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Nonlinear Dynamics and Quantum Chaos

An Introduction

Sandro Wimberger (Autor)

Buch | Hardcover

XIII, 206 Seiten

2014
Springer International Publishing (Verlag)
978-3-319-06342-3 (ISBN)

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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.

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

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.

"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)

Erscheint lt. Verlag	27.5.2014
Reihe/Serie	Graduate Texts in Physics
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	437 g
Einbandart	gebunden
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Optik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	EKB Quantization • Gutzwiller's Trace Formula • Hamilton-Jacobi theory • KAM Theorem • Kolmogorovsche Differentialgleichung • Kolmogorov-Sinai Entropy • Liouville, Joseph • Liouville's Theorem • Lyapunov exponent • Nichtlineares dynamisches System • nonlinear dynamical systems • Poincare-Birkhoff Theorem • quantum systems • Weyl Transform • WKBJ Approximation
ISBN-10	3-319-06342-1 / 3319063421
ISBN-13	978-3-319-06342-3 / 9783319063423
Zustand	Neuware