Time evolution of non-Hermitian Hamiltonian systems

Abstract

We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian Hamiltonians, which are therefore pseudo-Hermitian and in addition in some cases also invariant under PT-symmetry. In particular, for the harmonic oscillator perturbed by a cubic non-Hermitian term, we evaluate explicitly various transition amplitudes, for the situation when these systems are exposed to a monochromatic linearly polarized electric field.

25 pages Latex, 1 eps figure, references added

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• Adiabatic theorem for non-hermitian time-dependent open systems
• PT-Symmetric Quantum Electrodynamics
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Cited by in corpus (77)

• Pseudo-Hermitian Representation of Quantum Mechanics
• Time-dependent version of cryptohermitian quantum theory
• Unitary quantum evolution for time-dependent quasi-Hermitian systems with non-observable Hamiltonians
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Time Dependent $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Spectral and transport properties of time-periodic PT-symmetric tight-binding lattices
• Delta-Function Potential with a Complex Coupling
• The non-Hermitian Swanson model with a time-dependent metric
• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• Geometric Phase in PT-Symmetric Quantum Mechanics
• On the invariant method for the time-dependent non-Hermitian Hamiltonians
• Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians
• 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
• Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
• 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
• PT-symmetric deformations of integrable models
• Non-Hermitian Hamiltonians of Lie algebraic type
• Eternal life of entropy in non-Hermitian quantum systems
• Irreversibility of the renormalization group flow in non-unitary quantum field theory
• Isospectral Hamiltonians from Moyal products
• Solvable two dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime
• Generalized Swanson models and their solutions
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields
• The quantum brachistochrone problem for non-Hermitian Hamiltonians
• Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions
• Non-Hermitian Heisenberg representation
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Crypto-unitary forms of quantum evolution operators
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• Exactly solvable time-dependent non-Hermitian quantum systems from point transformations
• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• Non-Hermitian coupled cluster method for non-stationary systems and its interaction-picture reinterpretation
• From Pseudo-bosons to Pseudo-Hermiticity via multiple generalized Bogoliubov transformations
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Pseudo supersymmetric partners for the generalized Swanson model
• Real spectra for non-Hermitian Dirac equation in 1+1 dimensions with a most general coupling
• Quantum centrality testing on directed graphs via PT-symmetric quantum walks
• Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
• Metric versus observable operator representation, higher spin models
• Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
• Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians
• Conformal bridge transformation and PT symmetry
• Non linear pseudo-bosons versus hidden Hermiticity
• On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
• Non-Hermitian multi-particle systems from complex root spaces
• Solvable non-Hermitian discrete square well with closed-form physical inner product
• Time-dependent metric for the two dimensional, non-Hermitian coupled oscillator
• Non-Hermitian systems of Euclidean Lie algebraic type with real eigenvalue spectra
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Solvable dilation model of $\mathcal{P}\mathcal{T}$-symmetric systems
• Anomalous real spectra of non-Hermitian quantum graphs in strong-coupling regime
• The Bender-Dunne basis operators as Hilbert space operators
• Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations
• 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
• Quasi-Hermitian formulation of quantum mechanics using two conjugate Schrödinger equations
• Exact solutions for time-dependent complex symmetric potential well
• Theory Including Future Not Excluded -- Formulation of Complex Action Theory II --
• Instantaneous modulations in time-varying complex optical potentials
• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians
• Lewis-Riesenfeld invariants for PT-symmetrically coupled oscillators from two dimensional point transformations and Lie algebraic expansions
• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity
• A real expectation value of the time-dependent non-Hermitian Hamiltonians
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• Consistent treatment of quantum systems with a time-dependent Hilbert space
• Three alternative model-building strategies using quasi-Hermitian time-dependent observables
• Euler Polynomials and Identities for Non-Commutative Operators
• Infinite series of time-dependent Dyson maps
• Emergence and localization of exceptional points in an exactly solvable toy model
• Mutual compatibility/incompatibility of quasi-Hermitian quantum observables
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry