{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:26:08Z","timestamp":1763537168936,"version":"3.45.0"},"reference-count":38,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["KFU253490"],"award-info":[{"award-number":["KFU253490"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>This paper introduces a symmetric group dynamics on quantum Markov chains on Cayley trees (QMCCT). By applying symmetric group actions, we establish a novel algebraic perspective that enables the systematic study of local correlation functions in QMCCT. This approach provides a powerful tool for investigating phase transitions and characterizing ergodic properties in these systems. We further extend this framework to explore QMCCT associated with Open Quantum Random Walks (OQRWs). The integration of symmetric group dynamics allows for a detailed analysis of the interplay between group-theoretic symmetries and the stochastic processes underlying QMCCT, particularly in the context of OQRWs. Our results demonstrate the potential of this approach to uncover new insights into the structure and behaviour of quantum Markov chains.<\/jats:p>","DOI":"10.1142\/s1230161225500106","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":["Symmetric Group Action on Quantum Markov Chains on Cayley Trees and Open Quantum Walks Dynamics"],"prefix":"10.1142","volume":"32","author":[{"given":"Abdessatar","family":"Souissi","sequence":"first","affiliation":[{"name":"Department of Management Information Systems, College of Business Management, Qassim University, Buraydah 52571, Saudi Arabia"}]},{"given":"Abdessatar","family":"Barhoumi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa PO.Box: 400, 31982, Saudi Arabia"}]}],"member":"219","published-online":{"date-parts":[[2025,11,15]]},"reference":[{"key":"S1230161225500106BIB001","first-page":"268","volume-title":"Proceedings international school of mathematical physics","author":"Accardi L.","year":"1974"},{"key":"S1230161225500106BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0219025720500162"},{"key":"S1230161225500106BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0219025703001079"},{"key":"S1230161225500106BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S021902571100447X"},{"key":"S1230161225500106BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-011-0107-2"},{"key":"S1230161225500106BIB008","volume-title":"Lecture notes in mathematics","author":"Accardi L.","year":"1989"},{"key":"S1230161225500106BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-012-0491-0"},{"key":"S1230161225500106BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-015-1261-6"},{"key":"S1230161225500106BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-015-0396-y"},{"key":"S1230161225500106BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-015-2466-x"},{"key":"S1230161225500106BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s13324-023-00790-1"},{"key":"S1230161225500106BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2024.115252"},{"key":"S1230161225500106BIB015","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976465.59"},{"key":"S1230161225500106BIB016","doi-asserted-by":"publisher","DOI":"10.22331\/q-2017-08-17-26"},{"issue":"2","key":"S1230161225500106BIB017","first-page":"201","volume":"13","author":"Dobrushin R.L.V.","year":"1968","journal-title":"Teoriya Veroyatnostei i ee Primeneniya"},{"key":"S1230161225500106BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112644"},{"key":"S1230161225500106BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02520-8"},{"key":"S1230161225500106BIB020","doi-asserted-by":"publisher","DOI":"10.1142\/S0129055X1950020X"},{"key":"S1230161225500106BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/BF02099178"},{"key":"S1230161225500106BIB022","doi-asserted-by":"publisher","DOI":"10.31390\/josa.1.4.04"},{"key":"S1230161225500106BIB023","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-012-0668-6"},{"key":"S1230161225500106BIB024","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/1150287309"},{"key":"S1230161225500106BIB025","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-015-1217-x"},{"key":"S1230161225500106BIB026","doi-asserted-by":"publisher","DOI":"10.1142\/S0219749921500283"},{"key":"S1230161225500106BIB027","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-016-1495-y"},{"key":"S1230161225500106BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/s11040-019-9308-6"},{"key":"S1230161225500106BIB029","doi-asserted-by":"publisher","DOI":"10.3390\/axioms12090864"},{"key":"S1230161225500106BIB030","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161222500032"},{"key":"S1230161225500106BIB031","doi-asserted-by":"publisher","DOI":"10.1007\/s11128-023-03980-9"},{"key":"S1230161225500106BIB033","doi-asserted-by":"publisher","DOI":"10.1063\/1.532213"},{"key":"S1230161225500106BIB034","doi-asserted-by":"publisher","DOI":"10.1007\/s10773-023-05276-1"},{"key":"S1230161225500106BIB035","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2013.04.002"},{"key":"S1230161225500106BIB036","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161223500191"},{"key":"S1230161225500106BIB037","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161218500178"},{"key":"S1230161225500106BIB038","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-013-0910-x"},{"key":"S1230161225500106BIB039","doi-asserted-by":"publisher","DOI":"10.1007\/s40509-024-00332-9"},{"key":"S1230161225500106BIB040","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6336-8"},{"key":"S1230161225500106BIB041","doi-asserted-by":"publisher","DOI":"10.1007\/s11128-012-0432-5"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161225500106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:21:18Z","timestamp":1763536878000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1230161225500106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":38,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10.1142\/S1230161225500106"],"URL":"https:\/\/doi.org\/10.1142\/s1230161225500106","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":"2550010"}}