Anderson localization for multi-dimensional systems at large disorder or large energy
The multidimensional discrete Schrödinger (self-adjoint) operator H acting on \(I^ 2(Z^ d)\) is defined by: \((H\Psi)(x)=-\sum_{| x- y| =1}\Psi (y)+V(x)\Psi (x)\) where \(\{V(x)\}_{x\in Z^ d}\) is a random potential chosen with a probability distribution P. It is proven for a large class of probability distributions that, with probability one, H has only pure point spectrum of multiplicity one and exponentially decaying eigenfunctions. This result holds all over the spectrum at large disorder (large V) or for large energy (eigenvalue) for a smaller disorder.
scientific article; zbMATH DE number 3921648