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 17IntroductionNotes "Course overview"
Oct 22Local relaxation of many-body quantum systems

Notes "Equilibration and eigenstate thermalization"

Exercises

Notebook

Oct 24Aspects of Random Matrix Theory and Eigenstate Thermalization
Oct 29Tutorial and Fluctuation-Dissipation Relations
Oct 31Public Holiday 
Nov 5Quench Dynamics in Free-Fermionic Models

Notes "Quench dynamics in the Transverse Field Ising Model"

Notebook

Nov 7The Transverse-Field Ising Model
Nov 12Adiabatic theoremProblem set 2 (due Nov 19)
adiabatic theorem, Aharonov-Bohm effect
Nov 14Adiabatic gauge potentials and counterdiabatic drivinggauge potentials
Nov 19Tutorial: AGPs & CD drivingsolution to PS2, notebook
Nov 21Variational counterdiabatic drivingvariational_CD_driving
Nov 26Periodically driven systems: Floquet theoremFloquet systems
Kapitza pendulum video
Paul trap (rotating saddle) video
Nov 28Inverse frequency expansionsProblem set 3 (due Dec 5)
Floquet_theory
Dec 3Floquet engineeringFloquet engineering
Dec 5Geometric Floquet theoryGeometric Floquet Theory
Dec 10  
Dec 12  
Dec 17  
Dec 19  
Jan 7  
Jan 9  
Jan 14  
Jan 21  
Jan 23  
Jan 28  
Jan 30  
Feb 4  
Feb 6