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The full, interacting<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi mathvariant=\"normal\">S<\/mml:mi><mml:mi mathvariant=\"normal\">R<\/mml:mi><\/mml:math>dynamics is unitary. The reservoir has a stationary state but otherwise dissipative dynamics. We identify a main part of the full dynamics, which approximates it for small values of the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi mathvariant=\"normal\">S<\/mml:mi><mml:mi mathvariant=\"normal\">R<\/mml:mi><\/mml:math>coupling constant, uniformly for all times<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>t<\/mml:mi><mml:mo>&amp;#x2265;<\/mml:mo><mml:mn>0<\/mml:mn><\/mml:math>. The main part consists of explicit oscillating and decaying parts. We show that the reduced system evolution is Markovian for all times. The technical novelty is a detailed analysis of the link between the dynamics and the spectral properties of the generator of the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi mathvariant=\"normal\">S<\/mml:mi><mml:mi mathvariant=\"normal\">R<\/mml:mi><\/mml:math>dynamics, based on Mourre theory. We allow for<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi mathvariant=\"normal\">S<\/mml:mi><mml:mi mathvariant=\"normal\">R<\/mml:mi><\/mml:math>interactions with little regularity, meaning that the decay of the reservoir correlation function only needs to be polynomial in time, improving on the previously required exponential decay.In this work we distill the structural and technical ingredients causing the characteristic features of oscillation and decay of the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi mathvariant=\"normal\">S<\/mml:mi><mml:mi mathvariant=\"normal\">R<\/mml:mi><\/mml:math>dynamics. In the companion paper [27] we apply the formalism to the concrete case of an<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>N<\/mml:mi><\/mml:math>-level system linearly coupled to a spatially infinitely extended thermal bath of non-interacting Bosons.<\/jats:p>","DOI":"10.22331\/q-2022-01-03-615","type":"journal-article","created":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T16:04:20Z","timestamp":1641225860000},"page":"615","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":17,"title":["Dynamics of Open Quantum Systems I, Oscillation and Decay"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3990-6155","authenticated-orcid":false,"given":"Marco","family":"Merkli","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John&apos;s, A1C 5S7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,1,3]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"R. 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