Classification of the conditionally observable spectra exhibiting central symmetry

TL;DR

This paper introduces a classification method for PT-symmetric quantum systems with central symmetry, simplifying the analysis of their energy level mergers by leveraging spectral duality.

Contribution

It presents a novel approach to classify spectra of PT-symmetric systems using spectral duality and symmetry considerations.

Findings

Spectral duality simplifies classification of energy levels.

Central symmetry leads to specific merger patterns.

Method enhances understanding of PT-symmetric spectral structures.

Abstract

We show how in PT-symmetric 2J-level quantum systems the assumption of an upside-down symmetry (or duality) of their spectra simplifies their classification based on the non-equivalent pairwise mergers of the energy levels.