CONDUCTANCE FOR THE TWO DIMENSIONAL DISCRETE RANDOM SCHRÖDINGER OPERATOR WITH SMALL DISORDER

Abstract. As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We consider the discrete random Schrödinger operator on the integer lattice Z2. Based on a recent mathematical result we introduce a new numerical approach to the Anderson (de)localization problem. As an application we show numerically the following unexpected result: For small disorder, this random operator allows extended states with positive proba-bility. This approach eliminates potential problems due to boundary effects, and the numer-ical part is rather simple compared with other experiments in the field. Further, we provide a mathematical derivation of a quantity closely related to Thouless ’ dimensionless scaling parameter. No new information is gained regarding the energy regimes at which diffusion occurs. 1