Abstract
We study localization of states and transmittance of a one-dimensional lattice with incommensurate rapidly varying pseudo-random potential, when site energies are dimerized. The chosen model potential, V=V0 cos (2 pi alpha nnu ), alpha irrational, nu >1 and dimerization, is a peculiar generalization of the random-dimer binary model and allows careful control of the localization properties for varying degrees of disorder. We find that insertion of short-range order in the form of adjacent site energy dimerization, causes, in general, a strong increase of the localization lengths and the behaviour of the Lyapunov exponent as a function of the energy is similar to commensurate situations. In particular for nu >2, the binary alloy situation is reproduced and we confirm the presence of extended states near the two-site energies.
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