Three types of spectra in one-dimensional systems with random correlated   binary potential
  The stationary one-dimensional tight-binding Schredinger equation with a weak diagonal long-range correlated disorder in the potential is studied. An algorithm for constructing the discrete binary on-site potential exhibiting a hybrid spectrum with three different spectral components (absolutely continuous, singular continuous and point) ordered in any predefined manner in the region of energy and/or wave number is presented. A new approach to generating a binary sequence with the long-range memory based on a concept of additive Markov chains (Phys. Rev. E 68, 061107 (2003)) is used. 
O. V. Usatenko, S. S. Melnik, V. A. Yampol'skii, M. Johansson, L.   Kroon, and R. Riklund