[{"intvolume":"       403","has_accepted_license":"1","scopus_import":"1","isi":1,"title":"Derivations and KMS-symmetric quantum Markov semigroups","date_updated":"2024-01-30T12:16:32Z","oa":1,"article_processing_charge":"Yes (via OA deal)","publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}],"oa_version":"Published Version","day":"01","file":[{"date_updated":"2024-01-30T12:15:11Z","date_created":"2024-01-30T12:15:11Z","checksum":"cca204e81891270216a0c84eb8bcd398","file_id":"14905","file_name":"2023_CommMathPhysics_Vernooij.pdf","success":1,"access_level":"open_access","relation":"main_file","file_size":481209,"content_type":"application/pdf","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"month":"10","author":[{"full_name":"Vernooij, Matthijs","first_name":"Matthijs","last_name":"Vernooij"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","orcid":"0000-0002-0519-4241","first_name":"Melchior","full_name":"Wirth, Melchior"}],"arxiv":1,"status":"public","type":"journal_article","date_created":"2023-07-30T22:01:03Z","citation":{"short":"M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416.","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.","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>","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.","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>.","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>"},"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).","year":"2023","doi":"10.1007/s00220-023-04795-6","file_date_updated":"2024-01-30T12:15:11Z","article_type":"original","_id":"13319","external_id":{"isi":["001033655400002"],"arxiv":["2303.15949"]},"abstract":[{"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.","lang":"eng"}],"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"},"publication_status":"published","page":"381-416","department":[{"_id":"JaMa"}],"volume":403,"quality_controlled":"1","publisher":"Springer Nature","date_published":"2023-10-01T00:00:00Z","license":"https://creativecommons.org/licenses/by/4.0/","project":[{"name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833"}]},{"has_accepted_license":"1","scopus_import":"1","intvolume":"        23","isi":1,"title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","article_processing_charge":"Yes (via OA deal)","issue":"1","date_updated":"2023-06-28T11:54:35Z","oa":1,"publication":"Journal of Evolution Equations","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":422612,"creator":"dernst","date_created":"2023-01-20T10:45:06Z","date_updated":"2023-01-20T10:45:06Z","success":1,"checksum":"1f34f3e2cb521033de6154f274ea3a4e","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","file_id":"12325"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","oa_version":"Published Version","month":"01","publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"author":[{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870"},{"full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241"}],"status":"public","type":"journal_article","article_number":"9","ec_funded":1,"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)."},"date_created":"2023-01-08T23:00:53Z","year":"2023","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).","doi":"10.1007/s00028-022-00859-7","_id":"12104","article_type":"original","file_date_updated":"2023-01-20T10:45:06Z","abstract":[{"lang":"eng","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."}],"external_id":{"isi":["000906214600004"]},"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"],"publication_status":"published","volume":23,"quality_controlled":"1","department":[{"_id":"JaMa"}],"date_published":"2023-01-01T00:00:00Z","publisher":"Springer Nature","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"},{"grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups"}]}]