Absence of diffusion in certain random lattices: Numerical evidence

Abstract

We demonstrate, by solving numerically the time-dependent Schroedinger equation, the physical character of electron localization in a disordered two-dimensional lattice. We show, in agreement with the prediction of P. W. Anderson, that the disorder prevents electron diffusion. The electron becomes spatially localized in a specific area of the system. Our numerical analysis confirms that the electron localization is a quantum effect caused by the wave character of electron propagation and has no analogy in classical mechanics.