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The Transition to Chaos - Conservative Classical Systems and Quantum Manifestations (Hardcover, 2nd ed. 2004)
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The Transition to Chaos - Conservative Classical Systems and Quantum Manifestations (Hardcover, 2nd ed. 2004)
Series: Institute for Nonlinear Science
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Based on courses given at the universities of Texas in Austin, and
California in San Diego, this book treats an active fields of
research that touches upon the foundations of physics and
chemistry. 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.
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