We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are n barriers and wells with statistically independent intensities and with a spatial extension l c which may contain an arbitrary number δ/2π of wavelengths, where δ = kl c .We analyze the average Landauer resistance and transmission coefficient of the chain as a function of n and the phase parameter δ. For weak scatterers, we find: i) a regime, to be called I, associated with an exponential behavior of the resistance with n, ii) a regime, to be called II, for δ in the vicinity of π, where the system is almost transparent and less localized, and iii) right in the middle of regime II, for δ very close to π, the formation of a band gap, which becomes ever more conspicuous as n increases. In regime II, both the average Landauer resistance and the transmission coefficient show an oscillatory behavior with n and δ. These characteristics of the system are found analytically, some of them exactly and some others approximately. The agreement between theory and simulations is excellent, which suggests a strong motivation for the experimental study of these systems. We also present a qualitative discussion of the results.

PACS 42.25.Dd -Wave propagation in random media PACS 72.15.Rn -Localization effects (Anderson or weak localization) PACS 72.10.-d -Theory of electronic transport; scattering mechanisms PACS 72.10.Bg -General formulation of transport theoryAbstract -An amazingly simple model of correlated disorder is a one-dimensional chain of n potential steps with a fixed width lc and random heights. A theoretical analysis of the average transmission coefficient and Landauer resistance as functions of n and δ = klc predicts two distinct regimes of behavior, one marked by extreme sensitivity and the other associated with exponential behavior of the resistance. The sensitivity arises in n and δ for δ ≈ π, where the system is nearly transparent. Numerical simulations match the predictions well, and they suggest a strong motivation for experimental study.