Pavel Stránský
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Last updated: 19.1.2022

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 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)

Schedule

The lectures are given on Tuesdays from 3:30pm to 5:30pm on ZOOM. Preliminary schedule is the following:

1st lecture 9/3/2021 Georgios
2nd lecture 16/3/2021 Georgios
3rd lecture 23/3/2021 Georgios
4th lecture 30/3/2021 Georgios
5th lecture 6/4/2021 Georgios
6th lecture 13/4/2021 Pavel Quantum integrability
Poisson nearest-neighbour spacing distribution
2D infinite potential well
7th lecture 20/4/2021 Pavel Density of quantum levels
Unfolding
3D infinite potential well
8th lecture 27/4/2021 Pavel Wigner surmise
Bohigas conjecture
Random matrix ensembles
9th lecture 4/5/2021 Pavel Spectral correlations in random matrices
Brody distribution
Long-range correlations
10th lecture 11/5/2021 Pavel 1/f šum in quantum spectra
Peres lattices
Wishard ensemble
Exam (Bc. students) 18/5/2021
Exam (Mgr. and Ph.D. students) 25/5/2021

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 all students of the 3rd year of bachelor studies, for master students, and for everyone interested in the topic.

Lecture notes and materials

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 - PDF