# Parallel dynamics between non-Hermitian and Hermitian systems

## TL;DR

This paper uncovers a fundamental link between non-Hermitian and Hermitian systems by demonstrating that their parallel dynamics can be combined to replicate Hermitian evolution, revealing new insights into their relationship.

## Contribution

It introduces a novel theoretical framework connecting non-Hermitian and Hermitian dynamics through exact solutions and superposition principles.

## Key findings

- Parallel dynamics in non-Hermitian systems relate to Hermitian conjugates.
- Superposition of parallel dynamics reproduces Hermitian evolution.
- The work reveals a fundamental connection between non-Hermitian and Hermitian systems.

## Abstract

We study the connection between a family of non-Hermitian Hamiltonians H and Hermitian ones H based on exact solutions. In general, for a dynamic process in a non-Hermitian system H, there always exists a parallel dynamic process governed by the corresponding Hermitian conjugate Hamiltonian H{\dag}. We show that a linear superposition of the two parallel dynamics is exactly equivalent to the time evolution of a state under a Hermitian Hamiltonian H. It reveals a novel connection between non-Hermitian and Hermitian systems.