Quantum Dynamics 2024

This is a specialized Lecture Course for the Summer Term 2024 at the Master Programme of the University of Cologne.

Content:

This is a specialized lecture course that will introduce students to the field of "Quantum Dynamics", with a special emphasis on Hamiltonian chaos. It will cover recent and exciting developments in an active area of research that combines aspects of condensed matter physics, quantum optics, quantum information, and statistical mechanics. The program will cover topics ranging from the theoretical foundations of Quantum Chaos in the semiclassical limit to the latest results in the Many-body context.

As part of this course, Master's students will have the opportunity to gain hands-on research experience by working on small numerical exercises and projects and presenting their findings.

The course is divided in:

Part I) Classical and semi-classical dynamics (hbar=0 or small);

Part II) Many-body dynamics: Random Matrix Theory, the Eigenstate Thermalization Hypothesis and its violations (hbar=1).

Art by Madeleine van Wassenhove

Previous expected knowledge:

Basic knowledge of quantum, classical, and statistical mechanics.

Practical information:

Information on the course will be communicated on this website and/or on ILIAS.
Please register on KLIPS 2.0 to attend the course.
When: Tuesday 12-13.45 and Thursday 10-11.45
Room 0.03 ThP

Tutors:

Karim Chahine chahine(at)thp.uni-koeln.de
Elisa Vallini evallini(at)thp.uni-koeln.de
Arnau Lira Solanilla lirasola(at)thp.uni-koeln.de

Lecture materials:

Notes (updated as the class goes on)
List of readings for the final presentations

Lectures day by day:

09.04.24: 1. introduction, 2.1 the language of classical dynamical systems, 2.2 integrability
11.04.24: 2.3 Local stability analysis, Lyapunov exponent and spectrum, the kicked top example
16.04.24: Generalized Lyapunov exponents, 2.4 KAM scenario
18.04.24 Tutorial 1: simulation of the Hénon-Heiles map and of the Kicked Top
23.04.24: 2.5 Emergence of Statistical Mechanics
25.04.24: 3.1 Quantum phase-space
30.04.24: 3.2 Dynamics of fully connected systems
02.05.24: Tutorial 2: simulation of the LMG model and its classical limit
07.05.24: 3.3 Entanglement, its dynamics and scrambling in semiclassical systems
14.05.24: 4.1 Intro to Random Matrix Theory: Gaussian ensembles ++
16.05.24: Tutorial 3: playing with Gaussian RMT eigenvalues
28.05.24: 4.2 Averages and Fluctuations
04.06.24: 4.3 Eigenvectors statistics
06.06.24: 5.1 Floquet dynamics
11.06.24: 5.2 Quantum quenches and equilibration 5.3 Eigenenergies statistics
18.06.24: 5.4 Eigenstate Thermalization Hypothesis
20.06.24: 5.4.5: Dynamical correlation functions in ETH and correlations
25.06.24: Tutorial 5: ETH in the Ising model with tilted field
27.06.24: Tutorial 6: Entanglement entropy dynamics in chaotic spin chains
02.07.24: 5.5 Violations of thermalizations - integrability
03.07.24: 5.5 Many-Body Quantum scars
11.07.24 Presentation n.1
12.07.24 Presentation n.8
16.07.24 Presentation n.3,7
28.07.24 Presentation n.2,6

Useful links:

Cvitanović's ChaosBook - online textbook on the theory of deterministic stochastic and quantum chaotic/turbulent systems
Wheeler's essays - "more a way to understanding than from understanding"