Contents

• Stochastic Webs in Classical Mechanics
  • The Kicked Harmonic Oscillator
    • Newtonian Equations of Motion
    • Canonical Formulation
    • Discrete Dynamics -- The Web Map
    • Generalized Web Maps
  • The Stochastic Web
    • Symmetries of the Web
    • The Skeleton of the Web
    • The Influence of the Kick Amplitude
    • Diffusive Energy Growth in the Channels
  • The Complementary Case: Nonresonance
  
  
• Quantum Mechanics of the Kicked Harmonic Oscillator
  • The Quantum Map
    • FLOQUET Theory
    • The FLOQUET Operator of the Kicked Harmonic Oscillator
    • Matrix Elements of the FLOQUET operator
  • The Classical Limit
  • Discussion of the Parameter Dependence
  
  
• Numerical Methods
  • Finite Differences
    • An Algorithm Based on the TROTTER Formula
    • The GOLDBERG Algorithm
  • Numerical Evaluation of the Propagator in the Position Representation
  • The Propagator in the Eigenrepresentation of the Free Harmonic Oscillator
  • Discussion of the Numerical Methods
  
  
• Quantum Stochastic Webs
  • Numerical Indications of Quantum Stochastic Webs
    • The Quantum Skeleton
    • Diffusing Wave Packets
  • An Analytical Explanation of Quantum Stochastic Webs
    • Translational Invariance of the Quantum Skeleton
    • Energy Growth within Quantum Stochastic Webs
  
  
• ANDERSON Localization
  • ANDERSON Localization in the Quantum Kicked Rotor
    • The Kicked Rotor
    • ANDERSON Localization on One-dimensional Lattices
    • Mapping of the Quantum Kicked Rotor onto the ANDERSON Model
  • Localized Wave Packets in the Quantum Kicked Harmonic Oscillator
    • Numerical Indications of Localization
    • Dependence on Initial Conditions
  • The Nonresonant Quantum Kicked Harmonic Oscillator is ANDERSON-localized
    • Mapping of the Quantum Kicked Harmonic Oscillator onto an ANDERSON-like Model
    • Localization Established
    • Localization in All but the Pathological Cases
    • Discussion
  
  
• Quantum Phase Space Distribution Functions
  • Definition of Quantum Phase Space Distribution Functions
  • Special Distribution Functions
  • Minimum Uncertainty States and the HUSIMI Distribution Function
    • Coherent States
    • Squeezed States
    • The HUSIMI Distribution Function
  • Dynamics
  • On the Interpretation as Probability Densities
  • Typical Applications
  
  
• Random Products of Unimodular Matrices
• A Picture Book of Quantum Stochastic Webs and Localization
  • Rectangular Quantum Stochastic Webs
    • ,
    • ,
  • Hexagonal Quantum Stochastic Webs
    • ,
    • ,
  • ,
  • Examples of Quantum Localization
    • ,
    • ,
  
  
• List of Tables
• Bibliography
• Danksagung