Closed formula for the metric in the Hilbert space of a PT-symmetric model

Abstract

We introduce a very simple, exactly solvable PT-symmetric non-Hermitian model with real spectrum, and derive a closed formula for the metric operator which relates the problem to a Hermitian one.

LaTeX, 13 pages; to appear in Journal of Physics A

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Cited by in corpus (56)

• Pseudo-Hermitian Representation of Quantum Mechanics
• Mathematical and physical aspects of complex symmetric operators
• Pseudospectra in non-Hermitian quantum mechanics
• On the metric operator for the imaginary cubic oscillator
• Breaking of PT-symmetry in bounded and unbounded scattering systems
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Discrete PT-symmetric models of scattering
• Non-Hermitian Hamiltonians of Lie algebraic type
• A return to observability near exceptional points in a schematic PT-symmetric model
• Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
• Perfect transmission scattering as a PT-symmetric spectral problem
• PT-symmetric models in curved manifolds
• Non-self-adjoint graphs
• Complete Set of Inner Products for a Discrete PT-symmetric Square-well Hamiltonian
• On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators
• Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry
• The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics
• PT-symmetric deformations of Calogero models
• Non-Hermitian spectral effects in a PT-symmetric waveguide
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Three solvable matrix models of a quantum catastrophe
• Exact Isospectral Pairs of PT-Symmetric Hamiltonians
• Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?
• Quantum star-graph analogues of PT-symmetric square wells
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• Thermodynamics of Pseudo-Hermitian Systems in Equilibrium
• Unbounded C-symmetries and their nonuniqueness
• Solvable non-Hermitian discrete square well with closed-form physical inner product
• Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration
• Non-Hermitian multi-particle systems from complex root spaces
• Hilbert space inner products for PT-symmetric Su-Schrieffer-Heeger models
• Non-Hermitian Hamiltonians and similarity transformations
• Exponential decay for the Schr{ö}dinger equation on a dissipative waveguide
• The Pauli equation with complex boundary conditions
• A generalized family of discrete PT-symmetric square wells
• Quantum graphs: self-adjoint, and yet exhibiting a nontrivial $\mathcal{P}\mathcal{T}$-symmetry
• Metric operators for non-Hermitian quadratic su(2) Hamiltonians
• Complex magnetic fields: An improved Hardy-Laptev-Weidl inequality and quasi-self-adjointness
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
• Equivalent Hermitian operator from supersymmetric quantum mechanics
• Nonuniqueness of the C operator in PT-symmetric quantum mechanics
• Quantum star-graph analogues of PT-symmetric square wells. II: Spectra
• On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials
• Guiding structures with multiply connected cross-sections: evolution of propagation in external fields at complex Robin parameters
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Discrete spectrum of thin PT-symmetric waveguide
• Hidden symmetries in non-self-adjoint graphs
• CPT-symmetric discrete square well
• Bifurcation of nonlinear eigenvalues in problems with antilinear symmetry
• Surprising spectra of PT-symmetric point interactions
• Contact interactions and Kronig-Penney Models in Hermitian and PT-symmetric Quantum Mechanics
• Origin of folded bands in metamaterial crystals
• Mathematical and physical meaning of the crossings of energy levels in $\mathcal{P}\mathcal{T}-$symmetric systems
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity