Teaching

Type:	Time:	Place:	Start:
PJSE 2 std.	Do 11:30-13:00	SR10	3.10

Random and almost periodic Schrödinger operators serve in solid state physics as models of disordered systems such as alloys, glasses and amorphous materials in the so called tight binding approximation. In quantum mechanics, crystals are modeled by Schrödinger operators with periodic potentials. It is an important problem to understand what happens to a crystal if random impurities are introduced. Indeed, in a more realistic setting such crystals will contain impurities, the precise locations of which are in general unknown. All one might know is that these impurities occur with a certain probability. During the last three decades, random Schrödinger operators became an extremely extensive topic and much effort has been put to understand the properties of random and almost periodic operators. Our main aim is to shed some light on a circle of ideas and problems and to the mathematical machinery that has recently been built to investigate it.

Date:	Title:	Speaker:	References:
10.10	Introduction: Why random Schrödinger operators	Gerald Teschl	[Ki]
24.10	Discrete Schrödinger operators and spectral calculus	Markus Holzleitner	[Ki]
31.10	Random potentials	Tobias Schubhart	[Ki]
07.11	Ergodic operators	Damir Ferizović	[Ki]
14.11	The density of states: Definitions and existence	Franz Berger	[Ki]
21.11	The density of states: The geometric resolvent equation	Melanie Graf	[Ki]
28.11	The Wegner estimate	Oliver Skocek	[Ki]
12.12	Lifshitz tails	Noema Nicolussi	[Ki]
23.01	The spectrum and its physical interpretation	Zouhair Hadded	[Ki]

References:

1. J. Bourgain, Green's Function Estimates for Lattice Schrödinger Operators and Applications, Princeton UP, 2005.
2. H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger Operators, 2nd ed., Springer, 2008.
3. W. Kirsch, An invitation to random Schrödinger operators, in: Panor. Syntheses, 25, Random Schrödinger operators, 1-119, 2008.
4. A. Klein, Multiscale analysis and localization of random operators, in: Panor. Syntheses, 25, Random Schrödinger operators, 121-159, 2008.
5. G. Teschl, Jacobi Operators and Completely Integrable Nonlinear Lattices, AMS, 2000.

Preparation and presentation of a chosen topic.

Majors in Mathematics (master program, code MANS), Physics, ...