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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
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Martin Engel 2004-01-01