Trace distance ergodicity for quantum Markov semigroups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866916113278828544 |
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| author | Bertini, Lorenzo De Sole, Alberto Posta, Gustavo |
| author_facet | Bertini, Lorenzo De Sole, Alberto Posta, Gustavo |
| contents | We discuss the quantitative ergodicity of quantum Markov semigroups in terms of the trace distance from the stationary state, providing a general criterion based on the spectral decomposition of the Lindblad generator. We then apply this criterion to the bosonic and fermionic Ornstein-Uhlenbeck semigroups and to a family of quantum Markov semigroups parametrized by semisimple Lie algebras and their irreducible representations, in which the Lindblad generator is given by the adjoint action of the Casimir element. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_11923 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Trace distance ergodicity for quantum Markov semigroups Bertini, Lorenzo De Sole, Alberto Posta, Gustavo Mathematical Physics Statistical Mechanics Representation Theory Primary 81S22, Secondary 47A35, 17B10 We discuss the quantitative ergodicity of quantum Markov semigroups in terms of the trace distance from the stationary state, providing a general criterion based on the spectral decomposition of the Lindblad generator. We then apply this criterion to the bosonic and fermionic Ornstein-Uhlenbeck semigroups and to a family of quantum Markov semigroups parametrized by semisimple Lie algebras and their irreducible representations, in which the Lindblad generator is given by the adjoint action of the Casimir element. |
| title | Trace distance ergodicity for quantum Markov semigroups |
| topic | Mathematical Physics Statistical Mechanics Representation Theory Primary 81S22, Secondary 47A35, 17B10 |
| url | https://arxiv.org/abs/2206.11923 |