Classical and Quantum Dynamical Systems
This course will start with a review on a section of topics from analytical mechanics as the basis for what follows. In particular, on topics such as non-integrability criteria, KAM theory, Lyapunov coefficients. The bridge to quantum dynamics will be built via semiclassical theory based on the Weyl representation. Standard topics of quantum chaos will be presented, i.e. dynamical/Anderson and many-body localisation, spectral definitions of chaos and their relation to semiclassics. Modern application such as driven Floquet systems and thermalisation in isolated quantum systems will be touched upon in specific examples.
- "Semiclassical Physics", by Matthias Brack and Rajat K. Bhaduri, Addison-Wesley, Reading MA, 1997
- "Nonlinear Dynamics and Quantum Chaos", by S. Wimberger, Springer, 2014