Signatures of three coalescing eigenfunctions

TL;DR

This paper characterizes the behaviors of symmetric non-Hermitian quantum systems with three coalescing eigenfunctions, revealing distinct patterns under parameter perturbations and proposing an experimentally accessible physical system.

Contribution

It introduces a perturbation theory-based characterization of three-eigenfunction coalescence in symmetric Hamiltonians, expanding understanding beyond two eigenfunction degeneracies.

Findings

Identification of two main types of eigenvalue and eigenvector patterns

Use of perturbation theory for non-Hermitian operators

Proposal of a physical system for experimental observation

Abstract

Parameter dependent non-Hermitian quantum systems typically not only possess eigenvalue degeneracies, but also degeneracies of the corresponding eigenfunctions at exceptional points. While the effect of two coalescing eigenfunctions on cyclic parameter variation is well investigated, little attention has hitherto been paid to the effect of more than two coalescing eigenfunctions. Here a characterisation of behaviours of symmetric Hamiltonians with three coalescing eigenfunctions is presented, using perturbation theory for non-Hermitian operators. Two main types of parameter perturbations need to be distinguished, which lead to characteristic eigenvalue and eigenvector patterns under cyclic variation. A physical system is introduced for which both behaviours might be experimentally accessible.