Time-dependent \(\mathcal{C}\)-operators as Lewis-Riesenfeld invariants in non-Hermitian theories

DOI10.1016/j.physleta.2022.128458OpenAlexW4296652952MaRDI QIDQ2093742

Takanobu Taira, Andreas Fring, Rebecca Tenney

Publication date: 27 October 2022

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.10965

zbMATH Keywords

Lewis-Riesenfeld invariants\(\mathcal{PT}\)-symmetrytime-dependent systemsnon-Hermitian systems\(\mathcal{C}\)-operators

Mathematics Subject Classification ID

Quantum theory (81-XX) Statistical mechanics, structure of matter (82-XX)

Related Items (3)

Real energies and Berry phases in all PT-regimes in time-dependent non-Hermitian theories ⋮ Lewis–Riesenfeld invariants for PT-symmetrically coupled oscillators from two-dimensional point transformations and Lie algebraic expansions ⋮ Application of the Lewis-Riesenfeld quantum mechanical invariant method for description of electron tunneling transport in nitride multilayer quantum well nanostructures

Cites Work

• \(\mathcal P\mathcal T\)-symmetric quantum electrodynamics
• Dual \(\mathcal P\mathcal T\)-symmetric quantum field theories
• Time-dependent pseudo-Hermitian Hamiltonians defining a unitary quantum system and uniqueness of the metric operator
• Isospectral Hamiltonians from Moyal products
• Quasi-Hermitian operators in quantum mechanics and the variational principle
• Mending the broken PT-regime via an explicit time-dependent Dyson map
• Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
• Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories
• Exactly solvable time-dependent non-Hermitian quantum systems from point transformations
• Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians
• Semiclassical calculation of the \(\mathcal C\) operator in \(\mathcal{PT}\)-symmetric quantum mechanics
• Complex Extension of Quantum Mechanics
• Time-dependent $\mathcal {P}$$\mathcal {T}$-symmetric quantum mechanics
• Non-Selfadjoint Operators in Quantum Physics
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• Choice of a metric for the non-Hermitian oscillator
• Metrics and isospectral partners for the most generic cubic {\cal PT} -symmetric non-Hermitian Hamiltonian
• Metric operators for quasi-Hermitian Hamiltonians and symmetries of equivalent Hermitian Hamiltonians
• A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field
• 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
• Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• Exact Quantization Conditions. II
• PT Symmetry
• Time evolution of non-Hermitian Hamiltonian systems
• Non-Hermitian Hamiltonians of Lie algebraic type
• Exotic entanglement for non-Hermitian Jaynes–Cummings Hamiltonians
• Infinite series of time-dependent Dyson maps
• On biorthogonal systems
• Unnamed Item

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