Pseudo Hermitian Generalized Dirac Oscillators

TL;DR

This paper investigates complex interactions in generalized Dirac oscillators, demonstrating their pseudo-Hermitian properties, providing exact solutions, and establishing connections with well-known quantum models like Jaynes Cummings.

Contribution

It introduces a class of pseudo-Hermitian generalized Dirac oscillators with exact solutions and links them to quantum optical models.

Findings

Dirac Hamiltonians are η pseudo-Hermitian with specific metrics

Exact solutions obtained for certain interactions

Connections established with Jaynes Cummings models

Abstract

We study generalized Dirac oscillators with complex interactions in $(1+1)$ dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are $\eta$ pseudo Hermitian with respect to certain metric operators $\eta$. Exact solutions of the generalized Dirac Oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with Anti Jaynes Cummings type model and by spin flip it can also be identified with Jaynes Cummings type model.