Introduction to classical and quantum Markov semigroups

Belton, Alexander (2019) Introduction to classical and quantum Markov semigroups. In: Open Quantum Systems. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhauser, Cham, pp. 1-54. ISBN 9783030130466

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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.

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05 Aug 2019 11:10
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21 Sep 2023 03:58