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