Pseudo-hermitian interaction between an oscillator and a spin half particle in the external magnetic field

TL;DR

This paper investigates a spin-half particle coupled to a harmonic oscillator via a pseudo-Hermitian interaction, demonstrating that the system's energy eigenvalues remain real despite the interaction lacking PT symmetry.

Contribution

It introduces a novel pseudo-Hermitian interaction model between a spin-half particle and an oscillator, showing real energy spectra without PT invariance.

Findings

Energy eigenvalues are real despite non-PT invariant interaction

Pseudo-Hermitian interactions can produce physically meaningful spectra

The model extends understanding of non-Hermitian quantum systems

Abstract

We consider a spin half particle in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction. We find that the energy eigenvalues for this system are real even though the interaction is not PT invariant.