Time-dependent version of cryptohermitian quantum theory

Abstract

For many quantum models an apparent non-Hermiticity of observables corresponds to their hidden Hermiticity in another, physical Hilbert space. For these models we show that the existence of observables which are manifestly time-dependent may require the use of a manifestly time-dependent representation of the physical Hilbert space of states.

14 pp

References in corpus (25)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Time evolution of non-Hermitian Hamiltonian systems
• Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
• Conceptual Problems in Scattering from Localized non-Hermitian Potentials
• Quantum Mechanics of Klein-Gordon-Type Fields and Quantum Cosmology
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Scattering theory with localized non-Hermiticities
• Quantum Mechanics of Klein-Gordon Fields I: Hilbert Space, Localized States, and Chiral Symmetry
• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
• Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
• Pseudo-Hermitian approach to energy-dependent Klein-Gordon models
• Anomalies in PT-Symmetric Quantum Field Theory
• Propagation of Electromagnetic Waves in Linear Media and Pseudo-Hermiticity
• Thermodynamics of Pseudo-Hermitian Systems in Equilibrium
• Time-dependent quasi-Hermitian Hamiltonians and the unitarity of quantum evolution
• Wave Function of the Universe and Its Meaning
• On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm
• Which operator generates time evolution in Quantum Mechanics?
• Dynamics of charged fluids and 1/L perturbation expansions
• Quasistationary quaternionic Hamiltonians and complex stochastic maps

Cited by in corpus (84)

• Unitary quantum evolution for time-dependent quasi-Hermitian systems with non-observable Hamiltonians
• Time Dependent $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Three-Hilbert-Space Formulation of Quantum Mechanics
• The non-Hermitian Swanson model with a time-dependent metric
• Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians
• Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism
• Non-Hermitian interaction representation and its use in relativistic quantum mechanics
• Time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics in generic non-Hermitian systems
• Energy Observable for a Quantum System with a Dynamical Hilbert Space and a Global Geometric Extension of Quantum Theory
• Mending the broken PT-regime via an explicit time-dependent Dyson map
• Passive $\mathcal{P}\mathcal{T}$-symmetry breaking transitions without exceptional points in dissipative photonic systems
• Eternal life of entropy in non-Hermitian quantum systems
• Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics
• Unitarity corridors to exceptional points
• Solvable two dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime
• The problem of coexistence of several non-Hermitian observables in PT-symmetric quantum mechanics
• Non-Hermitian Heisenberg representation
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Exactly solvable time-dependent non-Hermitian quantum systems from point transformations
• Crypto-unitary forms of quantum evolution operators
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
• Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Multiply Degenerate Exceptional Points and Quantum Phase Transitions
• Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach
• Repeatability of measurements: Equivalence of hermitian and non-hermitian observables
• Complex symmetric Hamiltonians and exceptional points of order four and five
• Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians
• Hidden PT Symmetry and quantization of coupled-oscillators model of QASER
• Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
• Metric versus observable operator representation, higher spin models
• Enhancement of photon creation through the pseudo-Hermitian dynamical Casimir effect
• Non linear pseudo-bosons versus hidden Hermiticity
• Unitary evolution for a two-level quantum system in fractional-time scenario
• Wheeler-DeWitt equation and the applicability of crypto-Hermitian interaction representation in quantum cosmology
• Phase space representation of non-Hermitian system with $\mathcal{P}\mathcal{T}$-symmetry
• Time-dependent metric for the two dimensional, non-Hermitian coupled oscillator
• Spectrum and normal modes of non-hermitian quadratic boson operators
• Quantum Big Bang without fine-tuning in a toy-model
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Hybrid form of quantum theory with non-Hermitian Hamiltonians
• Composite quantum Coriolis forces
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Solvable dilation model of $\mathcal{P}\mathcal{T}$-symmetric systems
• The Pauli equation with complex boundary conditions
• Anomalous real spectra of non-Hermitian quantum graphs in strong-coupling regime
• Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories
• Real energies and Berry phases in all PT-regimes in time-dependent non-Hermitian theories
• Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems
• Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions
• Paths of unitary access to exceptional points
• Quasi-Hermitian formulation of quantum mechanics using two conjugate Schrödinger equations
• Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
• Broken Hermiticity phase transition in Bose-Hubbard model
• Exact solutions for time-dependent complex symmetric potential well
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• Pseudo-Hermitian continuous-time quantum walks
• Quantization of Big Bang in crypto-Hermitian Heisenberg picture
• Scattering in pseudo-Hermitian quantum field theory and causality violation
• Non-stationary non-Hermitian "wrong-sign'' quantum oscillators and their meaningful physical interpretation
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Balanced gain and loss in spatially extended non-$\mathcal{P}\mathcal{T}$-symmetric multi-well potentials
• Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
• Lewis-Riesenfeld invariants for PT-symmetrically coupled oscillators from two dimensional point transformations and Lie algebraic expansions
• Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• A real expectation value of the time-dependent non-Hermitian Hamiltonians
• Quantum control and the challenge of non-Hermitian model-building
• Quantum implementation of non-unitary operations with biorthogonal representations
• Features, paradoxes and amendments of perturbative non-Hermitian quantum mechanics
• Intrinsic exceptional point -- a challenge in quantum theory
• Comment on 'The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'
• Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: I. Inherited and genuine singularities
• Anti-$\mathcal{P}\mathcal{T}$-symmetric Qubit: Decoherence and Entanglement Entropy
• Entanglement of pseudo-Hermitian random states
• Three alternative model-building strategies using quasi-Hermitian time-dependent observables
• Consistent treatment of quantum systems with a time-dependent Hilbert space
• PT-symmetric quantum models living in an auxiliary Pontryagin space
• Infinite series of time-dependent Dyson maps
• The dynamical problem for a non self-adjoint Hamiltonian
• Emergence and localization of exceptional points in an exactly solvable toy model
• Anisotropy and asymptotic degeneracy of the physical-Hilbert-space inner-product metrics in an exactly solvable crypto-unitary quantum model
• Mutual compatibility/incompatibility of quasi-Hermitian quantum observables