Non-Hermitian physics and master equations

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.

Scale-free localization and PT symmetry breaking from local non-Hermiticity

“…Whereas NHSE stems from the non-Hermiticity of the entire system, another common scenario in non-Hermitian physics is that the system is subject to local non-Hermiticity. For example, it is often the case that the gain or loss occurs only at the boundaries, preserving the Hermiticity of the bulk system [27][28][29][30][31][32]. The system can be modeled by a Hermitian Hamiltonian with local non-Hermitian terms.…”