Non-Hermitian formalism and nonlinear physics

TL;DR

This paper clarifies that the features of non-Hermitian formalism in open quantum systems are essentially nonlinearities linked to exceptional points, explaining complex phenomena and system dynamics.

Contribution

It demonstrates that non-Hermitian features are fundamentally nonlinearities associated with exceptional points, simplifying understanding of the formalism.

Findings

Non-Hermitian features are nonlinearities.

Exceptional points are key to system behavior.

Explains counterintuitive experimental results.

Abstract

The non-Hermitian formalism is used at present in many papers for the description of open quantum systems. A special language developed in this field of physics which makes it difficult for many physicists to follow and to understand the corresponding papers. We show that the characteristic features of the non-Hermitian formalism are nothing but nonlinearities that may appear in the equations when the Hamiltonian is non-Hermitian. They are related directly to singular points (called mostly exceptional points, EPs). At low level density, they may cause counterintuitive physical results which allow us to explain some puzzling experimental results. At high level density, they determine the dynamics of the system.