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Dynamics, Information and Complexity in Quantum Systems

  • Book
  • © 2009

Overview

Authors:
  1. Fabio Benatti

    1. Dipto. Fisica Teorica, University of Trieste, Miramare, Italy

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  • Offers a self-contained overview of the entropic approach to quantum dynamical systems
  • Addresses complexity issues in quantum dynamical systems and quantum information theory
  • Provides a unified view of the classical and quantum aspects of complexity as formulated in classical and quantum ergodic, information and algorithmic complexity theories

Part of the book series: Theoretical and Mathematical Physics (TMP)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Fabio Benatti
      Pages 1-4

  3. Classical Dynamical Systems

    1. Front Matter

      Pages 6-7
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    2. Classical Dynamics and Ergodic Theory

      • Fabio Benatti
      Pages 9-69

    3. Dynamical Entropy and Information

      • Fabio Benatti
      Pages 71-104

    4. Algorithmic Complexity

      • Fabio Benatti
      Pages 105-134

  4. Quantum Dynamical Systems

    1. Front Matter

      Pages 135-136
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    2. Quantum Mechanics of Finite Degrees of Freedom

      • Fabio Benatti
      Pages 139-254

    3. Quantum Information Theory

      • Fabio Benatti
      Pages 255-315

    4. Quantum Mechanics of Infinite Degrees of Freedom

      • Fabio Benatti
      Pages 317-406

  5. Quantum Dynamical Entropies and Complexities

    1. Front Matter

      Pages 407-409
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    2. Quantum Dynamical Entropies

      • Fabio Benatti
      Pages 411-481

    3. Quantum Algorithmic Complexities

      • Fabio Benatti
      Pages 483-515

  6. Back Matter

    Pages 517-535
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Keywords

About this book

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.

Reviews

From the reviews: “This book fits very well with the recent trends in theoretical and mathematical physics exploiting the interrelations between quantum theory, statistical mechanics and information theory. … The book is clearly written and contains a reasonable amount of elementary background material illustrated by numerous examples, and therefore can serve very well students at the graduate level and researchers entering the field of quantum dynamics and quantum information.” (Robert Alicki, Mathematical Reviews, Issue 2010 c)

Authors and Affiliations

  • Dipto. Fisica Teorica, University of Trieste, Miramare, Italy

    Fabio Benatti

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