EXPONENTIAL LOCALIZATION FOR MULTIDIMENSIONAL SCHRODINGER OPERATOR WITH RANDOM POINT POTENTIAL

We consider a Schrodinger operator -Delta(alpha(w)) on L-2(R-d) (d = 2 , 3) whose potential is a sum of point potentials, centered at sites o f Z(d), with independent and identically distributed random amplitudes . We prove the existence of the pure point spectrum and the exponentia l decay of the corresponding eigenfunctions at the negative semi-axis for certain regimes of the disorder. In order to prove localization re sults, we elucidate the structure of the generalized eigenfunctions of -Delta(alpha(w)) and the relation between its negative spectrum and t he spectra of a family of infinite-order operators on l(2)(Z(d)). We a pply the multiscale analysis scheme to investigate the point spectrum of these operators. We also prove the absolute continuity of the integ rated density of states of the operator on the negative part of its sp ectrum.