Henrik Ueberschär: Spectral geometry of tori with random impurities

Abstract-

An important object of study in the theory of disordered quantum systems
are Schroedinger operators with a random potential. In 1958, Anderson
discovered that for sufficiently strong disorder their eigenfunctions
could be exponentially localized at the bottom of the spectrum. A major
question in the mathematical physics of disordered systems considers the
existence of a delocalization transition. I. e.  if the disorder is
sufficiently weak compared with the energy do there exist delocalized
eigenfunctions? I will address this question in the case of Poisson
distributed random delta potentials.