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

The dynamics of Markovian open quantum systems are governed by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation. A fundamental property of this equation is the possible degeneracy of its steady states. In particular, when the steady state is unique, any initial state will eventually relax to it. There has been extensive research on the uniqueness of steady states for GKSL equations with time-independent generators. Recently, the interplay between periodic driving and dissipation has attracted growing interest. However, general results concerning the uniqueness of steady states in time-periodic settings remain limited. In this talk, we present a general and rigorous criterion for the uniqueness of steady states in GKSL equations with time-periodic generators, assuming Hermitian jump operators.