The Transition to Chaos In Conservative Classical Systems: Quantum Manifestations
resonances. Nonlinear resonances cause divergences in conventional perturbation expansions. This occurs because nonlinear resonances cause a topological change locally in the structure of the phase space and simple perturbation theory is not adequate to deal with such topological changes. In Sect. (...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1992, 1992
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| Edition: | 1st ed. 1992 |
| Series: | Institute for Nonlinear Science
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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