Physics and Mathematics of Geometric Phases


Lecture details

The lecture will be given by Professor Wegewijs and Professor Mokrousov.

This course is suitable for master students as well as PhD students
within the RTG program.
In particular, for the RTG students we offer a few extra Tutorials and
Lectures that further deepen and broaden the material.

Program mathematics part: foundations of differential geometry

1 Introduction: Fiber bundles and physics
2 General topology
3 Differentiable manifolds
4 Tangent structure
5 Fields and vector bundles
6 Differential forms
7 Cohomology
8 Lie groups
9 Fiber bundles
10 Connections
11 Characteristic classes

Program physics part: applications in solid-state physics

1 Geometric phase in quantum physics
2 Adiabatic approximation and AB effect
3 Spin-1/2 and Dirac monopole
4 Non-adiabatic dynamics
5 Kato formulation
6 Non-Abelian Berry phase
7 Electric polarization and quantization
8 Chern and topological insulators
9 Electron dynamics and Hall Effects
10 Orbital magnetization and Berry phase
11 Berry phase and magnetic interactions

Additonal teaching offers:

In addition to the main course material listed below we will offer

  • Special lectures on:
    - Homology
    - Homotopy
  • Special Tutorials, extending the applications to topics in quantum nformation:
    - Distance measures for quantum states
    - Holonomic quantum computing / Quantum error correction

An additional description can be found in the university calendar.

Time Topic Room Starts
Mon., 1.15pm - 2.40pm Mathematics (M. Wegewijs) 4284 (28 D 001) 13.10.2014 (15 dates)
Mon., 2.50pm - 4.15pm Physics (Y. Mokrousov) 4284 (28 D 001) 13.10.2014 (15 dates)
Thurs., 1pm - 2.30pm Exercise (Thilo Plücker) 4272 (MBP1 015) 16.10.2014 (15 dates)