Spinning particles : semiclassics and spectral statistics /
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Author / Creator: | Keppeler, Stefan, 1973- |
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Imprint: | Berlin ; New York : Springer, ©2003. |
Description: | 1 online resource (ix, 189 pages) : illustrations. |
Language: | English |
Series: | Springer tracts in modern physics, 0081-3869 ; v. 193 Springer tracts in modern physics ; v. 193. |
Subject: | |
Format: | E-Resource Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11065338 |
Table of Contents:
- 1. Introduction
- References
- 2. Warming up: Oscillators
- 2.1. Semiclassical Trace Formulae
- 2.2. Spectral Statistics
- References
- 3. Trace Formulae with Spin
- 3.1. The Pauli Hamiltonian
- 3.2. Deriving Trace Formulae: General Strategy
- 3.3. Semiclassical Time Evolution for Pauli Hamiltonians
- 3.4. Spin Transport and Spin Precession
- 3.5. Semiclassical Trace Formulae
- 3.5.1. The Weyl term
- 3.5.2. Hyperbolic Systems
- 3.5.3. Integrable Systems
- 3.6. Examples
- 3.6.1. Reprise: Oscillators
- 3.6.2. Spin-Orbit Coupling in 2 Dimensions - sp-Billiards
- 3.6.3. The sp-Torus
- 3.6.4. Spin-Orbit Coupling in Non-Relativistic Hydrogen
- 3.7. Trace Formula for the Dirac Equation
- 3.7.1. Reprise: The Dirac Oscillator
- 3.8. A Different Limit of the Pauli Equation
- References
- 4. Classical Dynamics of Spinning Particles - the Skew Product
- 4.1. The Skew Products Y t and Y c tl
- 4.2. Excursion: Observables for Spinning Particles
- 4.3. Ergodic Properties of the Skew Product
- 4.4. Integrable Systems
- 4.4.1. Hamiltonian Systems - the Theorem of Liouville and Arnold
- 4.4.2. Integrability of the Skew Product
- 4.5. Reprise: Trace Formula for Integrable Systems
- References
- 5. Torus Quantisation
- 5.1. Quantum Mechanical Integrability
- 5.2. EBK-Quantisation
- 5.3. Torus Quantisation and Spin Rotation Angles
- 5.4. Examples
- 5.4.1. Homogeneous Magnetic Field
- 5.4.2. The sp-Torus
- 5.4.3. Rotationally Invariant Systems
- 5.4.4. Spin-Orbit Coupling in Non-Relativistic Hydrogen
- 5.5. Spin Rotation Angles in the Dirac Case
- 5.6. The Sommerfeld Formula
- 5.7. Excursion: Remarks on the General Case
- References
- 6. Classical Sum Rules
- 6.1. Basic Idea
- 6.2. Some Remarks on the Status of Sum Rules
- 6.3. Hannay-Ozorio de Almeida Sum Rules
- 6.3.1. Chaotic Systems
- 6.3.2. Integrable Systems
- 6.4. Classical Time Evolution Operators for Spinning Particles
- 6.5. Spin in Classical Sum Rules
- 6.5.1. Chaotic Systems
- 6.5.2. Integrable Systems
- 6.5.3. Partially Integrable Systems
- References
- 7. Spectral Statistics and Spin
- 7.1. Symmetries and Unfolding
- 7.2. Time Reversal Invariance in the Trace Formula
- 7.3. Spectral Two-Point Form Factor
- 7.3.1. Diagonal Approximation
- 7.3.2. Chaotic Systems
- 7.3.3. Integrable Systems
- 7.3.4. Partially Integrable Systems
- 7.4. Illustration: The sp-Rectangle
- 7.5. Other Statistical Measures
- 7.5.1. The Number Variance
- 7.5.2. e
- 7.5.3. R 2 (s) and the Bogomolny-Keating Bootstrap
- References
- Appendices
- A. The Poisson Summation Formula
- B. Solution of the Scalar Transport Equation
- C. Some Facts About the Groups SU(2) and SO(3)
- D. The Method of Stationary Phase
- E. Wigner-Weyl Calculus
- F. Remarks on the Numerical Calculation of the Spectral Form Factor
- References
- Index