Graduate Seminar on Interacting Random Systems: Selected topics in random matrices and random operators
Winter Term 2023/2024
Lecturer: Prof. Dr. Johannes Alt
The seminar deals with random Schrödinger operators. From the point of view of physics, they describe the behaviour of an electron in a disordered crystal and explain when conducting or insulating behaviour emerges. The aim of the seminar is an introduction into the mathematical rigorous analysis of random Schrödinger operators.
Prerequisites: Functional Analysis. Some basic knowledge in measure theory and probability is helpful but not necessary. No knowledge of physics is required!
Files:
References
The following list contains some introductory references about the mathematics of random Schrödinger operators. Most of the seminar talks will be based on [Sto11].
[AW15] | M. Aizenman and S. Warzel, Random operators, Graduate Studies in Mathematics, vol. 168, American Mathematical Society, Providence, RI, 2015, Disorder effects on quantum spectra and dynamics. |
[Hun08] | Dirk Hundertmark, A short introduction to Anderson localization, Analysis and stochastics of growth processes and interface models, Oxford Univ. Press, Oxford, 2008, pp. 194–218. Preprint available at https://faculty.math.illinois.edu/~dirk/preprints/localization3.pdf |
[Kir08] | W. Kirsch, An invitation to random Schrödinger operators, Random Schrödinger operators, Panor. Synthèses, vol. 25, Soc. Math. France, Paris, 2008, With an appendix by Frédéric Klopp, pp. 1–119. Preprint available at https://arxiv.org/pdf/0709.3707.pdf |
[Sto11] | G. Stolz, An introduction to the mathematics of Anderson localization, Entropy and the quantum II, Contemp. Math., vol. 552, Amer. Math. Soc., Providence, RI, 2011, pp. 71–108. Preprint available at https://arxiv.org/pdf/1104.2317 |