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To quantify the interplay between quantum chaos and decoherence away from the semi-classical limit, we investigate the relation of this generalized SFF with the corresponding l<\/mml:mi>1<\/mml:mn><\/mml:msub><\/mml:math>-norm of coherence. As a working example, we introduce Parametric Quantum Channels (PQC), a discrete-time model of unitary evolution mixed with the effects of measurements or transient interactions with an environment. The Energy Dephasing (ED) dynamics arises as a specific case in the Markovian limit. We demonstrate our results in a series of random matrix models.<\/jats:p>","DOI":"10.22331\/q-2024-08-27-1446","type":"journal-article","created":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T15:16:21Z","timestamp":1724771781000},"page":"1446","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["Quantum Chaos and Coherence: Random Parametric Quantum Channels"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5517-0224","authenticated-orcid":false,"given":"Apollonas S.","family":"Matsoukas-Roubeas","sequence":"first","affiliation":[{"name":"Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G. D. 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