Nonlinear Dynamics and Quantum Chaos

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)