{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:26:07Z","timestamp":1763537167452,"version":"3.45.0"},"reference-count":41,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"SONATA BIS","award":["2019\/34\/E\/ST2\/00369"],"award-info":[{"award-number":["2019\/34\/E\/ST2\/00369"]}]},{"name":"Quantum Sensing and Modelling for One-Health","award":["QuaSiModO"],"award-info":[{"award-number":["QuaSiModO"]}]},{"name":"PNRR MUR","award":["PE0000023-NQSTI"],"award-info":[{"award-number":["PE0000023-NQSTI"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>We study the asymptotic dynamics of open quantum systems in the Heisenberg picture. We find an explicit expression for the attractor subspace and the dynamics that takes place in it. We present the relationship between the attractor subspaces in the Schr\u00f6dinger and Heisenberg pictures and, in particular, the connection between their algebraic structures. An unfolding theorem of the asymptotics, as well as the fine structure of the recently introduced Choi-Effros decoherence-free algebra, are also discussed. Finally, we show how to extend all the results to the class of Schwarz maps.<\/jats:p>","DOI":"10.1142\/s1230161225500143","type":"journal-article","created":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:21:11Z","timestamp":1763536871000},"source":"Crossref","is-referenced-by-count":0,"title":["Asymptotic Dynamics in the Heisenberg Picture: Attractor Subspace and Choi-Effros Product"],"prefix":"10.1142","volume":"32","author":[{"given":"Daniele","family":"Amato","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Bari, I-70126 Bari, Italy"},{"name":"INFN, Sezione di Bari, I-70126 Bari, Italy"}]},{"given":"Paolo","family":"Facchi","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Bari, I-70126 Bari, Italy"},{"name":"INFN, Sezione di Bari, I-70126 Bari, Italy"}]},{"given":"Arturo","family":"Konderak","sequence":"additional","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland"}]}],"member":"219","published-online":{"date-parts":[[2025,11,15]]},"reference":[{"key":"S1230161225500143BIB001","doi-asserted-by":"publisher","DOI":"10.22331\/q-2019-06-06-151"},{"key":"S1230161225500143BIB002","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-024-64040-5"},{"key":"S1230161225500143BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-99-5884-9_5"},{"key":"S1230161225500143BIB004","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/acd828"},{"key":"S1230161225500143BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-96-3584-9_3"},{"key":"S1230161225500143BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161208000110"},{"key":"S1230161225500143BIB008","doi-asserted-by":"publisher","DOI":"10.1515\/9781400827787"},{"key":"S1230161225500143BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2023.08.020"},{"key":"S1230161225500143BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/BF01328531"},{"key":"S1230161225500143BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/BF01379806"},{"key":"S1230161225500143BIB013","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/088"},{"key":"S1230161225500143BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-019-00861-9"},{"key":"S1230161225500143BIB015","first-page":"271","volume":"4","author":"Choi M.-D.","year":"1980","journal-title":"J. Oper. Theory"},{"key":"S1230161225500143BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(77)90052-0"},{"key":"S1230161225500143BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2022.09.003"},{"key":"S1230161225500143BIB018","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.127.050401"},{"key":"S1230161225500143BIB019","doi-asserted-by":"publisher","DOI":"10.1142\/S123016122050016X"},{"key":"S1230161225500143BIB020","volume-title":"Quantum theory of open systems","author":"Davies E. B.","year":"1976"},{"key":"S1230161225500143BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/BF01614091"},{"key":"S1230161225500143BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-003-0268-0"},{"key":"S1230161225500143BIB023","doi-asserted-by":"publisher","DOI":"10.1063\/1.5030954"},{"key":"S1230161225500143BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/BF01196936"},{"key":"S1230161225500143BIB026","first-page":"197","volume":"12","author":"Gel\u2019fand I.","year":"1943","journal-title":"Mat. Sb."},{"key":"S1230161225500143BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/BF01328377"},{"key":"S1230161225500143BIB029","doi-asserted-by":"publisher","DOI":"10.1140\/epjqt\/s40507-022-00138-x"},{"key":"S1230161225500143BIB030","doi-asserted-by":"publisher","DOI":"10.1023\/A:1007581027660"},{"key":"S1230161225500143BIB031","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.78.042307"},{"key":"S1230161225500143BIB032","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/adaa3f"},{"key":"S1230161225500143BIB033","volume-title":"Quantum computation and quantum information","author":"Nielsen M. A.","year":"2002"},{"key":"S1230161225500143BIB034","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/ab0c1c"},{"key":"S1230161225500143BIB035","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/45\/48\/485301"},{"key":"S1230161225500143BIB036","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2018-12109-8"},{"key":"S1230161225500143BIB037","doi-asserted-by":"publisher","DOI":"10.3836\/tjm\/1270130489"},{"key":"S1230161225500143BIB038","volume-title":"Completely bounded maps and operator algebras","author":"Paulsen V.","year":"2002"},{"key":"S1230161225500143BIB041","doi-asserted-by":"publisher","DOI":"10.1007\/BF00420668"},{"key":"S1230161225500143BIB042","first-page":"211","volume":"6","author":"Stinespring W. F.","year":"1955","journal-title":"Proc. Amer. Math. Soc."},{"key":"S1230161225500143BIB043","volume-title":"Positive Linear Maps of Operator Algebras","author":"rmer E.","year":"2013"},{"key":"S1230161225500143BIB044","doi-asserted-by":"publisher","DOI":"10.1038\/nphys1342"},{"key":"S1230161225500143BIB045","doi-asserted-by":"publisher","DOI":"10.1017\/9781316848142"},{"key":"S1230161225500143BIB048","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.79.3306"},{"key":"S1230161225500143BIB049","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.240406"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161225500143","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:21:13Z","timestamp":1763536873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1230161225500143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":41,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10.1142\/S1230161225500143"],"URL":"https:\/\/doi.org\/10.1142\/s1230161225500143","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9]]},"article-number":"2550014"}}