UniqueNESS: Graph Theory Approach to the Uniqueness of Non-Equilibrium Stationary States of the Lindblad Master Equation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915247426633728 |
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| author | Seltmann, Martin Buca, Berislav |
| author_facet | Seltmann, Martin Buca, Berislav |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_12507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | UniqueNESS: Graph Theory Approach to the Uniqueness of Non-Equilibrium Stationary States of the Lindblad Master Equation Seltmann, Martin Buca, Berislav Quantum Physics Statistical Mechanics Mathematical Physics 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. |
| title | UniqueNESS: Graph Theory Approach to the Uniqueness of Non-Equilibrium Stationary States of the Lindblad Master Equation |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2504.12507 |