From Pseudo-bosons to Pseudo-Hermiticity via multiple generalized Bogoliubov transformations

Abstract

We consider the special type of pseudo-bosonic systems that can be mapped to standard bosons by means of generalized Bogoliubov transformation and demonstrate that a pseudo-Hermitian systems can be obtained from them by means of a second subsequent Bogoliubov transformation. We employ these operators in a simple model and study three different types of scenarios for the constraints on the model parameters giving rise to a Hermitian system, a pseudo-Hermitian system in which the second the Bogoliubov transformations is equivalent to the associated Dyson map and one in which we obtain D-quasi bases.

10 pages, 1 figure

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Cited by in corpus (5)

• Exactly solvable time-dependent non-Hermitian quantum systems from point transformations
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
• Spectrum and normal modes of non-hermitian quadratic boson operators
• Exact solution for the time dependent non-Hermitian generalized Swanson oscillator
• Swanson Hamiltonian: non-PT-symmetry phase