Dynamics, Information and Complexity in Quantum Systems (Hardcover)

Fabio Benatti

ISBN 10: 1402093055 / ISBN 13: 9781402093050

Verlag: Springer-Verlag New York Inc., New York, NY, 2009

Beschreibung

Hardcover. The aim of this book is to o?er a self-consistent overview of a series of - sues relating entropy, information and dynamics in classical and quantum physics. My personal point of view regarding these matters is the result of what I had the good fortune to learn in the course of the years from various scientists: Heide Narnhofer in the ?rst place, who introduced me to qu- tum dynamical entropies and was a precious guide ever since, then Robert Alicki, Mark Fannes, Giancarlo Ghirardi, Andreas Knauf, John Lewis, - o?rey Sewell, Franco Strocchi, Walter Thirring, Armin Uhlmann. To me, all of them have been a constant example of rigorous mathematics and physical intuition jointly at work. Last but not least, my deep gratitude goes to my family and to the many friends on whom I could always count for support and encouragement with a special thought for Traude and Wolfgang Georgiades. This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Bestandsnummer des Verkäufers 9781402093050

Bibliografische Details

• Titel: Dynamics, Information and Complexity in Quantum Systems (Hardcover)
• Verlag: Springer-Verlag New York Inc., New York, NY
• Erscheinungsjahr: 2009
• Sprache: Englisch
• ISBN-10: 1402093055
• ISBN-13: 9781402093050
• Einband: Hardcover
• Zustand: new

Über diesen Titel

Inhaltsangabe

1 Introduction Part I Classical Dynamical Systems2 Classical Dynamics and Ergodic Theory 2.1 Classical Dynamical Systems 2.2 Symbolic Dynamics 2.3 Ergodicity and Mixing 2.4 Information and Entropy 3 Dynamical Entropy and Information 3.1 Dynamical Entropy 3.2 Codes and Shannon Theorems 4 Algorithmic Complexity 4.1 Kolmogorov Complexity 4.2 Algorithmic Complexity and Entropy Rate 4.3 Pre_x Algorithmic Complexity Part II Quantum Dynamical Systems5 Quantum Mechanics of Finite Degrees of Freedom 5.1 Hilbert Space and Operator Algebras 5.2 Algebras of Bounded Operators on H 5.3 Quantum Systems with Finite Degrees of Freedom 5.4 Quantum States 5.5 Dynamics and State-Transformations 6 Quantum Information Theory 6.1 Quantum Information Theory 6.2 Bipartite Entanglement 6.3 Relative Entropy7 Quantum Mechanics of Infinite Degrees of Freedom7.1 Observables, States and Dynamics7.2 Entropy Density 7.3 Quantum Spin Chains as Quantum SourcesPart III Quantum Dynamical Entropies and Complexities8 Quantum Dynamical Entropies 8.1 CNT Entropy: Decompositions of States 8.2 AFL Entropy: OPUs 9 Quantum Algorithmic Complexity9.1 Quantum Algorithmic Complexities References

Von der hinteren Coverseite

The leading theme of the book is complexity in quantum dynamics. This issue is addressed by comparison with the classical ergodic, information and algorithmic complexity theories.

Of particular importance is the notion of Kolmogorov-Sinai dynamical entropy and of its inequivalent quantum extensions formulated by Connes, Narnhofer and Thirring on one hand and Alicki and Fannes on the other. Their connections with extensions to quantum systems of Kolmogorov-Chaitin-Solomonoff algorithmic complexity theory is also presented. The technical tools employed are those of the algebraic approach to quantum statistical mechanics which offers a unifying view of classical and quantum dynamical systems. Proofs and examples are provided in order to make the presentation self consistent.