Nonlinear Dynamics and Quantum Chaos

An Introduction

Sandro Wimberger

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English

Springer International Publishing AG
03 September 2016

Cybernetics & systems theory; Non-linear science; Classical mechanics; Light (optics); Mathematical physics

Series: Graduate Texts in Physics

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.

By: Sandro Wimberger
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 1st ed. 2014
Dimensions: Height: 235mm, Width: 155mm, Spine: 12mm
Weight: 472g
ISBN: 9783319343327
ISBN 10: 3319343327
Series: Graduate Texts in Physics
Pages: 206
Publication Date: 03 September 2016
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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

Reviews for Nonlinear Dynamics and Quantum Chaos: An Introduction

This book is designed to introduce nonlinear dynamics and quantum chaos in a coherent and succinct presentation. It is aimed at advanced undergraduates and graduate students and is intended to serve as a textbook for a one-semester course. ... this book is one of the few that treats the subject in the context of quantum mechanics with quantum chaos. Along the way it provides a modest number of exercises for the student as well as a good bibliography. (William J. Satzer Jr., zbMATH, Vol. 1365.37001, 2017)