On the AC Spectrum of One-dimensional Random Schrödinger Operators with Matrix-valued Potentials

We consider discrete one-dimensional random Schrödinger operators with decaying matrix-valued, independent potentials. We show that if the ℓ2-norm of this potential has finite expectation value with respect to the product measure then almost surely the Schrödinger operator has an interval of purely absolutely continuous (ac) spectrum. We apply this result to Schrödinger operators on a strip. This work provides a new proof and generalizes a result obtained by Delyon et al. (Ann. Inst. H. Poincaré Phys. Théor. 42(3):283–309, 1985).