Pavel Stránský
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Last updated: 6.6.2023

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. 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 Tuesdays 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 21/2/2023 Georgios Symplectic maps, variational principles, and transport
Non-linear effects in EMRI dynamics and their imprints on gravitational waves
2nd lecture 28/2/2023 Georgios
3rd lecture 7/3/2023 Georgios
4th lecture 14/3/2023 Georgios
5th lecture 21/3/2023 Pavel Quantum integrability
Poisson nearest-neighbour spacing distribution
2D infinite potential well
6th lecture 28/3/2023 Pavel Density of quantum levels
Unfolding
3D infinite potential well
7th lecture 4/4/2023 Pavel Chaotic systems
Wigner surmise, Bohigas-Giannoni-Schmit conjecture
Gaussian ensembles of random matrices
Wigner-Dyson nearest-neighbour spacing distribution
8th lecture 11/4/2023 Pavel Wigner semicircle law
Long-range correlations (Δ3, Σ2)
Ratio of consecutive levels
Mixed systems, Brody distribution
9th lecture 18/5/2023 Pavel Quantum billiards
Peres lattices
10th lecture 25/5/2023 Pavel 1/f noise in quantum spectra
Wishart ensemble
Exam 23/5/2023

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