Department Mathematik
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Mathematisches Seminar: Random Schrödinger Operators

Wednesday 18 – 20     Room B 252


Synopsis

The seminar is about an active field of Mathematical Physics that lies in between functional analysis and probability theory.

We study spectral properties of random linear operators of the type H= -Δ +V. Here, Δ denotes the Laplacian and V a random multiplication operator, which is ergodic w.r.t. translations. These operators are interesting from a mathematical and a physical point of view. On the mathematical side one should mention remarkable spectral properties such as a dense point spectrum. On the physical side, it is their role as a minimal model for the electronic properties of disordered materials such as doped semiconductors or the quantum Hall effect.

Wir will mostly follow the recent survey article of Kirsch.

Prerequisites

Basic knowledge of functional analysis, spectral theory of self-adjoint operators and probability theory



Literature
  • R. Carmona and J.Lacroix, Spectral theory of random Schrödinger operators, Birkhäuser, Boston, MA, 1990
  • W. Kirsch, Random Schrödinger operators: a course, pp. 264–370 in H. Holden and A. Jensen (Eds.), Schrödinger operators, Lecture Notes in Physics 345, Springer, Berlin, 1989
  • W. Kirsch, An invitation to random Schrödinger operators, Panoramas et Synthèses 25, 1–119 (2008)
  • L. Pastur and A. Figotin, Spectra of random and almost-periodic operators, Springer, Berlin, 1992
  For a very brief overview see