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© 2020

Unstable Systems

Book

Part of the Mathematical Physics Studies book series (MPST)

Table of contents

  1. Front Matter
    Pages i-x
  2. Lawrence Horwitz, Yosef Strauss
    Pages 1-9
  3. Lawrence Horwitz, Yosef Strauss
    Pages 11-30
  4. Lawrence Horwitz, Yosef Strauss
    Pages 31-45
  5. Lawrence Horwitz, Yosef Strauss
    Pages 47-86
  6. Lawrence Horwitz, Yosef Strauss
    Pages 87-111
  7. Lawrence Horwitz, Yosef Strauss
    Pages 113-136
  8. Lawrence Horwitz, Yosef Strauss
    Pages 159-160
  9. Back Matter
    Pages 161-221

About this book

Introduction

This book focuses on unstable systems both from the classical and the quantum mechanical points of view and studies the relations between them. The first part deals with quantum systems. Here the main methods are critically described, such as the Gamow approach, the Wigner-Weisskopf formulation, the Lax-Phillips theory, and a method developed by the authors using the dilation construction proposed by Nagy and Foias. The second part provides a description of approaches to classical stability analysis and introduces geometrical methods recently developed by the authors, which show to be highly effective in diagnosing instability and, in many cases, chaotic behavior. Part three shows that many of the aspects of the classical picture display properties that can be associated with underlying quantum phenomena, as should be expected in the real world.

Keywords

unstable quantum system Gamow approach Wigner-Weisskopf formulation rigged Hilbert spaces Gel'fand triples Lax-Phillips scattering Stark effect Relativistic Lee-Friedrichs model second quantization resonances in semiconductors Cooper pairs dilation

Authors and affiliations

  1. 1.School of Physics, Raymond and Beverly Sackler, Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael
  2. 2.Department of MathematicsBen-Gurion University of the NegevBeér ShevaIsrael

Bibliographic information

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