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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

Model Systems

Model Systems

(p.240) 13 Model Systems
Quantum Dynamical Systems

Robert Alicki

Mark Fannes

Oxford University Press

This chapter presents additional computations concerning dynamical entropy. It first computes the dynamical entropy of the quantum cat map. It then defines, for a class of non-commutative dynamical systems with a tracial invariant state, a kind of non-commutative Riemannian structure connected to Dirichlet forms that allows the definition of non-commutative Lyapunov exponents and proves Ruelle's inequality. Finally, dynamical entropy is computed for a class of quasi-free Fermionic systems. The proof exploits some ideas from scattering theory like Cook's criterion.

Keywords:   Ruelle's inequality, Riemannian structure, Dirichlet form, Cook's criterion, quantum cat map

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