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Such kind of consideration allows us to investigate phase transition phenomena associated for OQRW within QMC scheme. Furthermore, we first propose a new construction of QMC on trees, which is an extension of QMC considered in [10]. Using such a construction, we are able to construct QMCs on tress associated with OQRW. Our investigation leads to the detection of the phase transition phenomena within the proposed scheme. This kind of phenomena appears for the first time in this direction. Moreover, mean entropies of QMCs are calculated.<\/jats:p>","DOI":"10.1142\/s1230161222500032","type":"journal-article","created":{"date-parts":[[2022,8,31]],"date-time":"2022-08-31T03:01:15Z","timestamp":1661914875000},"source":"Crossref","is-referenced-by-count":14,"title":["Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions"],"prefix":"10.1142","volume":"29","author":[{"given":"Farrukh","family":"Mukhamedov","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, United Arab Emirates University 15551, Al-Ain, United Arab Emirates"},{"name":"Institute of Mathematics named after V. I. 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