UniqueNESS: Graph Theory Approach to the Uniqueness of Non-Equilibrium Stationary States of the Lindblad Master Equation

The dimensionality of kernels for Lindbladian superoperators is of physical interest in various scenarios out of equilibrium, for example in mean-field methods for driven-dissipative spin lattice models that give rise to phase diagrams with a multitude of non-equilibrium stationary states in specific parameter regions. We show that known criteria established in the literature for unique fixpoints of the Lindblad master equation can be better treated in a graph-theoretic framework via a focus on the connectivity of directed graphs associated to the Hamiltonian and jump operators.