The Uniqueness of Steady States of the Gorini-Kossakowski-Sudarshan-Lindblad Equation: A Simple Proof

The dynamics of Markovian open quantum systems are described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. In the presence of dissipation, quantum systems relax to a steady state. In the language of the GKSL equation, the steady state is an eigenmode with zero eigenvalue. There always exists at least one steady state in a finite-dimensional system, but its uniqueness depends on the system.

In this talk, we discuss a simple proof of a sufficient condition for the uniqueness of the steady state and demonstrate its applications using examples of open quantum many-body systems.