Analysis of multiple exceptional points related to three interacting eigenmodes in a non-Hermitian Hamiltonian

TL;DR

This paper explores the behavior of three interacting eigenmodes near exceptional points in non-Hermitian systems, revealing how encircling multiple EPs affects mode evolution and recovery.

Contribution

It introduces a detailed analysis of multiple exceptional points involving three modes, including numerical validation with microdisks and matrix models.

Findings

Encircling two EPs three times restores initial mode configuration.

Encircling three EPs twice also recovers the initial modes.

Numerical simulations confirm theoretical predictions.

Abstract

We have investigated the exceptional points (EPs) which are degeneracies of a non-Hermitian Hamiltonian, in the case that three modes are interacting with each other. Even though the parametric evolution of the modes cannot be uniquely determined when encircling more than two EPs once, we can recover the initial configuration of the modes by encircling two EPs three times or three EPs twice. We confirm our expectation by numerically calculating the modes of an open quantum system, two dielectric microdisks, and 3$\times$3 matrix model.