Uniqueness of steady states of Gorini-Kossakowski-Sudarshan-Lindblad equations: a simple proof

TL;DR

This paper provides a straightforward proof for the uniqueness of steady states in GKSL equations and demonstrates its application to various quantum models, enhancing understanding of non-equilibrium quantum systems.

Contribution

It introduces a simple proof for the uniqueness condition of steady states in GKSL equations and applies it to multiple quantum models.

Findings

The proof confirms conditions for unique steady states in GKSL equations.

Applications to models show the practical relevance of the condition.

Examples include the transverse-field Ising, XYZ, and dephasing models.

Abstract

We present a simple proof of a sufficient condition for the uniqueness of non-equilibrium steady states of Gorini-Kossakowski-Sudarshan-Lindblad equations. We demonstrate the applications of the sufficient condition using examples of the transverse-field Ising model, the XYZ model, and the tight-binding model with dephasing.