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We show that for fixed, small values of the coupling constant<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>&amp;#x03BB;<\/mml:mi><\/mml:math>, the true reduced dynamics of the system is approximated by the completely positive, trace preserving Markovian semigroup generated by the Davies-Lindblad generator. The difference between the true and the Markovian dynamics is<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>O<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo stretchy=\"false\">|<\/mml:mo><\/mml:mrow><mml:mi>&amp;#x03BB;<\/mml:mi><mml:msup><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo stretchy=\"false\">|<\/mml:mo><\/mml:mrow><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mn>1<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>4<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>for all times, meaning that the solution of the Gorini-Kossakowski-Sudarshan-Lindblad master equation is approximating the true dynamics to accuracy<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>O<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo stretchy=\"false\">|<\/mml:mo><\/mml:mrow><mml:mi>&amp;#x03BB;<\/mml:mi><mml:msup><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo stretchy=\"false\">|<\/mml:mo><\/mml:mrow><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mn>1<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mn>4<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>for all times. Our method is based on a recently obtained expansion of the full system-bath propagator. It applies to reservoirs with correlation functions decaying in time as<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>1<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:msup><mml:mi>t<\/mml:mi><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mn>4<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math>or faster, which is a significant improvement relative to the previously required exponential decay.<\/jats:p>","DOI":"10.22331\/q-2022-01-03-616","type":"journal-article","created":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T19:06:14Z","timestamp":1641236774000},"page":"616","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":23,"title":["Dynamics of Open Quantum Systems II, Markovian Approximation"],"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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