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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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Quantum Irreversibility

Quantum Irreversibility

Chapter:
(p.146) 8 Quantum Irreversibility
Source:
Quantum Dynamical Systems
Author(s):

Robert Alicki

Mark Fannes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198504009.003.0008

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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