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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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Model Systems

Model Systems

Chapter:
(p.240) 13 Model Systems
Source:
Quantum Dynamical Systems
Author(s):

Robert Alicki

Mark Fannes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198504009.003.0013

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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