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

• URL: http://arxiv.org/abs/2504.12507v1
• Date: Wed, 16 Apr 2025 21:59:05 GMT
• Title: UniqueNESS: Graph Theory Approach to the Uniqueness of Non-Equilibrium Stationary States of the Lindblad Master Equation
• Authors: Martin Seltmann, Berislav Buca,
• Abstract summary: dimensionality of kernels for Lindbladian superoperators is of physical interest in various scenarios out of equilibrium.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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