Deterministic Chaos in Infinite Quantum Systems
Aus der Reihe
Trieste Notes in Physics
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Sprache:Englisch
Fr. 137.00
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Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
03.11.1993
Verlag
Springer BerlinSeitenzahl
225
Maße (L/B/H)
23.5/15.5/1.3 cm
Gewicht
358 g
Auflage
Softcover reprint of the original 1st ed. 1993
Sprache
Englisch
ISBN
978-3-540-57017-2
The purpose of this volume is to give a detailed account of a series of re sults concerning some ergodic questions of quantum mechanics which have the past six years following the formulation of a generalized been addressed in Kolmogorov-Sinai entropy by A.Connes, H.Narnhofer and W.Thirring. Classical ergodicity and mixing are fully developed topics of mathematical physics dealing with the lowest levels in a hierarchy of increasingly random behaviours with the so-called Bernoulli systems at its apex showing a structure that characterizes them as Kolmogorov (K-) systems. It seems not only reasonable, but also inevitable to use classical ergodic theory as a guide in the study of ergodic behaviours of quantum systems. The question is which kind of random behaviours quantum systems can exhibit and whether there is any way of classifying them. Asymptotic statistical independence and, correspondingly, complete lack of control over the distant future are typical features of classical K-systems. These properties are fully characterized by the dynamical entropy of Kolmogorov and Sinai, so that the introduction of a similar concept for quantum systems has provided the opportunity of raising meaningful questions and of proposing some non-trivial answers to them. Since in the following we shall be mainly concerned with infinite quantum systems, the algebraic approach to quantum theory will provide us with the necessary analytical tools which can be used in the commutative context, too.
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