Notes on Anderson localization

Abstract

Localization phenomena in disordered systems have attracted great theoretical interest since the second half of the 20th century. In this article we give an introduction to the theory of Anderson-localization. We perform numerical calculations of eigenstates of disordered tight-binding Hamilto-nians in 1D and 3D and review recent experimental evidence of localization of bosonic wavefunctions in a 1D-magneto-optical trap. Additionally, we provide a brief overview of the effect of Hubbard electron-electron interactions and their implications on the Eigenstate Thermalization Hypothesis.