Spinning particles : semiclassics and spectral statistics /

Spinning particles : semiclassics and spectral statistics /

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Bibliographic Details
Author / Creator:Keppeler, Stefan, 1973-
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:
Nuclear spin.
Particles (Nuclear physics)
Quantum chaos.
Nuclear spin.
Particles (Nuclear physics)
Quantum chaos.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11065338
Hidden Bibliographic Details
ISBN:9783540366133
354036613X
3540011846
9783540011842
Notes:Includes bibliographical references.
Summary:The book deals with semiclassical methods for systems with spin, in particular methods involving trace formulae and torus quantisation and their applications in the theory of quantum chaos, e.g. the characterisation of spectral correlations. The theoretical tools developed here not only have immediate applications in the theory of quantum chaos - which is the second focus of the book - but also in atomic and mesoscopic physics. Thus the intuitive understanding of semiclassical spin dynamics will also be helpful in emerging subjects like spintronics and quantum computation.
Other form:Print version: Keppeler, Stefan, 1973- Spinning particles. Berlin ; New York : Springer, ©2003
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

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