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Table of Contents
Intro
Organization
Preface
Contents
Contributors
Chaos
Diffusion Without Spreading of a Wave Packet in Nonlinear Random Models
1 Introduction
1.1 Difference Between Spreading and Diffusion
1.2 Discussion of the Boltzmann Ergodic Hypothesis
2 Dynamics of Hamiltonians with a Finite Number of Degrees of Freedom
2.1 KAM Tori in Finite Nearly Integrable Hamiltonian Systems
2.2 Arnold Diffusion Conjecture and Extension
2.3 Anti Integrable Limit
3 Dynamics of Hamiltonians on Infinite Lattices
3.1 KAM Tori in Infinite Hamiltonian Systems on Lattices with Linear Discrete Spectrum
3.2 Numerical Observation of KAM Tori in Large Non Integrable Hamiltonian Systems
4 Long Time Behavior of Wave Packets
4.1 A Criterion for the Long Time Behavior of a Wave Packet
4.2 Discussion of the Long Time Behavior of Wave Packets
5 Exact Results for Ding Dong Models
5.1 Definition
5.2 Regular Trajectories and a Lemma
5.3 Some Exact Results
5.4 Non Genericity of DD Models
6 Concluding Remarks
References
Nonlinear Phenomena Shaping the Structure of Spiral Galaxies
1 Introduction
2 Order and Chaos
2.1 Two Dimensional (2D) Models
2.2 Three Dimensional (3D) Models
3 Discussion
References
Phase Space Transport and Dynamical Matching in a Caldera-Type Hamiltonian System
1 Introduction
2 Hamiltonian Model
3 Lagrangian Descriptors in Caldera-Type Hamiltonian Systems
4 Numerical Results
5 Conclusions
References
The Building Blocks of Spiral Arms in Galaxies
1 Introduction
2 Spiral Arms in Grand Design Galaxies
2.1 The Model
2.2 Spiral Density Waves from Precessing Ellipses
3 Spiral Arms in Barred Spiral Galaxies
3.1 The Model
3.2 Manifold Spirals
4 Conclusion
References
Ordered and Chaotic Bohmian Trajectories
1 Introduction
2 Nodal Point-X-Point Complex Mechanism
3 Chaos and Entanglement in Bohmian Qubits
4 Summary
References
A Brief Introduction to Quantum Chaos of Generic Systems
1 Introduction
2 Quantum Mechanics of Classically Integrable Systems
3 Quantum Chaos in Classically Ergodic Systems
4 Quantum Chaos in Generic Systems
4.1 The Wigner Functions
4.2 The Principle of Uniform Semiclassical Condensation (PUSC) of Wigner Functions
4.3 Spectral Statistics in the Mixed-type Systems
4.4 Quantum Localization of the Chaotic Eigenstates
5 The Poincar-̀ŒHusimi Functions in Billiards
6 The Phase Space Localization Measures of Chaotic Eigenstates
7 The Distribution of the Localization Measures
8 Semiclassical Limiting Approach to the Regime of PUSC
9 Discussion and Conclusions
References
Dynamics and Statistics of Weak Chaos in a 4-D Symplectic Map
1 Introduction
2 Statistical Analysis of Weak Chaos
3 Evidence of Weak Chaos in 4DMM Maps.
Organization
Preface
Contents
Contributors
Chaos
Diffusion Without Spreading of a Wave Packet in Nonlinear Random Models
1 Introduction
1.1 Difference Between Spreading and Diffusion
1.2 Discussion of the Boltzmann Ergodic Hypothesis
2 Dynamics of Hamiltonians with a Finite Number of Degrees of Freedom
2.1 KAM Tori in Finite Nearly Integrable Hamiltonian Systems
2.2 Arnold Diffusion Conjecture and Extension
2.3 Anti Integrable Limit
3 Dynamics of Hamiltonians on Infinite Lattices
3.1 KAM Tori in Infinite Hamiltonian Systems on Lattices with Linear Discrete Spectrum
3.2 Numerical Observation of KAM Tori in Large Non Integrable Hamiltonian Systems
4 Long Time Behavior of Wave Packets
4.1 A Criterion for the Long Time Behavior of a Wave Packet
4.2 Discussion of the Long Time Behavior of Wave Packets
5 Exact Results for Ding Dong Models
5.1 Definition
5.2 Regular Trajectories and a Lemma
5.3 Some Exact Results
5.4 Non Genericity of DD Models
6 Concluding Remarks
References
Nonlinear Phenomena Shaping the Structure of Spiral Galaxies
1 Introduction
2 Order and Chaos
2.1 Two Dimensional (2D) Models
2.2 Three Dimensional (3D) Models
3 Discussion
References
Phase Space Transport and Dynamical Matching in a Caldera-Type Hamiltonian System
1 Introduction
2 Hamiltonian Model
3 Lagrangian Descriptors in Caldera-Type Hamiltonian Systems
4 Numerical Results
5 Conclusions
References
The Building Blocks of Spiral Arms in Galaxies
1 Introduction
2 Spiral Arms in Grand Design Galaxies
2.1 The Model
2.2 Spiral Density Waves from Precessing Ellipses
3 Spiral Arms in Barred Spiral Galaxies
3.1 The Model
3.2 Manifold Spirals
4 Conclusion
References
Ordered and Chaotic Bohmian Trajectories
1 Introduction
2 Nodal Point-X-Point Complex Mechanism
3 Chaos and Entanglement in Bohmian Qubits
4 Summary
References
A Brief Introduction to Quantum Chaos of Generic Systems
1 Introduction
2 Quantum Mechanics of Classically Integrable Systems
3 Quantum Chaos in Classically Ergodic Systems
4 Quantum Chaos in Generic Systems
4.1 The Wigner Functions
4.2 The Principle of Uniform Semiclassical Condensation (PUSC) of Wigner Functions
4.3 Spectral Statistics in the Mixed-type Systems
4.4 Quantum Localization of the Chaotic Eigenstates
5 The Poincar-̀ŒHusimi Functions in Billiards
6 The Phase Space Localization Measures of Chaotic Eigenstates
7 The Distribution of the Localization Measures
8 Semiclassical Limiting Approach to the Regime of PUSC
9 Discussion and Conclusions
References
Dynamics and Statistics of Weak Chaos in a 4-D Symplectic Map
1 Introduction
2 Statistical Analysis of Weak Chaos
3 Evidence of Weak Chaos in 4DMM Maps.