Lawrence Horwitz,Yosef Strauss
Unstable Systems
Unstable Systems
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This book discusses unstable systems from classical and quantum mechanical perspectives, exploring methods like the Gamow approach and the Wigner-Weisskopf method. It also introduces geometrical methods for stability analysis and demonstrates how to construct canonical transformations for Hamiltonian models in symplectic manifolds.
Format: Paperback / softback
Length: 221 pages
Publication date: 16 July 2021
Publisher: Springer Nature Switzerland AG
This comprehensive book delves into the realm of unstable systems, exploring their dynamics from both classical and quantum mechanical perspectives. It examines the intricate connections between these two domains and sheds light on the underlying principles governing their behavior.
In the first part, the authors delve into the world of quantum systems. They critically analyze the prevalent methods employed today, such as the Gamow approach and the Wigner-Weisskopf method. Additionally, they introduce their groundbreaking quantum mechanical Lax-Phillips theory, which is built upon the dilation theory of Nagy and Foias and extends to approximate semigroup evolution. This theory provides a deep understanding of quantum mechanics and its applications.
The second part of the book focuses on classical stability analysis. Here, the authors introduce their innovative geometrical methods, which have proven to be highly effective in diagnosing instability and, in many cases, chaotic behavior. They showcase how these methods can be applied to various systems, ranging from mechanical systems to complex biological networks.
Furthermore, the book demonstrates that within the framework of symplectic manifolds, there exists a systematic algorithm for constructing a canonical transformation of any standard potential model Hamiltonian to geometric form. This transformation opens up a vast array of powerful geometric methods for stability analysis in a wide range of applications.
By combining classical and quantum mechanical principles, this book offers a comprehensive and insightful exploration of unstable systems. It provides researchers and practitioners with valuable tools and techniques to analyze and understand the complex dynamics of these systems, paving the way for advancements in various fields, including physics, engineering, and biology.
Weight: 361g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030315726
Edition number: 1st ed. 2020
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