Absence of localization in a random-dimer model

TLDR: The dual of the random-dimer model is also shown to exhibit an absence of localization and is shown to be relevant to transmission resonances in Fibonacci lattices.

Abstract: We consider here a 1D tight-binding model with two uncorrelated random site energies ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$ and ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{b}}$ and a constant nearest-neighbor matrix element V. We show that if one (or both) of the site energies is assigned at random to pairs of lattice sites (that is, two sites in succession), an initially localized particle can become delocalized. Its mean-square displacement at long times is shown to grow in time as ${\mathit{t}}^{3/2}$ provided that -2V${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$-${\mathrm{\ensuremath{\epsilon}}}_{\mathit{b}}$2V. Diffusion occurs if ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{a}}$-${\mathrm{\ensuremath{\epsilon}}}_{\mathit{b}}$=\ifmmode\pm\else\textpm\fi{}2V and localization otherwise. The dual of the random-dimer model is also shown to exhibit an absence of localization and is shown to be relevant to transmission resonances in Fibonacci lattices.