Introduction to the chaotic dynamics of classical Hamiltonian systems and to the spectral properties of their quantum counterparts.
For addition information about the subject consult SIS.
Dr. Georgios Loukes-Gerakopoulos, Astronomical Institute CAS (classical chaos)
Dr. Pavel Stránský, Institute of Particle and Nuclear Physics MFF UK (quantum chaos)
Theory demonstrated by practical problems solved on computers ("hands-on").
Classical theoretical mechanics, quantum mechanics and programming. The course is intended for students master and doctoral students of theoretical programmes. but everybody interested in the topic is welcome.
1st lecture | 21/2/2023 | Georgios |
Symplectic maps, variational principles, and transport Non-linear effects in EMRI dynamics and their imprints on gravitational waves |
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2nd lecture | 28/2/2023 | Georgios | |
3rd lecture | 7/3/2023 | Georgios | |
4th lecture | 14/3/2023 | Georgios | |
5th lecture | 21/3/2023 | Pavel | Quantum integrability Poisson nearest-neighbour spacing distribution 2D infinite potential well |
6th lecture | 28/3/2023 | Pavel | Density of quantum levels Unfolding 3D infinite potential well |
7th lecture | 4/4/2023 | Pavel | Chaotic systems Wigner surmise, Bohigas-Giannoni-Schmit conjecture Gaussian ensembles of random matrices Wigner-Dyson nearest-neighbour spacing distribution |
8th lecture | 11/4/2023 | Pavel | Wigner semicircle law Long-range correlations (Δ3, Σ2) Ratio of consecutive levels Mixed systems, Brody distribution |
9th lecture | 18/5/2023 | Pavel | Quantum billiards Peres lattices |
10th lecture | 25/5/2023 | Pavel | 1/f noise in quantum spectra Wishart ensemble |
Exam | 23/5/2023 |
Lecture notes on quantum chaos and solutions of the tasks are in the repository on GitHub.
1/f noise and scale invariance - PowerPoint presentation
Peres lattices, applications of Random matrix theory, demonstrated on Double pendulum - PowerPoint presentation
Blackboard copy 2021 - PDF