Pavel Stránský
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Last updated: 31.3.2025

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

Vojtěch Witzany (klasický chaos), Institute of teoretical physics MFF UK

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"). The course will include an introduction to Wolfram Mathematica, which will be used to solve these problems.

Please install Wolfram Mathematica before the first lecture and bring your laptops to the lectures.

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 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 27 February 2025 Vojtěch Introduction to Wolfram Mathematica
Wolfram Mathematica, discrete and continuous dynamical systems, pendulum with large amplitude
2nd lecture 6 March 2025 Vojtěch Integrable systems, unstable fixed point and local dynamics, periodic perturbation of the pendulum
3rd lecture 13 March 2025 Vojtěch Action-angle variables, Liouville integrability, homoclinic tangle (trellis)
4th lecture 20 March 2025 Vojtěch Periodic pertubation and tori break-up, rezonances, KAM theorem
5th lecture 27 March 2025 Vojtěch
6th lecture 3 April 2025 Pavel Quantum integrability
Poisson nearest-neighbour spacing distribution
2D infinite potential well
7th lecture 10 April 2025 Pavel Density of quantum levels
Unfolding
3D infinite potential well
8th lecture 17 April 2025 Pavel Chaotic systems
Wigner surmise, Bohigas-Giannoni-Schmit conjecture
Gaussian ensembles of random matrices
Wigner-Dyson nearest-neighbour spacing distribution
9th lecture 24 April 2025 Pavel Wigner semicircle law
Long-range correlations (Δ3, Σ2)
Ratio of consecutive levels
Mixed systems, Brody distribution
10th lecture 15 May 2025 Pavel Quantum billiards
1/f noise in quantum spectra
Peres lattices
Exam 22 May 2025
29 May 2025
(to be decided, on one of these days) 20-minute presentation of the assigned articles or of the completed computer project

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