[{"_id":"13319","article_type":"original","file_date_updated":"2024-01-30T12:15:11Z","doi":"10.1007/s00220-023-04795-6","year":"2023","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).","date_created":"2023-07-30T22:01:03Z","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.","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>","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.","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>.","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."},"project":[{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups"}],"date_published":"2023-10-01T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","volume":403,"department":[{"_id":"JaMa"}],"page":"381-416","publication_status":"published","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"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."}],"external_id":{"arxiv":["2303.15949"],"isi":["001033655400002"]},"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","article_processing_charge":"Yes (via OA deal)","date_updated":"2024-01-30T12:16:32Z","oa":1,"title":"Derivations and KMS-symmetric quantum Markov semigroups","isi":1,"has_accepted_license":"1","intvolume":"       403","scopus_import":"1","status":"public","type":"journal_article","arxiv":1,"author":[{"last_name":"Vernooij","first_name":"Matthijs","full_name":"Vernooij, Matthijs"},{"orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","first_name":"Melchior","full_name":"Wirth, Melchior"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"month":"10","file":[{"date_created":"2024-01-30T12:15:11Z","date_updated":"2024-01-30T12:15:11Z","success":1,"checksum":"cca204e81891270216a0c84eb8bcd398","file_id":"14905","file_name":"2023_CommMathPhysics_Vernooij.pdf","relation":"main_file","content_type":"application/pdf","file_size":481209,"access_level":"open_access","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","day":"01"},{"acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","year":"2023","date_created":"2023-01-08T23:00:53Z","citation":{"apa":"Dello Schiavo, L., &#38; Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>.","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>, vol. 23, no. 1, 9, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>.","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. 2023;23(1). doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>","ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” <i>Journal of Evolution Equations</i>, vol. 23, no. 1. Springer Nature, 2023.","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023)."},"ec_funded":1,"article_number":"9","file_date_updated":"2023-01-20T10:45:06Z","article_type":"original","_id":"12104","doi":"10.1007/s00028-022-00859-7","publication_status":"published","ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"isi":["000906214600004"]},"abstract":[{"text":"We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces.","lang":"eng"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833"}],"publisher":"Springer Nature","date_published":"2023-01-01T00:00:00Z","department":[{"_id":"JaMa"}],"volume":23,"quality_controlled":"1","date_updated":"2023-06-28T11:54:35Z","oa":1,"article_processing_charge":"Yes (via OA deal)","issue":"1","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","isi":1,"intvolume":"        23","has_accepted_license":"1","scopus_import":"1","language":[{"iso":"eng"}],"publication":"Journal of Evolution Equations","author":[{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870"},{"orcid":"0000-0002-0519-4241","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior","full_name":"Wirth, Melchior"}],"publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"month":"01","day":"01","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"creator":"dernst","relation":"main_file","content_type":"application/pdf","file_size":422612,"access_level":"open_access","success":1,"checksum":"1f34f3e2cb521033de6154f274ea3a4e","file_id":"12325","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","date_created":"2023-01-20T10:45:06Z","date_updated":"2023-01-20T10:45:06Z"}],"type":"journal_article","status":"public"}]