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The Transition to Chaos : I...
The subjects treated here are part of an active and rapidly growing field of research that touches on the foundations of physics and chemistry. Specifically, the book presents, in as simple and coherent a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include nonlinear 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 concludes by showing how to apply the ideas to stochastic systems. Appendices fill in much of the necessary mathematical background. Based on courses given at Universities in California, Texas, and China, the book will be useful both as a text and as a reference. The presentation is complete, and there are extensive references to the current research literature. Problems at the ends of the chapters will help students clarify their understanding of the concepts
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monografia Rebiun38928354 https://catalogo.rebiun.org/rebiun/record/Rebiun38928354 m o d cr mnu---uuaaa 130410s1992 nyu ob 001 0 eng 934976629 1058108309 1086562490 9781475743524 electronic bk.) 1475743521 electronic bk.) 9781475743548 1475743548 1475743521 10.1007/978-1-4757-4352-4 doi AU@ 000051692700 NZ1 15182335 AU@ eng pn AU@ GW5XE OCLCQ OCLCF UA@ COO OCLCQ EBLCP OCLCQ UAB OCLCQ LEAUB OCLCQ UKAHL OCLCO OCLCQ OCLCO OCLCL PHS bicssc PHDT bicssc SCI055000 bisacsh PHS thema PHDT thema 621 23 https://id.oclc.org/worldcat/ddc/E4djYmFy7KK4mwFQy33t3Tt7kT Reichl, L. E. The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations by L.E. Reichl New York, NY Springer New York 1992 New York, NY New York, NY Springer New York 1 online resource (xvi, 551 pages) 1 online resource (xvi, 551 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Institute for Nonlinear Science 1431-4673 Includes bibliographical references at the end of each chapters and indexes 1. Overview -- I Classical Systems -- 2. Fundamental Concepts -- 3. Area Preserving Maps -- 4. Global Properties -- II Quantum Systems -- 5. Quantum Integrability -- 6. Random Matrix Theory -- 7. Observed Spectra -- 8. Semi-Classical Theory -- 9. Driven Systems -- III Stochastic Systems -- 10. Stochastic Systems -- IV Appendices -- A. Classical Mechanics -- A.1 Newton's Equations -- A.2 Lagrange's Equations -- A.3 Hamilton's Equations -- A.4 The Poisson Bracket -- A.5 Phase Space Volume Conservation -- A.6 Action-Angle Variables -- A.7 Hamilton's Principle Function -- A.8 References -- B. Simple Models -- B.1 The Pendulum -- B.2 Double Well Potential -- B.3 Infinite Square Well Potential -- B.4 One-Dimensional Hydrogen -- C. Renormalization Integral -- C.3 References -- D. The Moyal Bracket -- D.1 The Wigner Function -- D.2 Ordering of Operators -- D.3 Moyal Bracket -- D.4 References -- E. SU(3) -- E.1 Special Unitary Groups -- E.2 References -- F. Space-Time Symmetries -- F.1 Linear and Antilinear Operators -- F.2 Infinitesimal Transformations -- F.3 Discrete Transformations -- F.4 References -- G. GOE Spectral Statistics -- G.5 References -- H. COE Spectral Statistics -- H.4 References -- I. Lloyd's Model -- L.1 Localization Length -- L.2 References -- J. Hydrogen in Parabolic Coordinates -- J.1 The Schrodinger Equation -- J.2 One-dimensional Hydrogen -- J.3 References -- Author Index The subjects treated here are part of an active and rapidly growing field of research that touches on the foundations of physics and chemistry. Specifically, the book presents, in as simple and coherent a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include nonlinear 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 concludes by showing how to apply the ideas to stochastic systems. Appendices fill in much of the necessary mathematical background. Based on courses given at Universities in California, Texas, and China, the book will be useful both as a text and as a reference. The presentation is complete, and there are extensive references to the current research literature. Problems at the ends of the chapters will help students clarify their understanding of the concepts English Physics Quantum theory Physique Théorie quantique physics. Physics. Quantum theory. Print version 9781475743548 Institute for Nonlinear Science