Authors:
- Addresses unstable systems from the classical and the quantum point of view providing a deeper level of understanding
- Extends the work of Lax and Phillips for classical wave systems to quantum systems
- Introduces geometrical methods highly effective in diagnosing instability
- Written by leading experts in the field
Part of the book series: Mathematical Physics Studies (MPST)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
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 generally used methods today, such as the Gamow approach, and the Wigner-Weisskopf method, are critically discussed. The quantum mechanical Lax-Phillips theory developed by the authors, based on the dilation theory of Nagy and Foias and its more general extension to approximate semigroup evolution is explained.
The second part provides a description of approaches to classical stability analysis and introduces geometrical methods recently developed by the authors, which are shown to be highly effective in diagnosing instability and, in many cases, chaotic behavior. It is then shown that, in the framework of the theory of symplectic manifolds, there is a systematic algorithm for the construction of a canonical transformation of any standard potential model Hamiltonian to geometric form, making accessible powerful geometric methods for stability analysis in a wide range of applications.
Authors and Affiliations
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School of Physics, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel
Lawrence Horwitz
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Department of Mathematics, Ben-Gurion University of the Negev, Beér Sheva, Israel
Yosef Strauss
Bibliographic Information
Book Title: Unstable Systems
Authors: Lawrence Horwitz, Yosef Strauss
Series Title: Mathematical Physics Studies
DOI: https://doi.org/10.1007/978-3-030-31570-2
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-31569-6Published: 12 June 2020
Softcover ISBN: 978-3-030-31572-6Published: 16 July 2021
eBook ISBN: 978-3-030-31570-2Published: 11 June 2020
Series ISSN: 0921-3767
Series E-ISSN: 2352-3905
Edition Number: 1
Number of Pages: X, 221
Number of Illustrations: 96 b/w illustrations, 2 illustrations in colour
Topics: Quantum Physics, Elementary Particles, Quantum Field Theory, Mathematical Physics