# State conversions around exceptional points

## TL;DR

This paper investigates state conversion in non-Hermitian PT-symmetric systems, establishing a theory for adiabatic evolution and topological features, revealing how systems can follow stable eigenstates under slow parameter changes.

## Contribution

It introduces a theoretical framework for adiabatic evolution in non-Hermitian systems and explains the mechanism of state conversion around exceptional points.

## Key findings

- System can adiabatically follow stable eigenstates regardless of initial conditions.
- The theory explains state conversion mechanisms in PT-symmetric systems.
- Topological features of dynamical circling are discussed.

## Abstract

We study state conversion in parity-time (PT) symmetry broken non-Hermitian two level system. We construct a theory and explain underlying mechanism for state conversion and define adiabatic evolutions in non-Hermitian systems. The adiabatic theorem can be used if initial state is an instantaneous eigenstate in Hermitian systems. We show that the system can adiabatically follow the modulationally stable instantaneous eigenstate sooner or later, regardless of initial state if the system parameters are varied slowly in non-Hermitian systems. We discuss the topological feature of dynamical circling in the parameter space.