General description of quasi-adiabatic dynamical phenomena near exceptional points

TL;DR

This paper investigates quasi-adiabatic phenomena near exceptional points in non-Hermitian systems, revealing a characteristic switching behavior and providing a framework to understand adiabatic breakdown and chiral effects.

Contribution

It introduces a general framework connecting quasi-adiabatic dynamics near exceptional points to stability loss delay, enhancing understanding of non-Hermitian system behaviors.

Findings

Identification of quasi-stationary periods with abrupt transitions

Quantitative description of stability loss delay effects

Prediction of adiabatic theorem breakdown and chiral behavior

Abstract

The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process predicted for an adiabatic encircling of an exceptional point. In this work we analyse this and related processes for the generic system of two coupled oscillator modes with loss or gain. We identify a characteristic system evolution consisting of periods of quasi-stationarity interrupted by abrupt non-adiabatic transitions, and we present a qualitative and quantitative description of this switching behaviour by connecting the problem to the phenomenon of stability loss delay. This approach makes accurate predictions for the breakdown of the adiabatic theorem as well as the occurrence of chiral behavior observed previously in this context, and provides a general framework to model and understand quasi-adiabatic dynamical effects in non-Hermitian systems.