Sandro Wimberger

Nonlinear Dynamics and Quantum Chaos (eBook, PDF)

An Introduction

• Format: PDF

Produktbeschreibung

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 206
• Erscheinungstermin: 13. Mai 2014
• Englisch
• ISBN-13: 9783319063430
• Artikelnr.: 43801985

Autorenporträt

Prof. Sandro Wimberger Institut für Theoretische Physik Universität Heidelberg Heidelberg, Germany

Inhaltsangabe

Introduction.- Fundamental terminology.- Complexity.- Classical versus quantum dynamics.- Problems.- References.- Dynamical systems.- Evolution law.- One-dimensional maps.- Problems.- References.- Nonlinear Hamiltonian systems.- Integrable examples.- Hamiltonian formalism.- Important techniques in the Hamiltonian formalism.- Integrable systems.- Non-integrable systems.- Perturbation of low-dimensional systems.- Canonical perturbation theory.- Transition to chaos in Hamiltonian systems.- Criteria for local and global chaos.- Appendix.- Problems.- References.- Aspects of quantum chaos.- Introductory remarks on quantum mechanics.- Semiclassical quantization of integrable systems.- Semiclassical description of non-integrable systems.- Wave functions in phase space.- Anderson and dynamical localization.- Universal level statistics.- Concluding remarks.- Appendix.- Problems.- References.- Index.

Rezensionen

"This book comprises a convincing introduction to nonlinear dynamics of conservative and dissipative systems and for the Hamiltonian systems it takes the discussion to their quantum manifestations. The treatment is crystal clear and quite thorough in many parts. ... The illustrations are valuable. ... The present book gives a lovely introduction and prepares the readers for more detailed treatments. ... this is a brilliant introduction with an excellent pedagogical value." (S. R. Jain, Mathematical Reviews, December, 2024)