The Transition to Chaos

Overview

Based on courses given at the universities of Texas in Austin, and California in San Diego, this book deals with the basic mechanisms that determine the dynamic evolution of classical and quantum systems. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; it continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and it concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature. Problems at the ends of chapters help students clarify their understanding. In this new edition, the presentation will be brought up to date throughout, and a new chapter on open quantum systems will be added.

Details

Publisher

Springer Science & Business Media

Published

2013-11-11

Pages

675

Language

EN

Categories

Science / System Theory, Science / Physics / Mathematical & Computational, Language Arts & Disciplines / Library & Information Science / General, Science / Physics / General

ISBN-13

9781475743500