Yosef Strauss: Unstable Systems

Cover: 9783030315696 | Unstable Systems | Yosef Strauss (u. a.) | Buch | x | Englisch | 2020

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Beschreibung

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.

Zusammenfassung

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

Inhaltsverzeichnis

Part I: Quantum Systems and Their Evolution.- Chapter 1: Gamow approach to the unstable quantum system. Wigner-Weisskopf formulation. Analyticity and the propagator. Approximate exponential decay. Rotation of Spectrum to define states. Difficulties in the case of two or more final states.- Chapter 2: Rigged Hilbert spaces (Gel'fand Triples). Work of Bohm and Gadella. Work of Sigal and Horwitz, Baumgartel. Advantages and problems of the method.- Chapter 3: Ideas of Nagy and Foias, invariant subspaces. Lax-Phillips Theory (exact semigroup). Generalization to quantum theory (unbounded spectrum). Stark effect.- Relativistic Lee-Friedrichs model.- Generalization to positive spectrum.- Relation to Brownian motion, wave function collapse.- Resonances of particles and fields with spin. Resonances of nonabelian gauge fields.- Resonances of the matter fields giving rise to the gauge fields. Resonence of the two dimensional lattice of graphene. Part II: Classical Systems.- Chapter 4: General dynamical systems and instability. Hamiltonian dynamical systems and instability. Geometrical ermbedding of Hamiltonian dynamical systems. Criterion for instability and chaos, geodesic deviation.

Part III: Quantization.- Chapter 5: Second Quantization of geometric deviation. Dynamical instability. Dilation along a geodesic.- Part IV: Applications.- Chapter 6: Phonons. Resonances in semiconductors. Superconductivity (Cooper pairs). Properties of grapheme. Thermodynamic properties of chaotic systems. Gravitational waves.

Erscheinungsjahr:	2020
Fachbereich:	Theoretische Physik
Genre:	Mathematik , Medizin , Naturwissenschaften , Physik , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	x 221 S. 96 s/w Illustr. 2 farbige Illustr. 221 p. 98 illus. 2 illus. in color.
ISBN-13:	9783030315696
ISBN-10:	303031569X
Sprache:	Englisch
Einband:	Gebunden
Autor:	Strauss, Yosef Horwitz, Lawrence
Auflage:	1st edition 2020
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 19 mm
Von/Mit:	Yosef Strauss (u. a.)
Erscheinungsdatum:	12.06.2020
Gewicht:	0,518 kg

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