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Introduction to classical and quantum Markov semigroups

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Publication date2019
Host publicationOpen Quantum Systems: A Mathematical Perspective
EditorsDorothea Bahns, Anke Pohl, Ingo Witt
Place of PublicationCham
Number of pages54
ISBN (electronic)9783030130466
ISBN (print)9783030130466, 9783030130459
<mark>Original language</mark>English

Publication series

NameTutorials, Schools, and Workshops in the Mathematical Sciences
PublisherBirkhäuser, Cham
ISSN (Print)2522-0969
ISSN (electronic)2522-0977


We provide a self-contained and fast-paced introduction to the theories of operator semigroups, Markov semigroups and quantum dynamical semigroups. The level is appropriate for well-motivated graduate students who have a background in analysis or probability theory, with the focus on the characterisation of infinitesimal generators for various classes of semigroups. The theorems of Hille–Yosida, Hille Yosida–Ray, Lumer–Phillips and Gorini–Kossakowski–Sudarshan–Lindblad are all proved, with the necessary technical prerequisites explained in full. Exercises are provided throughout.