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 (classical chaos), Astronomical Institute CAS

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

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 Thursdays at 9.00 am (classical chaos, till 4 April 2024) and Tuesdays from 2.50 pm (quantum chaos, from 9 April 2024) in the lecture room A920 at the Institute of Particle and Nuclear Physics, MFF CUNI, 8th floor at the Troja building. A preliminary schedule is the following:

1st lecture	29 February 2023	Georgios	Symplectic maps, variational principles, and transport Non-linear effects in EMRI dynamics and their imprints on gravitational waves
2nd lecture	7 March 2024	Georgios
3rd lecture	14 March 2024	Georgios
4th lecture	21 March 2024	Georgios	Hénon-Heiles system
5th lecture	28 March 2024	Georgios
6th lecture	4 April 2024	Vojtěch Witzany	Canonical perturbation theory
7th lecture	9 April 2024	Pavel	Quantum integrability Poisson nearest-neighbour spacing distribution 2D infinite potential well
8th lecture	16 April 2024	Pavel	Density of quantum levels Unfolding 3D infinite potential well
9th lecture	30 April 2024	Pavel	Chaotic systems Wigner surmise, Bohigas-Giannoni-Schmit conjecture Gaussian ensembles of random matrices Wigner-Dyson nearest-neighbour spacing distribution
10th lecture	7 April 2024	Pavel	Wigner semicircle law Long-range correlations (Δ3, Σ2) Ratio of consecutive levels Mixed systems, Brody distribution
11th lecture	14 May 2024	Pavel	Quantum billiards Peres lattices
Exam	21 May 2024 2.50 pm, A920

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