Prof. Dr. Daniel Peterseim (Universität Augsburg)
Wednesday, April 25, 2018 - 09:15
Humboldt-Universität, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin, Raum 3.007, Haus 3
Forschungsseminar "Numerische Mathematik"
Prof. C. Carstensen
This talk discusses spectral properties of linear Schrödinger operators under oscillatory high-amplitude potentials on bounded domains. Depending on the degree of disorder, the lowermost eigenstates exhibit strong localization in the form of an exponential decay. We quantify the rate of decay in terms of geometric parameters that characterize the potential and its disorder strength. This result is based on the convergence theory of iterative solvers for linear operator equations and their optimal local preconditioning by domain decomposition techniques. By the identification of spectral gaps for certain model potentials, we are able to predict the emergence of localized states. This is joint work with R. Altmann (Augsburg) and P. Henning (Stockholm).
submitted by S. Schmidt (sschmidt@math.hu-berlin.de, 2093 1820)