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Deterministic Chaos in Infinite Quantum Systems

  • Fabio Benatti

Part of the Trieste Notes in Physics book series (TRIESTE)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Fabio Benatti
    Pages 1-2
  3. Fabio Benatti
    Pages 3-52
  4. Fabio Benatti
    Pages 69-140
  5. Fabio Benatti
    Pages 141-207
  6. Fabio Benatti
    Pages 209-212
  7. Back Matter
    Pages 213-225

About this book

Introduction

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.

Keywords

Entropie Ergodentheorie Infinite Quantum System chaos deterministic chaos entropy ergodic theory quantum chaos

Authors and affiliations

  • Fabio Benatti
    • 1
  1. 1.Dipartimento di Fisica TeoricaUniversità di TriesteTriesteItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-84999-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57017-2
  • Online ISBN 978-3-642-84999-2
  • Buy this book on publisher's site