Anderson Localization and Generalized Diffusion

1 Introduction Disorder leads to important physical effects which are of quantum mechanical origin. This has been revealed by Anderson [1] in the study of a disordered tight-binding model. The problem has attracted great attention over many decades [2]. Subsequent to the ideas presented in our previous papers [3,4], we discuss here a new analytical approach to calculate the phase-diagram for the Anderson localization [1] in arbitrary spatial dimensions D. The transition from delocalized to localized states is treated as a generalized diffusion which manifests itself in the divergence of diagonal correlators. This divergence is controlled by the Lyapunov exponent γ which is the inverse of the localization length, ξ=1/γ.