Fabio Benatti

Deterministic Chaos in Infinite Quantum Systems (eBook, PDF)

• Format: PDF

Produktbeschreibung

The author presents the classical concept of Kolmogorov-Sinai entropy and its non-commutative analogue for infinite quantum systems. He then compares the irregular behaviour of classical versus quantum systems. These notes address both researchers and graduate students in statistical mechanics and mathematical physics.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 225
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642849992
• Artikelnr.: 53087120

Autorenporträt

The author presents the classical concept of Kolmogorov-Sinai entropy and its non-commutative analogue for infinite quantum systems. He then compares the irregular behaviour of classical versus quantum systems. These notes address both researchers and graduate students in statistical mechanics and mathematical physics.

Inhaltsangabe

1 Introduction.- 2 Classical Ergodic Theory.- 2.1 Irreversibility.- 2.2 Entropy.- 2.3 Topological Properties of Dynamical Systems.- 3 Algebraic Approach to Classical Ergodic Theory.- 3.1 Abelian C* Dynamical Systems.- 3.2 Abelian W* Dynamical Systems.- 3.3 W* Algebras: KS-Entropy and K-Systems.- 3.4 C* Algebras: Classical Topological Entropy.- 4 Infinite Quantum Systems.- 4.1 Useful Tools from Finite Quantum Systems.- 4.2 GNS-Construction.- 4.3 Ergodic Properties in Quantum Systems.- 4.4 Algebraic Quantum Kolmogorov Systems.- 5 Connes-Narnhofer-Thirring Entropy.- 5.1 Basic Ideas and Construction 1.- 5.2 Basic Ideas and Construction 2.- 5.3 CNT-Entropy: Applications.- 5.4 Short History of the Topic and Latest Developments.- 5.5 Entropic Quantum Kolmogorov Systems.- 5.6 Ideas for a Non-commutative Topological Entropy.- 6 Appendix.- References.- Index of Symbols.