Melnik S. Random dynamic systems with long-range correlations

A theory for propagation of excitations in one-dimensional random systems, characterized by discreteness of potential and long-range correlations is evolved. A mathematical model of additive many-step Markov chain, that allows one to describe efficiently correlation properties of discrete numerical sequences and to construct sequences with predefined statistical characteristics, is developed. Based upon the proposed model a method is worked out to construct a one-dimensional discrete random potential, which (in the framework of Anderson model) is characterized by a preset dependence of the localization length of excitations upon their frequency. An ability to construct the discrete potentials possessing the required arrangement of transparency and reflection windows at a frequency band is analyzed. A method of constructing the Josephson chain with a required transparency edge is developed.