Classical and Quantum Chaos

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.

Lecturers

Dr. Georgios Loukes-Gerakopoulos, Astronomical Institute CAS (classical chaos)

Dr. Pavel Stránský, Institute of Particle and Nuclear Physics MFF UK (quantum chaos)

Lecture style

Theory demonstrated by practical problems solved on computers ("hands-on").

Prerequisites

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.

Schedule

the course is held on Tuesdays at 10.40 am in the lecture room A836 at the Institute of Particle and Nuclear Physics, MFF CUNI, 8th floor at the Troja building. A preliminary schedule is the following:

1st lecture	21/2/2023	Georgios	Symplectic maps, variational principles, and transport Non-linear effects in EMRI dynamics and their imprints on gravitational waves
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 from previous years

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