Characteristic influence of exceptional points in quantum dynamics

TL;DR

This paper reviews how exceptional points in non-Hermitian quantum systems affect dynamics, classifies different types of these points, and explores their influence through simple models, highlighting the role of the continuum threshold.

Contribution

It introduces a classification of exceptional points in quantum systems and analyzes their impact on dynamics using simple models, emphasizing the role of the continuum threshold.

Findings

Exceptional points cause coalescence of eigenstates affecting quantum dynamics.

The continuum threshold significantly influences behavior near exceptional points.

Different types of exceptional points lead to distinct dynamical effects.

Abstract

We review some recent work on the occurrence of coalescing eigenstates at exceptional points in non-Hermitian systems and their influence on physical quantities. We particularly focus on quantum dynamics near exceptional points in open quantum systems, which are described by an outwardly Hermitian Hamiltonian that gives rise to a non-Hermitian effective description after one projects out the environmental component of the system. We classify the exceptional points into two categories: those at which two or more resonance states coalesce and those at which at least one resonance and the partnering anti-resonance coalesce (possibly including virtual states as well), and we introduce several simple models to explore the dynamics for both of these types. In the latter case of coalescing resonance and anti-resonance states, we show that the presence of the continuum threshold plays a strong role in shaping the dynamics, in addition to the exceptional point itself. We also briefly discuss the special case in which the exceptional point appears directly at the threshold.