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Derivations and KMS-Symmetric Quantum Markov Semigroups

We prove that the generator of the [Formula: see text] implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-na...

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Detalles Bibliográficos
Autores principales: Vernooij, Matthijs, Wirth, Melchior
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10520168/
https://www.ncbi.nlm.nih.gov/pubmed/37766789
http://dx.doi.org/10.1007/s00220-023-04795-6
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author Vernooij, Matthijs
Wirth, Melchior
author_facet Vernooij, Matthijs
Wirth, Melchior
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description We prove that the generator of the [Formula: see text] implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule.
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spelling pubmed-105201682023-09-27 Derivations and KMS-Symmetric Quantum Markov Semigroups Vernooij, Matthijs Wirth, Melchior Commun Math Phys Article We prove that the generator of the [Formula: see text] implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule. Springer Berlin Heidelberg 2023-07-20 2023 /pmc/articles/PMC10520168/ /pubmed/37766789 http://dx.doi.org/10.1007/s00220-023-04795-6 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Vernooij, Matthijs
Wirth, Melchior
Derivations and KMS-Symmetric Quantum Markov Semigroups
title Derivations and KMS-Symmetric Quantum Markov Semigroups
title_full Derivations and KMS-Symmetric Quantum Markov Semigroups
title_fullStr Derivations and KMS-Symmetric Quantum Markov Semigroups
title_full_unstemmed Derivations and KMS-Symmetric Quantum Markov Semigroups
title_short Derivations and KMS-Symmetric Quantum Markov Semigroups
title_sort derivations and kms-symmetric quantum markov semigroups
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10520168/
https://www.ncbi.nlm.nih.gov/pubmed/37766789
http://dx.doi.org/10.1007/s00220-023-04795-6
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