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Deterministic Chaos in Infinite Quantum Systems : Lecture Notes in Mathematics - Fabio Benatti

Deterministic Chaos in Infinite Quantum Systems

Lecture Notes in Mathematics

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The concept of entropy as established by Kolmogorov and Sinai turned out to be a useful tool in classical ergodic theory, especially for studying the irregular behaviour of systems. Recently an analogous concept of (non-commutative) entropy for infinite quantum systems was introduced using the algebraic framework of operator algebras. This book, which gives all the definitions and many examples, is a detailed review of this recent work. It compares classical and quantum random behaviour. The notion of quantum chaos is discussed in detail. The book is a review of important work still in progress; it addresses researchers and graduate students.

Introductionp. 1
Classical Ergodic Theoryp. 3
Irreversibilityp. 3
Entropyp. 22
Topological Properties of Dynamical Systemsp. 47
Algebraic Approach to Classical Ergodic Theoryp. 53
Abelian C* Dynamical Systemsp. 53
Abelian W* Dynamical Systemsp. 55
W* Algebras: KS-Entropy and K-Systemsp. 59
C* Algebras: Classical Topological Entropyp. 66
Infinite Quantum Systemsp. 69
Useful Tools from Finite Quantum Systemsp. 69
GNS-Constructionp. 83
Ergodic Properties in Quantum Systemsp. 106
Algebraic Quantum Kolmogorov Systemsp. 128
Connes-Narnhofer-Thirring Entropyp. 141
Basic Ideas and Construction 1p. 141
Basic Ideas and Construction 2p. 153
CNT-Entropy: Applicationsp. 162
Short History of the Topic and Latest Developmentsp. 183
Entropic Quantum Kolmogorov Systemsp. 187
Ideas for a Non-commutative Topological Entropyp. 198
Appendixp. 209
Referencesp. 213
Index of Symbolsp. 221
Indexp. 223
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540570172
ISBN-10: 3540570179
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 225
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.25
Weight (kg): 0.33