Relative Entropy as a Measure of Difference Between Hermitian and Non-Hermitian Systems

TL;DR

This paper uses relative entropy to quantify differences in eigenmodes between Hermitian and non-Hermitian systems in optical microcavities, revealing how interactions influence mode exchange.

Contribution

It introduces the use of relative entropy as a metric to compare eigenmodes in Hermitian and non-Hermitian systems, highlighting interaction-dependent behaviors.

Findings

Large relative entropy in the collective Lamb shift range

Small relative entropy in the self-energy range

Distinct eigenmode exchange behaviors under weak and strong interactions

Abstract

We employ the relative entropy as a measure to quantify the difference of eigenmodes between Hermitian and non-Hermitian systems in elliptic optical microcavities. We have found that the average value of the relative entropy in the range of the collective Lamb shift is large, while that in the range of self-energy is small. Furthermore, the weak and strong interactions in the non-Hermitian system exhibit rather different behaviors in term of the relative entropy, and thus it displays an obvious exchange of eigenmodes in the elliptic microcavity.