ON THE INTEGRATED DENSITY-OF-STATES FOR CRYSTALS WITH RANDOMLY DISTRIBUTED IMPURITIES

In the present paper, we discuss spectral properties of a periodic Sch rodinger operator which is perturbed by randomly distributed impuritie s; such operators occur as simple models for crystals (or semi-conduct ors) with impurities. While the spectrum itself is independent of the concentration p of impurities, for 0 < p < 1, we focus our attention o n the limiting behavior of the integrated density of states rho(p) of the random Schrodinger operator, inside a spectral gap of the periodic operator, as p --> 0. Denoting by U-0 the set of eigenvalues (in the gap) of the reference problem having precisely one impurity (located a t the origin, say), we show that the integrated density of states conc entrates around the points of U-0, in the sense that rho(p)(U-epsilon) is of order p, for any fixed epsilon-neighborhood U-epsilon of U-0, w hile rho(p)(K) less than or equal to C.p(2), for any compact subset K of the gap which does not intersect U-epsilon.