# 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) |