Converting non-Hermitian degeneracies of any order: Hierarchies of exceptional points and degeneracy manifolds

TL;DR

This paper explores how non-Hermitian degeneracies, specifically Exceptional Points, can be transformed under perturbations to create hierarchies of degeneracies, enhancing system sensitivity and engineering capabilities.

Contribution

It introduces a systematic method to convert and classify degeneracies of any order in non-Hermitian systems, expanding the understanding of their hierarchical structure.

Findings

Derogatory EPs can be converted into different structures without changing total degeneracy

Conversion can increase the size of Jordan blocks, boosting sensitivity

Hierarchies of degeneracies are characterized in systems with and without symmetry

Abstract

The emergence of various types of degeneracies plays a crucial role in optimizing and engineering different physical phenomena in non-Hermitian physics. In our work, we focus on the derogatory Exceptional Points (EPs), which are characterized by multiple Jordan blocks corresponding to the same eigenvalue. We demonstrate that, under certain infinitesimal perturbations, a derogatory EP can be converted into an EP of different structure without varying the total order of degeneracy. In particular, such conversion can increase the size of the largest Jordan block and, hence, the sensitivity of the eigenspectrum to parameter variation, which is an important feature for practical applications. Furthermore, by analyzing all possible conversions, we introduce hierarchies of degeneracies of the same order that appear when perturbing non-Hermitian systems. We systematically explore hierarchies in the absence of any symmetry and when pseudo-Hermitian symmetry is present. Our study facilitates engineering various degeneracies of non-Hermitian systems, paving the way to extending the implications of non-Hermitian physics.