Overview

Abstract

This book is about the nonlinear dynamics of conservative classical and quantum systems. Although classical and quantum mechanics are now rather old subjects (classical mechanics is over 300 years old and quantum mechanics is over 90 years old), the mechanisms affecting their dynamical evolution have only recently been understood. In this book we will focus on the transition to chaos in classical systems and the manifestations of chaos in quantum systems. One of the important discoveries in quantum physics in recent years is that the information content of quantum systems is extremized when the underlying classical system undergoes a transition to chaos. The information content approaches that of a system whose dynamics is governed by a random Hamiltonian matrix chosen to extremize information. For this reason, random matrix theory has become essential to quantum chaos theory. In this book we include a self-contained discussion of the random matrix theory and supersymmetry techniques necessary for the study of the statistical properties of quantum systems. Toward the end of the book, we include a short chapter showing that the manifestations of chaos can also appear in stochastic systems.