Fast decay of eigenfunction correlators in long-range continuous random alloys

Abstract

Abstract We study random Anderson Hamiltonians in Euclidean spaces with a long-range particle-media interaction potential {\mathfrak{u}(r)=r^{-A}} . Improving earlier results, for any {A>2d} , we establish spectral and strong dynamical localization with sub-exponential decay of eigenfunction correlators, both in the strong disorder regime and at low energies.