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.
Symplectic maps, variational principles, and transport
Non-linear effects in EMRI dynamics and their imprints on gravitational waves
|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
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
|10th lecture||25/5/2023||Pavel||1/f noise in quantum spectra
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