Quantum Matter 2 2022/2023:


The course comprises of 20 lectures. There are 2 problem sheets.

Synopsis

I. Elements of Quantum Statistical Mechanics
1. (Reduced) Density Matrices
2. Entropy, Ensembles and Typicality

II. Eigenstates of local many-particle Hamiltonians
3. Entanglement Measures
4. The AKLT model and Matrix Product States
5. Eigenstates at finite energy densities


III. Quantum Quenches and (generalized) Thermalization
6. Quantum Quenches

7. (Generalized) Thermalization
8. Eigenstate Thermalization Hypothesis

IV. BBGKY Hierarchy and Quantum Boltzmann Equation
9. BBGKY
10. Self-consistent time-dependent mean-field approximation
11. Quantum Boltzmann Equation
12. Time-dependent variational principle

IV. Periodically Driven Systems and Quantum Master Equations
13. Periodically Driven Systems
14. Quantum Master Equations



Problem Sheets:
Lecture Notes I
Lecture Notes II


Problem classes/assessment:

The tutor for the course will be Dr. Abhishodh Prakash, who will lead  2 problem classes this term. Each class is run in conjunction with a problem sheet, which you must complete and submit to Dr Prakash. For full homework completion credit, work must be submitted by the assigned deadline.

Deadline for problem sheet 1: May 15
Deadline for problem sheet 2:

In order to register for the problem classes (required to get credit for the course) email Dr Prakash by May 9 so that he can arrange suitable times.

Homework can either be emailed directly to Dr Prakash or else handed in at the Beecroft reception addressed to him.