Non-Hermitian physics and master equations

TL;DR

This paper reviews the connection between non-Hermitian Hamiltonians and GKSL master equations in open quantum systems, highlighting their relation and differences, especially regarding exceptional points and system evolution.

Contribution

It provides a concise overview of how non-Hermitian physics relates to traditional master equations in quantum mechanics, clarifying their interplay and applications.

Findings

Non-Hermitian Hamiltonians can be connected to GKSL master equations.

Exceptional points are a key feature of non-Hermitian systems.

The review clarifies the relation between two approaches in open quantum systems.

Abstract

A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with non-Hermitian Hamiltonians, which have attracted great interest in the last twenty years due to a number of unconventional properties, such as the appearance of exceptional points. Here, we present a short review of these two different approaches aiming in particular to highlight their relation and illustrate different ways of connecting non-Hermitian Hamiltonian to a GKSL master equation for the full density matrix.