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This paper analyzes the convergence properties of this semigroup. A key result shows that the exponential convergence rate of the quantum semigroup (quantified via the spectral gap) matches precisely the convergence rate of its classical diagonal counterpart towards the unique invariant measure. Furthermore, we provide explicit computations or estimates of the exponential convergence rate in specific examples. <\/jats:p>","DOI":"10.1142\/s1230161225500064","type":"journal-article","created":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T03:06:23Z","timestamp":1756782383000},"source":"Crossref","is-referenced-by-count":0,"title":["Exponential Convergence Rate of the Quantum Exclusion Semigroup Constructed by Quantum Bernoulli Noise"],"prefix":"10.1142","volume":"32","author":[{"given":"Jinshu","family":"Chen","sequence":"first","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, People\u2019s Republic of China"}]},{"given":"Siqi","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, People\u2019s Republic of China"}]}],"member":"219","published-online":{"date-parts":[[2025,9,3]]},"reference":[{"key":"S1230161225500064BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2017.05.003"},{"key":"S1230161225500064BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s002200050773"},{"key":"S1230161225500064BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/BF00398571"},{"key":"S1230161225500064BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-023-04795-6"},{"key":"S1230161225500064BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-022-01220-x"},{"key":"S1230161225500064BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01608499"},{"key":"S1230161225500064BIB007","doi-asserted-by":"publisher","DOI":"10.1063\/1.522979"},{"issue":"3","key":"S1230161225500064BIB008","volume":"24","author":"Chru\u015bci\u0144ski D.","year":"2017","journal-title":"Open Syst. 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