Non-Hermitian Oscillator and R-deformed Heisenberg Algebra

TL;DR

This paper explores a non-Hermitian oscillator model within R-deformed Heisenberg algebra, revealing its conformal symmetry, spectrum, and superconformal structure, and discusses an anomaly in the Hermitian counterpart's spectrum.

Contribution

It introduces a generalized non-Hermitian oscillator model with R-deformed algebra, diagonalizes it using Bogoliubov transformation, and analyzes its symmetry and spectral properties.

Findings

The Hamiltonian exhibits conformal symmetry.

The spectrum is obtained algebraically.

An anomaly in the Hermitian counterpart's spectrum is discussed.

Abstract

A non-Hermitian generalized oscillator model, generally known as the Swanson model, has been studied in the framework of R-deformed Heisenberg algebra. The non-Hermitian Hamiltonian is diagonalized by generalized Bogoliubov transformation. A set of deformed creation annihilation operators is introduced whose algebra shows that the transformed Hamiltonian has conformal symmetry. The spectrum is obtained using algebraic technique. The superconformal structure of the system is also worked out in detail. An anomaly related to the spectrum of the Hermitian counterpart of the non-Hermitian Hamiltonian with generalized ladder operators is shown to occur and is discussed in position dependent mass scenario.