breaking solutions ⋮ Exactly solvable two-dimensional complex model with a real spectrum ⋮ A new \(\eta\)-pseudo-Hermitian complex potential with PT symmetry ⋮ Symmetry broken and symmetry preserving multi-soliton solutions for nonlocal complex short pulse equation ⋮ Localized modes in \(\mathcal{PT}\)-symmetric sine-Gordon couplers with phase shift ⋮ Pseudomodes for non-self-adjoint Dirac operators ⋮ Fractional quantum couplers ⋮ Stability of one and two-dimensional spatial solitons in a cubic-quintic-septimal nonlinear Schrödinger equation with fourth-order diffraction and \(\mathcal{PT}\)-symmetric potentials ⋮ PDM Klein-Gordon oscillators in cosmic string spacetime in magnetic and Aharonov-Bohm flux fields within the Kaluza-Klein theory ⋮ Stabilization of fundamental solitons in the nonlinear fractional Schrödinger equation with \(\text{PT}\)-symmetric nonlinear lattices ⋮ Symmetry breaking solutions to nonlocal Alice-Bob Kadomtsev-Petviashivili system ⋮ From discrete nonlocal nonlinear Schrödinger equation to coupled discrete Heisenberg ferromagnet equation ⋮ Solitons in Kerr media with two-dimensional non-parity-time-symmetric complex potentials ⋮ \(\mathcal{PT}\)-symmetric peakon solutions in self-focusing/defocusing power-law nonlinear media: stability, interactions and adiabatic excitations ⋮ Quantum magnonics: when magnon spintronics meets quantum information science ⋮ Mass dimension one fermions: constructing darkness ⋮ Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs ⋮ Jordan blocks and the Bethe ansatz. I: The eclectic spin chain as a limit ⋮ Harmonic oscillators from displacement operators and thermodynamics ⋮ Parameter estimation with the steady states of non-Hermitian spin chains ⋮ On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation ⋮ Data-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learning ⋮ Interplay of fractionality and \(\mathcal{PT}\)- symmetry on a 1D lattice ⋮ \(P T\)-symmetric nonlocal Davey-Stewartson I equation: general lump-soliton solutions on a background of periodic line waves ⋮ Solitons supported by competing nonlinearity, higher order dispersion and \(\mathcal{PT}\)-symmetric potential ⋮ Nonstandard bilinearization and interaction phenomenon for \textbf{PT}-symmetric coupled nonlocal nonlinear Schrödinger equations ⋮ Pseudo-invariant approach for a particle in a complex time-dependent linear potential ⋮ Topological basis realization associated with spin-1 non-Hermitian XXZ model ⋮ Peregrine rogue wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity ⋮ Two dimensional gap solitons in self-defocusing media with PT-symmetric superlattice ⋮ One- and two-dimensional gap solitons and dynamics in the \(\mathcal{PT}\)-symmetric lattice potential and spatially-periodic momentum modulation ⋮ Resonant interaction of \(\phi^4\) kink with \(\mathcal{PT}\)-symmetric perturbation with spatially periodic gain/loss coefficient ⋮ Perturbative dynamics of stationary states in nonlinear parity-time symmetric coupler ⋮ Multi-dimensional stable fundamental solitons and excitations in \(\mathcal{PT}\)-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions ⋮ Integrability conditions and solitonic solutions of the nonlinear Schrödinger equation with generalized dual-power nonlinearities, PT-symmetric potentials, and space- and time-dependent coefficients ⋮ Dynamical control of solitons in a parity-time-symmetric coupler by periodic management ⋮ Nonlinear waves in an anti-Hermitian lattice with cubic nonlinearity ⋮ Rational soliton solutions in the parity-time-symmetric nonlocal coupled nonlinear Schrödinger equations ⋮ Families of fundamental and vortex solitons under competing cubic-quintic nonlinearity with complex potentials ⋮ Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data ⋮ Self-localized solitons of a \(q\)-deformed quantum system ⋮ Dissipative optical solitons in asymmetric Rosen-Morse potential ⋮ Hilbert space partitioning for non-Hermitian Hamiltonians: from off-resonance to Zeno subspaces ⋮ Degenerate and non-degenerate solutions of \(\mathcal{PT}\)-symmetric nonlocal integrable discrete nonlinear Schrödinger equation ⋮ General, symmetry non-preserving and preserving multiple soliton solutions of long wave-short wave resonant models ⋮ Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators ⋮ Controlled self-similar matter waves in PT-symmetric waveguide ⋮ Stability and collisions of quantum droplets in \(\mathcal{PT}\)-symmetric dual-core couplers ⋮ Dynamics of interaction between lumps and solitons in the Mel'nikov equation ⋮ Bicoherent-state path integral quantization of a non-Hermitian Hamiltonian ⋮ Optimal time evolution for pseudo-Hermitian Hamiltonians ⋮ The nonlocal multipoint problem with Dirichlet-type conditions for an ordinary differential equation of even order with involution ⋮ Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions ⋮ \(P T\)-symmetric nonlocal Davey-Stewartson I equation: soliton solutions with nonzero background ⋮ Unitarity of quantum tunneling decay for an analytical exact non-Hermitian resonant-state approach ⋮ Eigenvalue bifurcations in Kac-Murdock-Szegő matrices with a complex parameter ⋮ Gram determinant solutions to nonlocal integrable discrete nonlinear Schrödinger equations via the pair reduction ⋮ Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories ⋮ Variational approximations of soliton dynamics in the Ablowitz-Musslimani nonlinear Schrödinger equation ⋮ Bragg-induced oscillations in non-\textit{PT} complex photonic lattices ⋮ Stability boundaries of a Mathieu equation having \textit{PT} symmetry ⋮ Beat-like frequency pattern of extraordinary transmission and reflection in \(\mathcal{PT}\)-symmetric Fibonacci aperiodic optical networks of waveguide rings ⋮ Controlling decoherence via \(\mathcal{PT}\)-symmetric non-Hermitian open quantum systems ⋮ Comment on: ``PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian ⋮ Ring-frustrated non-Hermitian \(XY\) model ⋮ Breather solutions of the nonlocal nonlinear self-focusing Schrödinger equation ⋮ Active control of parity-time symmetry phase transition in terahertz metasurface ⋮ Complex BPS skyrmions with real energy ⋮ Integrable space-time shifted nonlocal nonlinear equations ⋮ Nonlinear integrable dynamics of coupled vibrational and intra-site excitations on a regular one-dimensional lattice ⋮ Exactly solvable time-dependent non-Hermitian quantum systems from point transformations ⋮ Gray solitons in parity-time-symmetric localized potentials with fractional-order diffraction ⋮ Quantum graphs: self-adjoint, and yet exhibiting a nontrivial \(\mathcal{PT}\)-symmetry ⋮ Time evolution of two-states non-Hermitian systems ⋮ To quantify the difference of \(\eta \)-inner products in \(\mathcal{PT}\)-symmetric theory ⋮ Normal mode splitting in a cavity optomechanical system with a cubic anharmonic oscillator ⋮ Impact of \(\mathcal{PT}\)-symmetric operation on concurrence and the first-order coherence ⋮ \( \mathcal{PT}\)-symmetry in compact phase space for a linear Hamiltonian ⋮ Understanding partial \(\mathcal{PT}\) symmetry as weighted composition conjugation in reproducing kernel Hilbert space: an application to non-Hermitian Bose-Hubbard type Hamiltonian in Fock space ⋮ Population dynamics based on ladder bosonic operators ⋮ Solitons and dynamics for the integrable nonlocal pair-transition-coupled nonlinear Schrödinger equation ⋮ Dynamics of lump-soliton solutions to the \(PT\)-symmetric nonlocal Fokas system ⋮ Quantum mechanics using two auxiliary inner products ⋮ Dromion solutions of PT-symmetric \((x,y)\)-nonlocal Davey-Stewartson I equation ⋮ Bounded solutions of the Dirac equation with a PT-symmetric kink-like vector potential in two-dimensional space-time ⋮ On the reality of the spectrum of a non-Hermitian discrete Hamiltonian ⋮ Bright and dark soliton solutions to the partial reverse space-time nonlocal Mel'nikov equation ⋮ Restoration of coherence by local PT-symmetric operator ⋮ Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential ⋮ Critical graph of a polynomial quadratic differential related to a Schrödinger equation with quartic potential ⋮ Deconfinement to confinement as PT phase transition ⋮ Vector solitons in nonlinear fractional Schrödinger equations with parity-time-symmetric optical lattices ⋮ Broken and unbroken \(\mathcal{PT}\)-symmetric solutions of semi-discrete nonlocal nonlinear Schrödinger equation ⋮ Stability of Gaussian-type soliton in the cubic-quintic nonlinear media with fourth-order diffraction and \(\mathcal{PT}\)-symmetric potentials ⋮ Non-Hermitian extensions of uncertainty relations with generalized metric adjusted skew information ⋮ Anti- \(\mathcal{PT}\)-symmetric harmonic oscillator and its relation to the inverted harmonic oscillator ⋮ Soliton solutions for two kinds of fourth-order nonlinear nonlocal Schrödinger equations ⋮ Dual-band unidirectional reflectionlessness in non-Hermitian quantum system consisting of a gain and a loss plasmonic cavities ⋮ Hybrid form of quantum theory with non-Hermitian Hamiltonians ⋮ Relatively bounded perturbations of \(J\)-non-negative operators ⋮ Band structure of the one-dimensional spin-orbit-coupled Su-Schrieffer-Heeger lattice with \(\mathcal{PT}\)-symmetric onsite imaginary potentials ⋮ Systematics of quasi-Hermitian representations of non-Hermitian quantum models ⋮ Nonlinear conical diffraction in fractional dimensions with a \(\mathcal{PT}\)-symmetric optical lattice ⋮ Nonlinear wave dynamics near phase transition in \(\mathcal{PT}\)-symmetric localized potentials ⋮ Spatial solitons in PT symmetric potential with competing gain and loss ⋮ Pseudo-Hermitian and \(\mathcal{P}T\)-symmetric quantum systems with energy-dependent potentials: bound-state solutions and energy spectra ⋮ Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials ⋮ Non-Hermitian Dirac Hamiltonian in three-dimensional gravity and pseudosupersymmetry ⋮ Pseudo-Hermitian systems with \(\mathcal {PT}\)-symmetry: degeneracy and Krein space ⋮ Solution of effective-mass Dirac equation with scalar-vector and pseudoscalar terms for generalized Hulthén potential ⋮ Spectral properties of the complex Airy operator on the half-line ⋮ Extension of the \(\operatorname C \operatorname P \operatorname T\) theorem to non-Hermitian Hamiltonians and unstable states ⋮ Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform ⋮ Coalescence of resonances in dissipationless resonant tunneling structures and \(\mathcal{PT}\)-symmetry breaking ⋮ A canonical formulation of dissipative mechanics using complex-valued Hamiltonians ⋮ The spectrum of the cubic oscillator ⋮ \({\mathcal {PT}}\) symmetry in Natanzon-class potentials ⋮ Shape invariance approach to exact solutions of the Klein-Gordon equation ⋮ Additional constraints on quasi-exactly solvable systems ⋮ Exact polynomial solution of \({\mathcal P}{\mathcal T}\)/Non-\({\mathcal P}{\mathcal T}\)-symmetric and non-Hermitian modified Woods-Saxon potential by the Nikiforov-Uvarov method ⋮ Some remarks on complex Hamiltonian systems ⋮ Accidental crossings of eigenvalues in the one-dimensional complex PT-symmetric Scarf-II potential ⋮ Hidden gauge symmetry in holomorphic models ⋮ From generalized Dirac equations to a candidate for dark energy ⋮ On the quantum mechanics of bicomplex Hamiltonian system ⋮ Eigenspectra of a complex coupled harmonic potential in three dimensions ⋮ Higher loop \(\beta\) function for non-Hermitian PT symmetric \(\iota g\phi^3\) theory ⋮ Two-state quantum systems revisited: a Clifford algebra approach ⋮ Long-time asymptotics for the integrable nonlocal focusing nonlinear Schrödinger equation for a family of step-like initial data ⋮ Novel higher-order rational solitons and dynamics of the defocusing integrable nonlocal nonlinear Schrödinger equation via the determinants ⋮ Non-Hermitian interaction representation and its use in relativistic quantum mechanics ⋮ Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays ⋮ Coupled oscillators with parity-time symmetry ⋮ Enhancement of photon creation through the pseudo-Hermitian dynamical Casimir effect ⋮ Completeness theorem for the system of eigenfunctions of the complex Schrödinger operator \(\mathscr{L}_{c , \alpha} = - d^2 / d x^2 + c x^\alpha \) ⋮ Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations ⋮ Stable solitons and interactions of the logarithmic nonlinear Schrödinger equation with two \(\mathcal{PT} \)-symmetric non-periodic potentials ⋮ The nth-Darboux transformation and explicit solutions of the PT-symmetry second-type derivative nonlinear Schrödinger equation ⋮ Coherence and complementarity based on modified generalized skew information ⋮ Quantum Fisher information of a two-level system controlled by non-Hermitian operation under depolarization ⋮ Conformal bridge transformation, \( \mathcal{PT}\)- and supersymmetry ⋮ Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations ⋮ Schwinger-Dyson equations and mass generation for an axion theory with a \(\mathcal{PT}\) symmetric Yukawa fermion interaction ⋮ Soliton formation and dynamics in the quintic nonlinear media with \(\mathcal{PT}\)-invariant harmonic-Gaussian potential ⋮ Mass deformed ABJM and $ \mathcal{P}\mathcal{T} $ symmetry ⋮ Conical diffraction modulation in fractional dimensions with a \(\mathcal{PT}\)-symmetric potential ⋮ Quantization of non-standard Hamiltonians and the Riemann zeros ⋮ Long time asymptotic behavior for the nonlocal mKdV equation in solitonic space-time regions ⋮ Moduli spaces for PT-regularized solitons ⋮ Stable matter-wave solitons, interactions, and excitations in the spinor \(F=1\) Bose-Einstein condensates with \(\mathcal{PT}\)- and non-\(\mathcal{PT}\)-symmetric potentials ⋮ Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation ⋮ Semiclassical calculation of the \(\mathcal C\) operator in \(\mathcal{PT}\)-symmetric quantum mechanics ⋮ Stable solitons and peakons, quantum information entropies, interactions, and excitations for generalized \(\mathcal{PT}\)-symmetric NLS equations ⋮ Darboux transformation and general soliton solutions for the reverse space-time nonlocal short pulse equation ⋮ Resolvent estimates for one-dimensional Schrödinger operators with complex potentials ⋮ \({\mathcal{PT}}\)-symmetric Klein-Gordon oscillator ⋮ Entanglement entropy distinguishes PT-symmetry and topological phases in a class of non-unitary quantum walks ⋮ Operator growth and Krylov construction in dissipative open quantum systems ⋮ Jordan blocks and the Bethe ansatz. II: The eclectic spin chain beyond \(K = 1\) ⋮ Non-Hermitian Hamiltonian deformations in quantum mechanics ⋮ Stationary hypergeometric solitons and their stability in a Bose-Einstein condensate with \(\mathcal{PT}\)-symmetric potential ⋮ Various scattering properties of a new PT-symmetric non-Hermitian potential ⋮ Kinematic and dynamic vortices in a thin film driven by an applied current and magnetic field ⋮ On a \(\mathcal{PT}\)-symmetric waveguide with a pair of small holes ⋮ Handedness of complex PT-symmetric potential barriers ⋮ Bound states of the Klein-Gordon equation with vector and scalar Rosen-Morse-type potentials ⋮ Conjecture on the interlacing of zeros in complex Sturm–Liouville problems ⋮ Supersymmetric solutions of \(PT\)-/non-\(PT\)-symmetric and non-hermitian screened Coulomb potential via Hamiltonian hierarchy inspired variational method ⋮ GENERATING COMPLEX POTENTIALS WITH REAL EIGENVALUES IN SUPERSYMMETRIC QUANTUM MECHANICS ⋮ Quantum motion in complex space ⋮ Time-dependent PT symmetric problems ⋮ Perturbation theory in a framework of iteration methods ⋮ Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass ⋮ On the simpleness of zeros of Stokes multipliers ⋮ On the eigenproblems of PT-symmetric oscillators ⋮ Simultaneous ordinary and type A \(\mathcal N\)-fold supersymmetries in Schrödinger, Pauli, and Dirac equations ⋮ Schrödinger operators with complex-valued potentials and no resonances ⋮ The real spectrum of the imaginary cubic oscillator: an expository proof ⋮ Nonautonomous cnoidal wave and soliton management in parity-time symmetric potentials ⋮ Developing a non-Hermitian algebraic theory with the \(\gamma_5\)-extension of mass ⋮ Non-Hermitian hydrogen atom ⋮ The \(N\)-wave equations with \(\mathcal{PT}\) symmetry ⋮ Three-dimensional optical solitons formed by the balance between different-order nonlinearities and high-order dispersion/diffraction in parity-time symmetric potentials ⋮ Complex symmetric evolution equations ⋮ Uncertainty relations based on modified Wigner-Yanase-Dyson skew information ⋮ Energy-sharing collisions and the dynamics of degenerate solitons in the nonlocal Manakov system ⋮ Dynamics of some novel breather solutions and rogue waves for the \textbf{PT}-symmetric nonlocal soliton equations ⋮ The complex 2-sphere in \(\mathbb{C}^3\) and Schrödinger flows ⋮ Restriction of the fermion mass spectrum in \(PT\)-symmetric systems and its implications for studying dark matter ⋮ The geometrical properties of parity and time reversal operators in two dimensional spaces ⋮ On the infinite-dimensional QR algorithm ⋮ Violation of the equivalence principle in non-Hermitian fermion theory ⋮ Effect of PT-symmetric operator on coherence under the non-Markovian environments ⋮ Quantum state conversion in two-level system without rotating-wave approximation via non-Hermitian shortcuts to adiabaticity ⋮ Squeezed atom laser for Bose-Einstein condensate with minimal length ⋮ Operator-based approach to \({\mathcal{P}}{\mathcal{T}}\)-symmetric problems on a wedge-shaped contour ⋮ Schrödinger equations with logarithmic self-interactions: from antilinear \(\mathcal{PT}\)-symmetry to the nonlinear coupling of channels ⋮ Critical blowup in coupled parity-time-symmetric nonlinear Schrödinger equations ⋮ On PT symmetry systems: invariance, conservation laws, and reductions ⋮ Explicit solutions to a nonlocal 2-component complex modified Korteweg-de Vries equation ⋮ Multi-rogue wave and multi-breather solutions in \(\mathcal{PT}\)-symmetric coupled waveguides ⋮ Hofstadter's Cocoon ⋮ Dynamical behaviors of optical solitons in parity-time (\(\mathcal{PT}\)) symmetric sextic anharmonic double-well potentials ⋮ Some Remarks on Quantum Brachistochrone ⋮ METRIC-SCALAR GRAVITY WITH TORSION AND THE MEASURABILITY OF THE NON-MINIMAL COUPLING ⋮ Generalized Bogoliubov transformations versus D-pseudo-bosons ⋮ Pseudospectra in non-Hermitian quantum mechanics ⋮ Particle injection into a chain: decoherence versus relaxation for Hermitian and non-Hermitian dynamics ⋮ Dynamics in ‐Symmetric Honeycomb Lattices with Nonlinearity ⋮ Real exact solutions to the relativistic spinless particle with modified Rosen-Morse potential and its 𝒫𝒯 symmetry ⋮ PT Symmetric Classical and Quantum Cosmology ⋮ Generalized Jaynes-Cummings Model with a Pseudo-Hermitian: A Path Integral Approach ⋮ Exceptional Points in a Non-Hermitian Extension of the Jaynes-Cummings Hamiltonian ⋮ The EMM and the Spectral Analysis of a Non Self-adjoint Hamiltonian on an Infinite Dimensional Hilbert Space ⋮ Geometric Aspects of Space-Time Reflection Symmetry in Quantum Mechanics ⋮ A Unifying E2-Quasi Exactly Solvable Model ⋮ Sublattice Signatures of Transitions in a $$\mathscr {PT}$$ PT -Symmetric Dimer Lattice ⋮ Some Features of Exceptional Points ⋮ Pseudo-Hermitian $$\beta $$ β -Ensembles with Complex Eigenvalues ⋮ Non-Hermitian $$\mathcal{PT}$$ PT -Symmetric Relativistic Quantum Theory in an Intensive Magnetic Field ⋮ Quasi-Hermitian Lattices with Imaginary Zero-Range Interactions ⋮ Quantization of Big Bang in Crypto-Hermitian Heisenberg Picture ⋮ REPRESENTATION DEPENDENCE OF SUPERFICIAL DEGREE OF DIVERGENCES IN QUANTUM FIELD THEORY ⋮ LINKED ${\mathcal{PT}}$-SYMMETRY TO SUPERSYMMETRY IN A CLASS OF NON-HERMITIAN HAMILTONIANS ⋮ MOMENTUM AND HAMILTONIAN IN COMPLEX ACTION THEORY ⋮ Supersymmetric analysis of the Dirac-Weyl operator within $\mathcal{PT}$PT symmetry ⋮ Coordinate representation for non-Hermitian position and momentum operators ⋮ 𝒫𝒯-symmetric and antisymmetric nonlinear states in a split potential box ⋮ Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential ⋮ PT-symmetric eigenvalues for homogeneous potentials ⋮ Effect of PT symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media ⋮ Complex Classical Motion in Potentials with Poles and Turning Points ⋮ Embedded States in the Continuum for PT-Symmetric Systems ⋮ Exponential Asymptotics for Solitons in PT-Symmetric Periodic Potentials ⋮ Supercritical Blowup in Coupled Parity-Time-Symmetric Nonlinear Schrödinger Equations ⋮ Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions ⋮ Rogue waves of the nonlocal Davey–Stewartson I equation ⋮ Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics ⋮ Solitons and Their Ghosts in $$\mathcal{P}\mathcal{T}$$ -Symmetric Systems with Defocusing Nonlinearities ⋮ The Nielsen–Ninomiya theorem, $ \renewcommand{\P}{{{\mathcal P}}} \newcommand{\PT}{{\mathcal {PT}}} \PT$ -invariant non-Hermiticity and single 8-shaped Dirac cone ⋮ Bender-Wu singularities ⋮ CONDITIONS FOR COMPLEX SPECTRA IN A CLASS OF ${\mathcal P}{\mathcal T}$ SYMMETRIC POTENTIALS ⋮ GENERALIZED CONTINUITY EQUATION AND MODIFIED NORMALIZATION IN PT-SYMMETRIC QUANTUM MECHANICS ⋮ SPONTANEOUS BREAKDOWN OF $\mathcal{PT}$ SYMMETRY IN THE SOLVABLE SQUARE-WELL MODEL ⋮ CREATION AND ANNIHILATION OPERATORS AND COHERENT STATES FOR THE PT-SYMMETRIC OSCILLATOR ⋮ Nonclassicality versus entanglement in a noncommutative space ⋮ A model of three coupled wave guides and third order exceptional points ⋮ Parity–time-symmetric closed form optical quadrimer waveguides ⋮ Parity-time symmetric coupled systems with varying loss/gain coefficient ⋮ A unified inverse scattering transformation for the local and nonlocal nonautonomous Gross-Pitaevskii equations ⋮ COMPLEXIFIED PSUSY AND SSUSY INTERPRETATIONS OF SOME PT-SYMMETRIC HAMILTONIANS POSSESSING TWO SERIES OF REAL ENERGY EIGENVALUES ⋮ Quantum graphs: PT-symmetry and reflection symmetry of the spectrum ⋮ On the Global Behavior of Solutions of a Coupled System of Nonlinear Schrödinger Equation ⋮ Time-delay and reality conditions for complex solitons ⋮ ON SUPERGROUPS WITH ODD CLIFFORD PARAMETERS AND SUPERSYMMETRY WITH MODIFIED LEIBNIZ RULE ⋮ REAL SPECTRUM OF NON-HERMITIAN HAMILTONIANS FOR HULTHÉN POTENTIAL ⋮ On the Spectral Stability of Kinks in 2D Klein-Gordon Model with Parity-Time-Symmetric Perturbation ⋮ Hamiltonians defined by biorthogonal sets ⋮ Infinite-dimensional representations of the rotation group and Dirac monopole problem ⋮ Transition probabilities in the two-level quantum system with PT-symmetric non-Hermitian Hamiltonians ⋮ Quantum entropy of systems described by non-Hermitian Hamiltonians ⋮ CONFORMAL ANOMALY IN NON-HERMITIAN QUANTUM MECHANICS ⋮ PHANTOM COSMOLOGY BASED ON PT SYMMETRY ⋮ Non-Hermitian spin chains with inhomogeneous coupling ⋮ PATH INTEGRALS FOR QUASI-HERMITIAN HAMILTONIANS ⋮ Fragile PT-symmetry in a solvable model ⋮ Recursive calculation of effective potential and variational resummation ⋮ PSEUDO-HERMITIAN INTERACTIONS IN DIRAC THEORY: EXAMPLES ⋮ Lorentz symmetric quantum field theory for symplectic fermions ⋮ Eigenstates and instabilities of chains with embedded defects ⋮ PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS ⋮ QUANTUM SYSTEMS AND ALTERNATIVE UNITARY DESCRIPTIONS ⋮ Bound states in waveguides with complex Robin boundary conditions ⋮ Smeared quantum lattices exhibiting 𝒫𝒯-symmetry with positive 𝒫 ⋮ A Bose-Einstein condensate in a 𝒫𝒯 symmetric double well ⋮ Braid operation of exceptional points ⋮ The quark-level linear σ model ⋮ Synthesis of lossless electric circuits based on prescribed Jordan forms ⋮ A GENERAL APPROACH OF QUASI-EXACTLY SOLVABLE SCHRÖDINGER EQUATIONS WITH THREE KNOWN EIGENSTATES ⋮ Mixed Local-Nonlocal Vector Schrödinger Equations and Their Breather Solutions ⋮ Nonlocal nonlinear Schrödinger equation and its discrete version: Soliton solutions and gauge equivalence ⋮ General theory of regular biorthogonal pairs and its physical operators ⋮ An Indefinite Convection-Diffusion Operator ⋮ Spontaneous ‐Symmetry Breaking in Nonlinearly Coupled van der Pol Oscillators ⋮ Bifurcation of eigenvalues in nonlinear problems with antilinear symmetry ⋮ COHERENT STATES AND SCHWINGER MODELS FOR PSEUDO GENERALIZATION OF THE HEISENBERG ALGEBRA ⋮ Intertwining operators for non-self-adjoint Hamiltonians and bicoherent states ⋮ Complex Extension of Quantum Mechanics ⋮ Visualization of Branch Points in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-Symmetric Waveguides ⋮ Faster than Hermitian Quantum Mechanics ⋮ Spatial Solitons in Parity-Time-Symmetric Photonic Lattices: Recent Theoretical Results ⋮ Manifestation of superposition and coherence in ${\mathcal P} {\mathcal T}$ -symmetry through the η-inner product ⋮ DARBOUX TRANSFORMATION FOR THE ONE-DIMENSIONAL STATIONARY DIRAC EQUATION WITH NON-HERMITIAN INTERACTION ⋮ ${\cal {PT}}$ PT symmetric, Hermitian and $\mathcal P$P-self-adjoint operators related to potentials in ${\cal {PT}}$PT quantum mechanics ⋮ PHANTOM UNIVERSE FROM CPT SYMMETRIC QFT ⋮ EIGENVALUES AND EIGENFUNCTIONS OF WOODS–SAXON POTENTIAL IN PT-SYMMETRIC QUANTUM MECHANICS ⋮ Darboux transformation and multi-soliton solutions of local/nonlocal N-wave interactions ⋮ Large-order perturbation theory for a non-Hermitian 𝓟𝓣-symmetric Hamiltonian ⋮ Dirac equation for generalized Pöschl-Teller scalar and vector potentials and a Coulomb tensor interaction by Nikiforov-Uvarov method ⋮ Lax-Phillips scattering theory for PT-symmetric ρ-perturbed operators ⋮ Solvable PT-symmetric model with a tunable interspersion of nonmerging levels ⋮ MHD α2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator ⋮ The potential (iz)m generates real eigenvalues only, under symmetric rapid decay boundary conditions ⋮ An investigation of PT -symmetry breaking in tight-binding chains ⋮ Non-Hermitian Physics and Master Equations ⋮ A Swanson-like Hamiltonian and the inverted harmonic oscillator ⋮ The operational foundations of PT-symmetric and quasi-Hermitian quantum theory ⋮ Swanson Hamiltonian: non-PT-symmetry phase ⋮ Local preservation of no-signaling in multiparty PT-symmetric evolutions ⋮ Complex Methods for Lie Symmetry Analysis ⋮ Thermodynamics of dissipative coherent states ⋮ Integrable nonlocal asymptotic reductions of physically significant nonlinear equations ⋮ PT-symmetric quantum graphs ⋮ Coalescence of two branch points in complex time marks the end of rapid adiabatic passage and the start of Rabi oscillations ⋮ Nonlinear eigenvalue problems for generalized Painlevé equations ⋮ Which metrics are consistent with a given pseudo-hermitian matrix? ⋮ Nonlinear eigenvalue problems ⋮ Many-body excitations in trapped Bose gas: A non-Hermitian approach ⋮ Symmetries of (${N \times N}$ ) non-Hermitian Hamiltonian matrices ⋮ Generalized Riesz systems and orthonormal sequences in Krein spaces ⋮ Stability of topologically protected edge states in nonlinear quantum walks: additional bifurcations unique to Floquet systems ⋮ Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian ⋮ Weak pseudo-Hermiticity and antilinear commutant ⋮ Transition elements for a non-Hermitian quadratic Hamiltonian ⋮ Spectrum and symmetries of the impulsive difference equations ⋮ Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: effect of disorder correlations ⋮ Spectral singularity in composite systems and simulation of a resonant lasing cavity ⋮ A systematic construction of parity-time ($\mathcal{PT}$ )-symmetric and non-$\mathcal{PT}$ -symmetric complex potentials from the solutions of various real nonlinear evolution equations ⋮ On the stability of standing waves for ${\mathcal P}{\mathcal T}$ symmetric Schrödinger and Klein-Gordon equations in higher space dimensions ⋮ Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator ⋮ Real eigenvalues of a non-self-adjoint perturbation of the self-adjoint Zakharov-Shabat operator ⋮ Irreversibility of the renormalization group flow in non-unitary quantum field theory ⋮ Degenerate multi-solitons in the sine-Gordon equation ⋮ Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control ⋮ Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator ⋮ Toward non-Hermitian quantum statistical thermodynamics ⋮ New scattering features of quaternionic point interaction in non-Hermitian quantum mechanics ⋮ PT-symmetry, indefinite metric, and nonlinear quantum mechanics ⋮ On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT- and non-PT-symmetric potentials ⋮ Discrete nonlocal nonlinear Schrödinger systems: Integrability, inverse scattering and solitons ⋮ Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics ⋮ Floquet exceptional points and chirality in non-Hermitian Hamiltonians ⋮ Solitons in a Hamiltonian $\newcommand{\PT}{\mathcal{ PT}}{\boldsymbol \PT}$ -symmetric coupler ⋮ Winding in non-Hermitian systems ⋮ Non-self-adjoint operators with real spectra and extensions of quantum mechanics ⋮ Dynamics of finite dimensional non-hermitian systems with indefinite metric ⋮ New families of non-parity-time-symmetric complex potentials with all-real spectra ⋮ Dynamics of soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation ⋮ Complex Magnetic Fields: An Improved Hardy--Laptev--Weidl Inequality and Quasi-Self-Adjointness ⋮ Contact interactions and Kronig–Penney models in Hermitian and $ \boldsymbol {\mathcal {PT}}$ symmetric quantum mechanics ⋮ The periodic Cauchy problem for PT-symmetric NLS, I: the first appearance of rogue waves, regular behavior or blow up at finite times ⋮ A quantum system with a non-Hermitian Hamiltonian ⋮ Correlations of indistinguishable particles in non-Hermitian lattices ⋮ Solutions of the nonlocal (2+1)-D breaking solitons hierarchy and the negative order AKNS hierarchy ⋮ ${ \mathcal P }{ \mathcal T }$-symmetry berry phases, topology and ${ \mathcal P }{ \mathcal T }$-symmetry breaking ⋮ Effect of power-law nonlinearity on ${ \mathcal P }{ \mathcal T }$-symmetric optical system with fourth-order diffraction ⋮ On the Lagrangian description of dissipative systems ⋮ Effects of Disorder on Non-unitary <i>PT</i> Symmetric Quantum Walks ⋮ Quantum mechanical settings inspired by RLC circuits ⋮ Generalized Heisenberg algebra and (non linear) pseudo-bosons ⋮ On the Construction of Non-Hermitian Hamiltonians with All-Real Spectra Through Supersymmetric Algorithms ⋮ Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with PT-symmetric potential ⋮ Solitons and their stability in the nonlocal nonlinear Schrödinger equation with PT-symmetric potentials ⋮ On completeness of coherent states in noncommutative spaces with the generalised uncertainty principle ⋮ The nonlinear Schrödinger equation with generalized nonlinearities and PT-symmetric potentials: Stable solitons, interactions, and excitations ⋮ Microscopic description of irreversibility in quantum Lorentz gas by complex spectral analysis of the Liouvillian outside the Hilbert space ⋮ General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions ⋮ Passage through exceptional point: case study ⋮ P, T, and PT−symmetries of impulsive Dirac systems ⋮ “Striped” rectangular rigid box with Hermitian and non-Hermitian PT symmetric potentials ⋮ Can Parity‐Time‐Symmetric Potentials Support Families of Non‐Parity‐Time‐Symmetric Solitons? ⋮ Isomorphic Hilbert spaces associated with different complex contours of the $\mathcal{PT}$-symmetric (-x4) theory ⋮ Parity-time symmetry broken by point-group symmetry ⋮ SUPERSYMMETRIC SOLUTION OF PT-/NON-PT-SYMMETRIC AND NON-HERMITIAN MORSE POTENTIAL VIA HAMILTONIAN HIERARCHY METHOD ⋮ Dirac equation with complex potentials ⋮ Deformation of dark solitons in a PT-invariant variable coefficients nonlocal nonlinear Schrödinger equation ⋮ Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime ⋮ Stable flat-top solitons and peakons in the PT-symmetric δ -signum potentials and nonlinear media ⋮ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:mrow></mml:math>-symmetric brachistochrone problem, Lorentz boosts, and nonunitary operator equivalence classes ⋮ Antilinearity rather than Hermiticity as a guiding principle for quantum theory ⋮ Using mixed many-body particle states to generate exact $\mathcal{PT} $ -symmetry in a time-dependent four-well system ⋮ Statistical behavior of the characteristic polynomials of a family of pseudo-Hermitian Gaussian matrices ⋮ Non-Hermitian Coherent States for Finite-Dimensional Systems ⋮ A Squeezed Review on Coherent States and Nonclassicality for Non-Hermitian Systems with Minimal Length ⋮ 𝓟𝓣-symmetric quantum mechanics ⋮ Ghost problems from Pauli–Villars to fourth-order quantum gravity and their resolution ⋮ On the Spectral Stability of Standing Waves of Nonlocal $$\mathcal {P}\mathcal {T}$$ Symmetric Systems ⋮ General stationary solutions of the nonlocal nonlinear Schrödinger equation and their relevance to the PT-symmetric system ⋮ On Some Aspects of Unitary Evolution Generated by Non-Hermitian Hamiltonians ⋮ Non-Hermitian Quantum Mechanics of Bosonic Operators ⋮ Defocusing nonlocal nonlinear Schr\"odinger equation with step-like boundary conditions: long-time behavior for shifted initial data ⋮ Exceptional points and domains of unitarity for a class of strongly non-Hermitian real-matrix Hamiltonians ⋮ Comment on: Quantum theory of a non-Hermitian time-dependent forced harmonic oscillator having 𝒫𝒯 symmetry ⋮ Complex symmetric completions of partial operator matrices ⋮ Phase space trajectories and quantization in PT-symmetric quantum mechanics ⋮ Weakly non-Hermitian square well ⋮ Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions ⋮ On integrability and pseudo-Hermitian systems with spin-coupling point interactions ⋮ Third-order spectral branch points in Krein space related setups: $$\mathcal{P}\mathcal{T}$$ -symmetric matrix toy model, MHD α 2-dynamo and extended Squire equation ⋮ Pseudo-Hermitian Hamiltonians: tale of two potentials ⋮ On (non-Hermitian) Lagrangeans in (particle) physics and their dynamical generation ⋮ Development of an approximate method for quantum optical models and their pseudo-Hermicity ⋮ Neutrino mass observables and non-Hermitian version of Type-I seesaw model ⋮ A novel Riemann–Hilbert approach via t-part spectral analysis for a physically significant nonlocal integrable nonlinear Schrödinger equation ⋮ Real energies and Berry phases in all PT-regimes in time-dependent non-Hermitian theories ⋮ Artificial Hawking radiation, weak pseudo-Hermiticity, and Weyl semimetal blackhole analogy ⋮ Rigged Hilbert space approach for non-Hermitian systems with positive definite metric ⋮ Lewis–Riesenfeld invariants for PT-symmetrically coupled oscillators from two-dimensional point transformations and Lie algebraic expansions ⋮ Time evolution for quantum systems with a dynamical Hilbert space ⋮ Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model ⋮ Integrability and trajectory confinement in -symmetric waveguide arrays ⋮ Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects ⋮ Single-hump and double-hump solitons in a symmetric complex potential ⋮ Approximate analytical description for the nonlinear ${ \mathcal P }{ \mathcal T }$-symmetric coupled-mode equations ⋮ A PSEUDO-UNITARY ENSEMBLE OF RANDOM MATRICES, PT-SYMMETRY AND THE RIEMANN HYPOTHESIS ⋮ A NOTE ON THE INTEGRABILITY OF NON-HERMITIAN EXTENSIONS OF CALOGERO–MOSER–SUTHERLAND MODELS ⋮ THERMODYNAMICS OF PSEUDO-HERMITIAN SYSTEMS IN EQUILIBRIUM ⋮ FRACTIONAL STATISTICS IN SOME EXACTLY SOLVABLE MODELS WITH PT INVARIANT INTERACTIONS ⋮ PT-SYMMETRIC NONPOLYNOMIAL OSCILLATORS AND HYPERBOLIC POTENTIAL WITH TWO KNOWN REAL EIGENVALUES IN A SUSY FRAMEWORK ⋮ ALTERNATIVE HAMILTONIAN DESCRIPTIONS FOR QUANTUM SYSTEMS AND NON-HERMITIAN OPERATORS WITH REAL SPECTRUM ⋮ PT-SYMMETRIC SQUARE WELL AND THE ASSOCIATED SUSY HIERARCHIES ⋮ ON THE PSEUDO-HERMITICITY OF A CLASS OF PT-SYMMETRIC HAMILTONIANS IN ONE DIMENSION ⋮ Fundamentals of quantum mechanics in Liouville space ⋮ Global conservative solutions of the nonlocal NLS equation beyond blow-up ⋮ Bootstrapping Calabi–Yau quantum mechanics ⋮ On the well-posedness of a nonlocal (two-place) FORQ equation via a two-component peakon system ⋮ Uncertainty relation for non-Hermitian operators ⋮ Fraction‐Dimensional Accessible Solitons in a Parity‐Time Symmetric Potential ⋮ Oscillatory stability of quantum droplets in -symmetric optical lattice ⋮ The Scattering Problem in PT‐Symmetric Periodic Structures of 1D Two‐Material Waveguide Networks ⋮ Singular Characteristics of Optical Thue–Morse Multilayers Composed of PT‐Symmetric Elements ⋮ Giant atom induced zero modes and localization in the nonreciprocal Su–Schrieffer–Heeger chain ⋮ 1D Solitons in Saturable Nonlinear Media with Space Fractional Derivatives ⋮ The foundations of spectral computations via the solvability complexity index hierarchy ⋮ Rational solitons and rogue waves for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation ⋮ Magnon Blockade in a PT‐Symmetric‐Like Cavity Magnomechanical System ⋮ The analytical transfer matrix method for PT-symmetric complex potential ⋮ Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation ⋮ QUANTUM HAMILTON–JACOBI ANALYSIS OF PT SYMMETRIC HAMILTONIANS ⋮ $\mathcal {CPT}$ CPT -conserved effective mass Hamiltonians through first and higher order charge operator $\mathcal {C}$C in a supersymmetric framework ⋮ Supersymmetry without Hermiticity within \(\mathcal{PT}\) symmetric quantum mechanics ⋮ Quantum complex Hénon-Heiles potentials ⋮ Bifurcation of Soliton Families from Linear Modes in Non‐‐Symmetric Complex Potentials ⋮ Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential ⋮ On an exactly solvable \(B_N\) type Calogero model with non-Hermitian PT invariant interaction ⋮ Construction of complex invariants for classical dynamical systems ⋮ Wave packet pseudomodes of variable coefficient differential operators ⋮ A PT-symmetric QES partner to the Khare-Mandal potential with real eigenvalues ⋮ Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: real spectrum of complex potentials ⋮ Bound states of non-Hermitian quantum field theories ⋮ On the eigenvalues and dynamics of non-Hermitian \(PT\) symmetric Hamiltonians in finite basis spaces ⋮ Supersymmetric generated complex potential with complete real spectrum ⋮ PT symmetry and shape invariance for a potential well with a barrier ⋮ Variational treatment for a complex PT-potential ⋮ Pseudo-Hermiticity of Hamiltonians under gauge-like transformation: real spectrum of non-Hermitian Hamiltonians ⋮ Entanglement entropy of non-unitary integrable quantum field theory ⋮ 𝒫𝒯-symmetric quantum field theory on the noncommutative spacetime ⋮ PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability ⋮ On the K-theoretic classification of dynamically stable systems ⋮ DEFORMED HARMONIC OSCILLATOR FOR NON-HERMITIAN OPERATOR AND THE BEHAVIOR OF PT AND CPT SYMMETRIES ⋮ GBDT and algebro-geometric approaches to explicit solutions and wave functions for nonlocal NLS ⋮ The finite ${\mathcal{PT}}$ -symmetric square well potential ⋮ Quantum dynamics of a parity-time-symmetric kicked particle in a 1D box ⋮ Multicomplex solitons ⋮ Scattering of particles in the presence of harmonic confinement perturbed by a complex absorbing potential ⋮ Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators ⋮ ℓ-oscillators from second-order invariant PDEs of the centrally extended conformal Galilei algebras ⋮ Unified algebraic method to non-Hermitian systems with Lie algebraic linear structure ⋮ Exactly solvable nonseparable and nondiagonalizable two-dimensional model with quadratic complex interaction ⋮ Order-dependent mappings: Strong-coupling behavior from weak-coupling expansions in non-Hermitian theories ⋮ A generalized Swanson Hamiltonian in a second-derivative pseudo-supersymmetric framework ⋮ Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics ⋮ Non-Hermitian trimers: PT-symmetry versus pseudo-Hermiticity ⋮ Yang–Baxter integrable dimers on a strip ⋮ Complex symmetry of first-order differential operators on Hardy space ⋮ Exact solution of D N-type quantum Calogero model through a mapping to free harmonic oscillators ⋮ Monopoles in non-Hermitian systems ⋮ Spectra of $\mathcal{PT}$-symmetric operators under rank-one perturbations ⋮ $\boldsymbol{\mathcal{PT}}$-symmetric potentials having continuous spectra ⋮ Balancing gain and loss in symmetrised multi-well potentials ⋮ Classical and quantum complex Hamiltonian curl forces ⋮ Spectral and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric tight-binding chain with gain and loss ⋮ Construction of potentials with multiple spectral singularities ⋮ On regular and chaotic dynamics of a non- PT -symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain ⋮ A new boson realization of fusion polynomial algebras in non-Hermitian quantum mechanics: γ-deformed su(2) generators, PT -symmetry in Fock space and Higgs algebra ⋮ Exotic entanglement for non-Hermitian Jaynes–Cummings Hamiltonians ⋮ No-signaling principle and Bell inequality in ${\mathcal{PT}}$ -symmetric quantum mechanics ⋮ From pseudo-bosons to pseudo-Hermiticity via multiple generalized Bogoliubov transformations ⋮ PT symmetric evolution, coherence and violation of Leggett–Garg inequalities ⋮ Nonlocality of observable algebras in quasi-Hermitian quantum theory ⋮ Regularization of energy-dependent pointlike interactions in 1D quantum mechanics ⋮ Effective entanglement recovery via operators ⋮ Dynamical symmetry algebras of two superintegrable two-dimensional systems ⋮ Temporal correlation beyond quantum bounds in non-Hermitian PT- symmetric dynamics of a two level system ⋮ Coupled Susy, pseudo-bosons and a deformed su(1,1) Lie algebra ⋮ Behavior of solitary waves of coupled nonlinear Schrödinger equations subjected to complex external periodic potentials with odd- PT symmetry ⋮ Phase transitions as a manifestation of spontaneous unitarity violation ⋮ Quantum thermodynamics aspects with a thermal reservoir based on PT -symmetric Hamiltonians ⋮ First-order nonlinear eigenvalue problems involving functions of a general oscillatory behavior ⋮ Infinite series of time-dependent Dyson maps ⋮ Spectral branch points of the Bloch–Torrey operator ⋮ Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems ⋮ Comment on ‘The operational foundations of PT-symmetric and quasi-Hermitian quantum theory’ ⋮ Robust Photon Transmission in Nonlinear Parity–Time‐Symmetric Cavities ⋮ Quasi‐Blackbody, Bidirectional Super Reflection, and New Total Reflection Produced by Periodic Optical Waveguide Networks Based on Three‐Order PT‐Symmetric Substructures ⋮ Quantum phase transitions in non-Hermitian \(\mathcal{PT}\)-symmetric transverse-field Ising spin chains ⋮ Unbounded Hamiltonians generated by Parseval frames ⋮ Determining the normalization of the quantum field theory vacuum, with implications for quantum gravity ⋮ A fully solvable model of fermionic interaction in \(3 + 1d\) ⋮ On the non-self-adjoint and multiscale character of passive scalar mixing under laminar advection ⋮ \(\mathcal{PT}\) breaking and RG flows between multicritical Yang-Lee fixed points ⋮ Extremely broken generalized \(\mathcal{PT}\) symmetry ⋮ Effect of Environment on the Scattering of Electrons by a Junction of Different Topological Materials ⋮ Non‐Adiabatic Transitions in Parabolic and Super‐Parabolic PT‐Symmetric Non‐Hermitian Systems in 1D Optical Waveguides ⋮ Non‐Hermitian Hartman Effect ⋮ Spin‐Chain‐Star Systems: Entangling Multiple Chains of Spin Qubits ⋮ Lüders Bounds of Leggett–Garg Inequalities, PT$\mathcal {PT}$‐ Symmetric Evolution and Arrow‐of‐Time ⋮ Generalized Gauge Transformation with PT$PT$‐Symmetric Non‐Unitary Operator and Classical Correspondence of Non‐Hermitian Hamiltonian for a Periodically Driven System ⋮ Perturbative light-matter interactions; from first principles to inverse design ⋮ Mini-workshop: Zero-range and point-like singular perturbations: for a spillover to analysis, PDE and differential geometry. Abstracts from the mini-workshop held October 2--8, 2022 ⋮ Electronic states in a quantum Beltrami surface ⋮ Non-linear Schrödinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interaction ⋮ Dynamics of cubic-quintic nonlinear \(\mathcal{PT}\)-symmetry mechanical oscillators ⋮ Dissimilar directional couplers showing ${\mathscr{P}}{\mathscr{T}}$-symmetric-like behavior ⋮ RelativisticZitterbewegungin non-Hermitian photonic waveguide systems ⋮ On the analytical continuation of lattice Liouville theory ⋮ Two-dimensional fractional \(\mathcal{PPT}\)-symmetric cubic-quintic NLS equation: double-loop symmetry breaking bifurcations, ghost states and dynamics ⋮ Data-driven vortex solitons and parameter discovery of 2D generalized nonlinear Schrödinger equations with a \(\mathcal{PT}\)-symmetric optical lattice ⋮ Constructible reality condition of pseudo entropy via pseudo-Hermiticity ⋮ Dynamical behaviour of solitons in a \(\mathcal{P} \mathcal{T} \)-invariant nonlocal nonlinear Schrödinger equation with distributed coefficients ⋮ Bright soliton solutions to a nonlocal nonlinear Schrödinger equation of reverse-time type ⋮ The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics ⋮ Exact solutions of the Schrödinger equation with a complex periodic potential ⋮ The partial-rogue ripple solutions of nonlocal Kadomtsev-Petviashvili equation ⋮ Eigenvalues and eigenfunctions of the perturbed non-Hermitian SSH Hamiltonian with PT symmetry ⋮ Singular spinors as expansion coefficients of local spin-half fermionic and bosonic fields: on the two-fold Wigner degeneracy ⋮ Ternary \(Z_3\)-symmetric algebra and generalized quantum oscillators ⋮ Complex dynamical invariant for a \(\mathcal{PT}\)-symmetric Hamiltonian system in higher dimensions ⋮ A class of exactly solvable real and complex PT symmetric reflectionless potentials ⋮ Dynamic behavior and stability analysis of nonlinear modes in the fourth-order generalized Ginzburg-Landau model with near \(\mathcal{PT}\)-symmetric potentials ⋮ The loom for general fishnet CFTs ⋮ Three-Wave Interaction Equations: Classical and Nonlocal ⋮ Exactly solvable complex PT symmetry potential A[sech(λx) + i tanh(λx)] ⋮ Demonstration of \(\mathcal{PT}\)-symmetric quantum state discrimination ⋮ Rational and semi-rational solutions to the nonlocal Davey-Stewartson III equation ⋮ Conjugations on \(L^2\) space on the real line ⋮ Analytical results for a spin–orbit coupled atom held in a non-Hermitian double well under synchronous combined modulations ⋮ Breakdown of the Meissner effect at the zero exceptional point in non-Hermitian two-band BCS model ⋮ Inverse scattering transform and dynamics of soliton solutions for nonlocal focusing modified Korteweg-de Vries equation ⋮ Graph theory approach to exceptional points in wave scattering ⋮ The beam control in two-channels PT-symmetric waveguide with fractional diffraction effect ⋮ Deep learning soliton dynamics and complex potentials recognition for 1D and 2D \(\mathcal{PT}\)-symmetric saturable nonlinear Schrödinger equations ⋮ Non-Hermitian Ising model at finite temperature ⋮ On \(\mathcal{PT}\)-symmetric semi-discrete coupled integrable dispersionless system ⋮ Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models ⋮ Dynamics of solitons and breathers on a periodic waves background in the nonlocal Mel'nikov equation ⋮ Ground-state and thermal entanglements in non-Hermitian XY system with real and imaginary magnetic fields ⋮ Field patterns without blow up ⋮ Class of finite-dimensional matrices with diagonals that majorize their spectrum ⋮ Solitons in ${\mathscr{P}}{\mathscr{T}}$-symmetric ladders of optical waveguides ⋮ Stable and oscillating solitons of \(\mathcal{PT}\)-symmetric couplers with gain and loss in fractional dimension ⋮ Exact solution of a non-Hermitian PT -symmetric spin chain ⋮ Jordan blocks and the Bethe ansatz III: class 5 model and its symmetries ⋮ Non-standard quantum algebras and finite dimensional PT -symmetric systems ⋮ What if \(\phi^4\) theory in 4 dimensions is non-trivial in the continuum? ⋮ Eigenstates swapping induced by encircling an exceptional point of the non-Hermitian Hamiltonian ⋮ Average spectral density of multiparametric Gaussian ensembles of complex matrices ⋮ Spectral decomposition of some non-self-adjoint operators ⋮ Complex integrals for 3-dimensional non-Hermitian Hamiltonian systems ⋮ Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System ⋮ Fundamental, dipole, and vortex solitons in fractional nonlinear Schrödinger equation with a parity-time-symmetric periodic potential ⋮ Focusing nonlocal nonlinear Schrödinger equation with asymmetric boundary conditions: large-time behavior ⋮ Analytic structure of the associated Legendre functions of the second kind ⋮ Unidirectional zero reflection as gauged parity-time symmetry ⋮ THE METRIC OPERATORS FOR PSEUDO-HERMITIAN HAMILTONIAN
Cites Work
This page was built for publication: Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
