Many-Body Quantum Dynamics (WiSe 2023/24)

This lecture course offers an introduction to quantum many-body dynamics, emphasizing recent exciting and fundamental developments in this rapidly developing field, and includes a 'hands-on' research component. 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, discrete time crystals, and quantum circuits as minimal models for many-body dynamics.

Master students will have the opportunity to gain first-hand research experience by doing a small project and presenting their results. These projects are supervised by the lecturers and will serve as an introduction to recent developments, consisting of a reproduction part and original research. The final month of lectures will consist of presentations of these student projects, as well as lectures by guest lecturers (depending on the number of student presentations).


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). Since this is an advanced course, there will be no weekly problem sets and no discussion/tutorial sessions. Besides attending lectures (at least 75% of lectures), students will choose a small research project to work out during the semester, and present their results in class in January. Example project topics are listed below, but students are free to choose their own topic, provided this topic is approved by one of the instructors. These projects are restricted to master students only, PhD students following the course are only expected to attend the lectures.

Final Exam: Oral exam starting with the student's research project, and going into related topics covered in class. Only for students taking the course for credit.

Time and Place:

Tue/Thu: 13:00 - 14:30
Venue: Seminar Room 1-3 (SR1-3), Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str 38, Dresden 01187 
Public holidays: Oct 31, Dec 21, Dec 26, Dec 28, Jan 2

Deadline to choose project: Nov 16


Marin Bukov, PhD
Pieter Claeys, PhD
Prof. Dr. Roderich Moessner

Possible student projects:




Lecture topic


Oct 10Logistics & IntroductionLecture notes
Oct 12Introduction to quantum spin systems using QuSpin

1. Basics of quspin notebook

2. Installation instructions for quspin 
(We recommend using conda; make sure you install quspin version 0.3.7)

3. Additional material: tutorial 1 (advanced usage: tutorial 2, examples)

Oct 17Random matrix theory and eigenstate thermalization

Lecture notes


Oct 19Random matrix theory and eigenstate thermalization
Oct 24Quench dynamics in the Transverse Field Ising Model

Lecture notes


Oct 26Quench dynamics in the Transverse Field Ising Model
Oct 31Public Holiday 
Nov 2Periodically-driven (Floquet) Systems

Lecture notes 1/3
Kapitza pendulum video
Paul trap (rotating saddle) video

Nov 7Inverse frequency expansionsLecture notes 2/3
Nov 9Floquet engineeringLecture notes 3/3
Nov 14Anderson LocalizationLecture Notes
Nov 16Many-Body Localization
Nov 21Adiabatic theorem. Landau-Zener problem. Aharonov-Bohm effectLecture notes 1/3
Nov 23Gauge potential. Counter-diabatic drivingLecture notes 2/3
Nov 28Symmetry protected topologyLecture Notes
Nov 30Discrete Time CrystalsLecture Notes
Dec 5Variational counter-diabatic drivingLecture notes 3/3
Dec 7Introduction to Unitary Circuit DynamicsLecture Notes
Dec 11Introduction to Unitary Circuit Dynamics
Dec 13Introduction to Unitary Circuit DynamicsLecture Notes (Sections I-II)
Jan 4Nonadiabatic Response and Quantum GeometryLecture Notes 1/2
Jan 9Nonadiabatic Response and Quantum GeometryLecture Notes 2/2
Jan 11Magic and Mana: guest lecture (Christopher Hooley)Lecture Notes 1/2
Jan 16Magic and Mana: guest lecture (Christopher Hooley)Lecture Notes 2/2
Mathematica notebook: nb, pdf
Jan 18Guest lecture (Jan Carl Budich) 
Jan 23Prethermalization 
Jan 25Student presentationsLukas Koenig (TU Dresden) -- Prethermalization in random multipolar driven systems
Zhaohui Zhi (TU Dresden) -- Quantum many body scars
Jan 30Student presentations

Hristo Tonchev (Sofia University) -- Discrete time crystals on quantum computers using qiskit
Teodora Serafimova (Sofia University) -- Eigenstate thermalization in Floquet dynamics

Feb 1Discussion & Outlook