Modified logarithmic Sobolev inequalities for Abelian quantum double models
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arXiv
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| Autores principales: | , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917511041122304 |
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| author | Stengele, Sebastian Capel, Ángela Gao, Li Lucia, Angelo Pérez-García, David Pérez-Hernández, Antonio Rouzé, Cambyse Warzel, Simone |
| author_facet | Stengele, Sebastian Capel, Ángela Gao, Li Lucia, Angelo Pérez-García, David Pérez-Hernández, Antonio Rouzé, Cambyse Warzel, Simone |
| contents | We establish rapid mixing for Davies Markov semigroups associated with 2D Abelian quantum double models at any positive temperature. A condition of Dobrushin-Shlosman (DS) type holds at any temperature, and we show that the latter implies a modified logarithmic Sobolev inequality for the Davies Lindbladian. A key step in the argument is to verify a strong martingale condition for the local conditional expectations of the Davies semigroup in the regime of validity of the DS condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19640 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modified logarithmic Sobolev inequalities for Abelian quantum double models Stengele, Sebastian Capel, Ángela Gao, Li Lucia, Angelo Pérez-García, David Pérez-Hernández, Antonio Rouzé, Cambyse Warzel, Simone Quantum Physics Mathematical Physics Probability We establish rapid mixing for Davies Markov semigroups associated with 2D Abelian quantum double models at any positive temperature. A condition of Dobrushin-Shlosman (DS) type holds at any temperature, and we show that the latter implies a modified logarithmic Sobolev inequality for the Davies Lindbladian. A key step in the argument is to verify a strong martingale condition for the local conditional expectations of the Davies semigroup in the regime of validity of the DS condition. |
| title | Modified logarithmic Sobolev inequalities for Abelian quantum double models |
| topic | Quantum Physics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2605.19640 |