Pavel Stránský

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Last updated: 5.6.2024

**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.

Dr. Georgios Loukes-Gerakopoulos (classical chaos), Astronomical Institute CAS

Dr. Pavel Stránský (quantum chaos), Institute of Particle and Nuclear Physics MFF UK

Theory demonstrated by practical problems solved on computers ("hands-on").

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.

The course is held on **Thursdays at 9.00 am** (classical chaos, till 4 April 2024) and **Tuesdays from 2.50 pm** (quantum chaos, from 9 April 2024)
**in the lecture room A920** at the Institute of Particle and Nuclear Physics, MFF CUNI, 8th floor at the Troja building.
A preliminary schedule is the following:

1st lecture | 29 February 2023 | Georgios |
Symplectic maps, variational principles, and transport Non-linear effects in EMRI dynamics and their imprints on gravitational waves |
---|---|---|---|

2nd lecture | 7 March 2024 | Georgios | |

3rd lecture | 14 March 2024 | Georgios | |

4th lecture | 21 March 2024 | Georgios | Hénon-Heiles system |

5th lecture | 28 March 2024 | Georgios | |

6th lecture | 4 April 2024 | Vojtěch Witzany | Canonical perturbation theory |

7th lecture | 9 April 2024 | Pavel | Quantum integrability Poisson nearest-neighbour spacing distribution 2D infinite potential well |

8th lecture | 16 April 2024 | Pavel | Density of quantum levels Unfolding 3D infinite potential well |

9th lecture | 30 April 2024 |
Pavel | Chaotic systems Wigner surmise, Bohigas-Giannoni-Schmit conjecture Gaussian ensembles of random matrices Wigner-Dyson nearest-neighbour spacing distribution |

10th lecture | 7 April 2024 | Pavel | Wigner semicircle law Long-range correlations (Δ3, Σ2) Ratio of consecutive levels Mixed systems, Brody distribution |

11th lecture | 14 May 2024 | Pavel | Quantum billiards Peres lattices |

Exam | 21 May 2024 2.50 pm, A920 |

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