Teaching
Many-Body Quantum Dynamics (WiSe 2024/25)
This lecture course offers an introduction to quantum many-body dynamics, emphasizing recent exciting and fundamental developments in this rapidly developing field. Quantum many-body dynamics combines aspects from condensed matter physics and quantum optics, based on a rich interplay between theoretical developments and experimental advances in quantum computing and quantum simulators. This course covers the foundations of this field, introducing aspects of quantum chaos and quantum quench dynamics, before moving on to topics of recent interest including many-body localization, prethermalization, periodically driven (Floquet) systems and Floquet engineering, quantum geometry, discrete time crystals, and quantum circuits as minimal models for many-body dynamics.
Prerequisites: Quantum Mechanics, Statistical Mechanics, basic familiarity with Python
Preliminary reading materials:
- J. J. Sakurai, Modern Quantum Mechanics, Chapters 1-4 and Chapter 7;
- basic notions of statistical mechanics and thermodynamics;
- Chris Laumann's Scientific Computing in Python lectures given at ICTP: lecture 1, lecture 2, lecture 3, notebooks.
ECTS Credits: 5 ECTS
Coursework: The course offers regular lectures (see table below for syllabus) and regular tutorial sessions. Regular attendance (at least 75% of the lectures) is expected.
Final Exam: Oral exam starting focusing on a set of topics covered in class. Only for students taking the course for credit.
Time and Place:
Tuesday and Thursday: 13:00 - 14:30
Venue: Seminar Room 4 (SR4), Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str 38, Dresden 01187
Public holidays: Oct 31, Dec 26, Dec 28, Dec 31, Jan 2
Lecturers:
Marin Bukov, PhD
Pieter Claeys, PhD
Prof. Dr. Roderich Moessner
Syllabus:
Date | Lecture topic | Material |
| Oct 17 | Introduction | Notes "Course overview" |
| Oct 22 | Local relaxation of many-body quantum systems | |
| Oct 24 | Aspects of Random Matrix Theory and Eigenstate Thermalization | |
| Oct 29 | Tutorial and Fluctuation-Dissipation Relations | |
| Oct 31 | Public Holiday | |
| Nov 5 | Quench Dynamics in Free-Fermionic Models | |
| Nov 7 | The Transverse-Field Ising Model | |
| Nov 12 | Adiabatic theorem | Problem set 2 (due Nov 19) adiabatic theorem, Aharonov-Bohm effect |
| Nov 14 | Adiabatic gauge potentials and counterdiabatic driving | gauge potentials |
| Nov 19 | Tutorial: AGPs & CD driving | solution to PS2, notebook |
| Nov 21 | Variational counterdiabatic driving | variational_CD_driving |
| Nov 26 | Periodically driven systems: Floquet theorem | Floquet systems Kapitza pendulum video Paul trap (rotating saddle) video |
| Nov 28 | Inverse frequency expansions | Problem set 3 (due Dec 5) Floquet_theory |
| Dec 3 | Floquet engineering | Floquet engineering |
| Dec 5 | Geometric Floquet theory | Geometric Floquet Theory |
| Dec 10 | Introduction to Quantum Geometry: Bloch states, Projectors, Bloch sphere | Lecture Notes (1-3) |
| Dec 12 | Introduction to Quantum Geometry: Berry phase, Quantum metric and its properties | Lecture Notes (2-3) |
| Dec 17 | Introduction to Quantum Geometry: Wannier functions, Polarization, Berry curvature and topology | Lecture Notes (3-3) |
| Dec 19 | ||
| Jan 7 | ||
| Jan 9 | ||
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| Jan 23 | ||
| Jan 28 | ||
| Jan 30 | ||
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| Feb 6 |