LOCALIZATION PHENOMENON IN GAPS OF THE SPECTRUM OF RANDOM LATTICE OPERATORS

We consider a class of random lattice operators including Schrodinger operators of the form H = -DELTA + w + gv, where w(x) is a real-valued periodic function, g is a positive constant, and v(x), x is-an-element-of Z(d), are independent, identically distributed real random variables. We prove that if the operator -DELTA + w, has gaps in the spectrum and g is sufficiently small, then the operator H develops pure point spectrum with exponentially decaying eigenfunctions in a vicinity of the gaps.