Perturbation theory of PT-symmetric Hamiltonians

TL;DR

This paper develops a perturbation theory framework to prove the reality of eigenvalues in PT-symmetric Hamiltonians, demonstrating stability under perturbations with additional PT-symmetric interactions.

Contribution

It introduces a stability-based perturbation method to establish eigenvalue reality in PT-symmetric quantum systems under perturbations.

Findings

Eigenvalues remain real under certain PT-symmetric perturbations

Stability techniques effectively analyze eigenvalue behavior

Method applicable to a class of PT-symmetric Hamiltonians

Abstract

In the framework of perturbation theory the reality of the perturbed eigenvalues of a class of $\PT$symmetric Hamiltonians is proved using stability techniques. We apply this method to $\PT$symmetric unperturbed Hamiltonians perturbed by $\PT$symmetric additional interactions.