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UNSTABLE SYSTEMS IBD

LAWRENCE HORWITZ / YOSEF STRAUSS
SPRINGER
06 / 2020
9783030315696
Inglés

Sinopsis

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. Hereáthe main generally used methods today, such as the Gamow approach, and the Wigner-Weisskopf method, are critically discussed. The quantumá mechanical Lax-Phillips theory developed by the authors, based on the dilation theory of Nagy and Foiasáand 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.áIt isá then shown that,áin the framework ofááthe theory of symplecticámanifolds, there is a systematicáalgorithm for the construction of a canonical transformationáof any standard potential model Hamiltonian to geometric form, making accessible powerful geometric methods forástability analysis ináa wide range of applications.