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Quantum Dynamical Systems$
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Robert Alicki and Mark Fannes

Print publication date: 2001

Print ISBN-13: 9780198504009

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780198504009.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 19 October 2021

Quantum Irreversibility

Quantum Irreversibility

(p.146) 8 Quantum Irreversibility
Quantum Dynamical Systems

Robert Alicki

Mark Fannes

Oxford University Press

Pure states and unitary dynamics suffice to handle perfectly isolated quantum systems. Measurements and interactions with an uncontrolled environment introduce irreversibility and call for a wider setting. This chapter provides the basic necessary mathematical tools like mixed states, POV-measures, and completely positive maps and semi-groups. It considers fundamental structural results such as Stinespring's theorem, Kraus decompositions, and Lindblad generators. It situates these mathematical results in a physical context and presents applications to spin systems and Fermionic systems.

Keywords:   POV-measures, complete positivity, Stinespring's theorem, Kraus decomposition, Lindblad generator, Fermionic system, spin system

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