Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians

Abstract

We propose a procedure to obtain exact analytical solutions to the time-dependent Schrödinger equations involving explicit time-dependent Hermitian Hamitonians from solutions to time-independent non-Hermitian Hamiltonian systems and the time-dependent Dyson relation together with the time-dependent quasi-Hermiticity relation. We illustrate the working of this method for a simple Hermitian Rabi-type model by relating it to a non-Hermitian time-independent system corresponding to the one-site lattice Yang-Lee model.

5 pages

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• Exactly solvable time-dependent non-Hermitian quantum systems from point transformations
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
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• Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories
• Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems
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• $\mathcal{P}\mathcal{T}$-symmetric quantum Rabi model: Solutions and exceptional points
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• Analytical Study of the Non-Hermitian Semiclassical Rabi Model
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• A real expectation value of the time-dependent non-Hermitian Hamiltonians
• Intrinsic exceptional point -- a challenge in quantum theory
• Anti-$\mathcal{P}\mathcal{T}$-symmetric Qubit: Decoherence and Entanglement Entropy
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• Anisotropy and asymptotic degeneracy of the physical-Hilbert-space inner-product metrics in an exactly solvable crypto-unitary quantum model
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