Nonlinear Dynamics and Quantum Chaos

Sandro Wimberger

ISBN 10: 303101250X ISBN 13: 9783031012501

Edit� par Springer International Publishing AG

Langue: anglais

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Titre

Nonlinear Dynamics and Quantum Chaos

�diteur

Springer International Publishing AG

Langue

anglais

ISBN � 10 chiffres

303101250X

ISBN � 13 chiffres

9783031012501

Reliure

PAP

�dition

2�me �dition

�tat de l'article

New

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Synopsis

Introduction.- Fundamental terminology.- Complexity.- Classical versus quantum dynamics.- Problems.- References.- Dynamical systems.- Evolution law.- One-dimensional maps.- Problems.- References.- Nonlinear Hamiltonian systems.- Integrable examples.- Hamiltonian formalism.- Important techniques in the Hamiltonian formalism.- Integrable systems.- Non-integrable systems.- Perturbation of low-dimensional systems.- Canonical perturbation theory.- Transition to chaos in Hamiltonian systems.- Criteria for local and global chaos.- Appendix.- Problems.- References.-

Dissipative systems - Introduction - Fixed points - Fixed point scenarios in two dimensional systems - Damped Oscillators - Harmonic oscillator - Nonlinear oscillators - Nonlinear damping - Poincar�-Bendixson Theorem - Damped forced oscillators - Driven one-Dimensional harmonic oscillator - Duffing oscillator - Lorenz model for turbulence - Fractals - Simple examples - Box-counting dimension - Examples from nature - Bifurcation scenarios - Examples of pitchfork bifurcations - Tangent bifurcations - Transcritical bifurcations - Higher-order bifurcations - Hopft bifurcations - Intermittency - Coupled Oscillators - Synchronisation - Kuramoto model - Increasing complexity - Problems - References. -

Aspects of quantum chaos.- Introductory remarks on quantum mechanics.- Semiclassical quantization of integrable systems.- Semiclassical description of non-integrable systems.- Wave functions in phase space.- Anderson and dynamical localization.- Universal level statistics.- Concluding remarks.- Appendix.- Problems.- References.- Index.

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