Localization for Discrete One Dimensional Random Word Models

Abstract

We consider Schrödinger operators in ${\ell }^2(\mathbb{Z})$ whose potentials are obtained by randomly concatenating words from an underlying set $\mathcal{W}$ according to some probability measure $\nu$ on $\mathcal{W}$. Our assumptions allow us to consider models with local correlations, such as the random dimer model or, more generally, random polymer models. We prove spectral localization and, away from a finite set of exceptional energies, dynamical localization for such models. These results are obtained by employing scattering theoretic methods together with Furstenberg's theorem to verify the necessary input to perform a multiscale analysis.

19 pages

References in corpus (2)

• Gordon-type arguments in the spectral theory of one-dimensional quasicrystals
• Dynamical Localization for the Random Dimer Model