Pavel Stránský
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Last updated: 14.5.2024

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.


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").


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.


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
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