Pavel Stránský
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Last updated: 20.6.2022

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. This lecture is intended for students of the 3rd year of bachelor studies, for master students, and for everyone interested in the topic.

Schedule

The lectures are given on Tuesdays from 9am to 11am. The first part of the course (classical chaos) will take place in the lecture hall 101 at the Astronomical Institute CAS, the second part (quantum chaos) will be held in the lecture room A836 at the Institute of Particle and Nuclear Physics, MFF CUNI, 8th floor at the Troja building. Preliminary schedule is the following:

1st lecture 22/2/2022 Georgios Symplectic maps, variational principles, and transport
Non-linear effects in EMRI dynamics and their imprints on gravitational waves
2nd lecture 1/3/2022 Georgios
3rd lecture 8/3/2022 Georgios
4th lecture 15/3/2022 Georgios
5th lecture 22/3/2022 Georgios
6th lecture 28/3/2022 Pavel Quantum integrability
Poisson nearest-neighbour spacing distribution
2D infinite potential well
7th lecture 4/4/2022 Pavel Density of quantum levels
Unfolding
3D infinite potential well
8th lecture 25/4/2022 Pavel Chaotic systems
Wigner surmise, Bohigas-Giannoni-Schmit conjecture
Gaussian ensembles of random matrices
9th lecture 2/5/2022 Pavel Wigner-Dyson nearest-neighbour spacing distribution
Wigner semicircle law
Ratio of consecutive levels
Mixed systems, Brody distribution
10th lecture 9/5/2022 Pavel Long-range correlations (Δ3, Σ2, 1/f noise)
Peres lattices
Exam 30/5/2022

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