{"acknowledgement":"The authors are grateful to Martijn Caspers for helpful comments on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. Open access funding provided by Austrian Science Fund (FWF).","status":"public","abstract":[{"lang":"eng","text":"We prove that the generator of the L2 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."}],"intvolume":"       403","date_updated":"2024-01-30T12:16:32Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"quality_controlled":"1","day":"01","external_id":{"arxiv":["2303.15949"],"isi":["001033655400002"]},"has_accepted_license":"1","article_type":"original","project":[{"name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N"}],"volume":403,"isi":1,"author":[{"last_name":"Vernooij","full_name":"Vernooij, Matthijs","first_name":"Matthijs"},{"last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","first_name":"Melchior","full_name":"Wirth, Melchior"}],"file_date_updated":"2024-01-30T12:15:11Z","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"381-416","date_created":"2023-07-30T22:01:03Z","publication":"Communications in Mathematical Physics","article_processing_charge":"Yes (via OA deal)","date_published":"2023-10-01T00:00:00Z","ddc":["510"],"file":[{"creator":"dernst","checksum":"cca204e81891270216a0c84eb8bcd398","file_id":"14905","success":1,"access_level":"open_access","relation":"main_file","file_size":481209,"date_created":"2024-01-30T12:15:11Z","file_name":"2023_CommMathPhysics_Vernooij.pdf","date_updated":"2024-01-30T12:15:11Z","content_type":"application/pdf"}],"year":"2023","title":"Derivations and KMS-symmetric quantum Markov semigroups","month":"10","_id":"13319","doi":"10.1007/s00220-023-04795-6","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"citation":{"apa":"Vernooij, M., &#38; Wirth, M. (2023). Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>","short":"M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416.","chicago":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>.","ieee":"M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 403. Springer Nature, pp. 381–416, 2023.","mla":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 403, Springer Nature, 2023, pp. 381–416, doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>.","ista":"Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 403, 381–416.","ama":"Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2023;403:381-416. doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>"},"type":"journal_article","oa_version":"Published Version","publisher":"Springer Nature","oa":1,"scopus_import":"1","publication_status":"published"}