Localization and the mobility edge in one-dimensional potentials with correlated disorder

We show that a mobility edge exists in 1D random potentials in the presence of specific long-range correlations. Our approach is based on the relation between the binary correlator of a site potential and the localization len gth. We present an algorithm to numerically construct potentials with mobil ity edges at any given energy inside the allowed zone. Another way to gener ate such potentials is to use chaotic trajectories of nonlinear maps. Our n umerical calculations for a few specific potentials demonstrate the presenc e of mobility edges in a 1D geometry.