Unstable Systems
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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 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.
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.
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
Autor*in
Lawrence Horwitz
Themen in »Unstable Systems«
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