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Title: Chaos in Classical and Quantum Mechanics (Interdisciplinary Applied Mathematics, Vol. 1) by Martin C. Gutzwiller ISBN: 0-387-97173-4 Publisher: Springer Verlag Pub. Date: January, 1991 Format: Hardcover Volumes: 1 List Price(USD): $63.95

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Average Customer Rating: 4.2 (5 reviews)

Rating: 2
Summary: We need more books on the subject
Comment: While the question of connecting quantum theory to classical
mechanics, ODEs, PDEs, etc is a very deep one, and the
author is a main contributor in the subject, the books
lacks of narrative momentum... Readers of, say, QFT a la
Itzkinson-Zuber will be accostumed to this, but I feel a
more focused work on the subject is still to be written.

Rating: 5
Summary: The Father of the Quasiclassical Approach to Quantum Chaos
Comment: Today the Gutzwiller trace formula is the standard quasiclassical approach to studies of the spectrum in quantum chaos research.
The most striking property of classics chaos is the sensitive dependence on initial conditions such that neighboring trajectories in phase space separate at an exponential rate. As result the long time behavior of the system is unpredictable. Instead of looking for exponential sensitivity, the main stream of quantum chaos research is currently concentrated on identifying the fingerprints of classical chaos in quantum systems. If one were to identify unique fingerprints of classical chaos in quantum mechanics, one could use these to define quantum chaos.
The starting point for the Gutzwiller quasiclassical analysis is the path integral formulation of the propagator. From this quantum expression one can deduce a formula that contains a sum over all classical periodic orbits. This is the main contribution of Gutzwiller.
Excellent Book!

Rating: 5
Summary: Absolute Reference for Quantum Chaos
Comment: Organization and presentation of the ideas of modern chaos theory for classical and quantum world without deeper mathematical proofs in perfect fashion meets in this book. Historical, mathematical and physical origins of the chaos and semiclassical quantization problems have appeared as an introductory. Topics covered with great care, If you like to have a good foundation in this field, this book is absolute must. It served as a guide where to go in quantum chaos. Read it word by word and consult many references in nature of classical, statistical and quantum mechanical, differential geometrical and applied mathematics. Excellent book.

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