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. This lecture is intended for students of the 3rd year of bachelor studies, for master students, and for everyone interested in the topic.
The lectures are given on Tuesdays from 9am to 11am. The first part of the course (classical chaos) will take place in the lecture hall 101 at the Astronomical Institute CAS, the second part (quantum chaos) will be held in the lecture room A836 at the Institute of Particle and Nuclear Physics, MFF CUNI, 8th floor at the Troja building. Preliminary schedule is the following:
Symplectic maps, variational principles, and transport
Non-linear effects in EMRI dynamics and their imprints on gravitational waves
|6th lecture||28/3/2022||Pavel||Quantum integrability
Poisson nearest-neighbour spacing distribution
2D infinite potential well
|7th lecture||4/4/2022||Pavel||Density of quantum levels
3D infinite potential well
|8th lecture||25/4/2022||Pavel||Chaotic systems
Wigner surmise, Bohigas-Giannoni-Schmit conjecture
Gaussian ensembles of random matrices
|9th lecture||2/5/2022||Pavel||Wigner-Dyson nearest-neighbour spacing distribution
Wigner semicircle law
Ratio of consecutive levels
Mixed systems, Brody distribution
|10th lecture||9/5/2022||Pavel||Long-range correlations (Δ3, Σ2, 1/f noise)
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