Nonlinear Dynamics and Quantum Chaos: An Introduction 2nd Edition By Sandro Wimberger
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Nonlinear Dynamics and Quantum Chaos: An Introduction 2nd Edition By Sandro Wimberger

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270
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5.64 MB
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About this ebook
The second edition of Nonlinear Dynamics and Quantum Chaos: An Introduction by Sandro Wimberger (published by Springer) expands upon the first edition by offering an integrated approach to classical and quantum chaotic systems. [1, 2]
The defining addition of the 2nd edition is a brand-new chapter dedicated specifically to dissipative nonlinear systems. [1]
The primary topics and core thematic chapters covered in the text include:
1. Fundamentals of Dynamical Systems
  • Formal Definitions: Mathematical frameworks for defining both classical and quantum dynamical systems.
  • Discrete Maps: Detailed exploration of one-dimensional discrete mappings (e.g., the logistic map) to illustrate fundamental chaotic behavior.
  • Chaotic Metrics: Core introductory tools used to diagnose and classify the properties of regular versus chaotic trajectories. [1]
2. Classical Nonlinear Hamiltonian Systems
  • Hamiltonian Mechanics: A review of the foundational concepts of continuous classical mechanics.
  • Integrability: Defining regular, predictable motion and the conditions under which a system is integrable.
  • Non-Integrability & Chaos: The transition from regular phase spaces to chaotic ones when perturbation destroys integrability. [, 2]
3. Dissipative Nonlinear Systems (New to the 2nd Edition)
  • Dissipative Dynamics: Moving beyond ideal Hamiltonian (energy-conserving) systems to analyze friction, damping, and energy-loss mechanisms.
  • Attractors: Study of stable fixed points, limit cycles, and strange attractors that characterize chaotic dissipation.
  • Bifurcation Theory: Analysis of how system states qualitatively split and transition into chaos as control parameters change. [1, 3]
4. Quantum Chaos & Semiclassics
  • Semiclassical Analysis: Comparing quantum evolution to classical analogs, blending classical intuition with quantum wave functions. []
  • Spectral Properties: Characterizing quantum chaoticity using the properties of the quantum energy spectrum. []
  • Random Matrix Theory (RMT): Utilizing random matrix ensembles to model and describe energy level statistics in highly chaotic quantum regimes. [1, 2, 3]
  • Quantum Localization: Phenomena such as dynamical localization (analogous to Anderson localization) where quantum interference suppresses classical chaotic diffusion. [, 2]
5. Practical Learning Elements
  • Worked Examples: Real-world applications to help readers bridge the gap between abstract equations and physical observation.
  • End-of-Chapter Exercises: Problems designed specifically for advanced physics or mathematics graduate coursework. [1, 2]

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Topics

Classical Nonlinear Hamiltonian Systems defining both classical and quantum dynamical systems Dissipative Nonlinear Systems dynamical localization (analogous to Anderson localization) one-dimensional discrete mappings (e.g. properties of the quantum energy spectrum Quantum Chaos & Semiclassics quantum interference suppresses classical chaotic diffusion Random Matrix Theory (RMT) Study of stable fixed points limit cycles. strange attractors that characterize chaotic dissipation the logistic map)
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