Exceptional points in open and PT symmetric systems

TL;DR

This paper investigates the role of exceptional points in open and PT symmetric systems, revealing how they influence system dynamics and symmetry breaking through analytical and numerical comparisons.

Contribution

It provides a comparative analysis of eigenvalues and eigenfunctions near exceptional points in open quantum and PT symmetric optical systems, highlighting their universal features.

Findings

Eigenvalues and eigenfunctions show characteristic features near EPs

Environmental influence is evident in both systems

Systems exhibit similar behavior despite differences

Abstract

Exceptional points (EPs) determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions (eigenfunctions of a non-Hermitian Hamiltonian) relative to one another are not rigid when an EP is approached. The system is therefore able to align with the environment to which it is coupled and, consequently, rigorous changes of the system properties may occur. We compare analytically as well as numerically the eigenvalues and eigenfunctions of a $2\times 2$ matrix that is characteristic of either open quantum systems at high level density or of PT symmetric optical lattices. In both cases, the results show clearly the influence of the environment onto the system in the neighborhood of EPs. Although the systems are very different from one another, the eigenvalues and eigenfunctions indicate the same characteristic features.