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

TL;DR

This paper explores how pseudo-bosonic systems can be transformed into pseudo-Hermitian systems through multiple generalized Bogoliubov transformations, revealing new links between these quantum frameworks.

Contribution

It demonstrates a method to derive pseudo-Hermitian systems from pseudo-bosonic ones using successive Bogoliubov transformations, expanding the understanding of their interrelation.

Findings

Pseudo-bosonic systems can be mapped to standard bosons via generalized Bogoliubov transformations.

Pseudo-Hermitian systems can be obtained through a second Bogoliubov transformation.

Different parameter constraints lead to Hermitian, pseudo-Hermitian, or D-quasi basis scenarios.

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.