On the AC spectrum of one-dimensional random Schrödinger operators with matrix-valued potentials
The authors are interested in the absolutely continuous spectrum of discrete one-dimensional random Schrödinger operators with decaying potentials. The problem is formulated in terms of matrix-valued independent potentials on the one-dimensional lattice \(\mathbb{Z}\). If the \(\ell^2\)-norm of the underlying potential has finite expectation value with respect to the product measure, then almost surely the Schrödinger operator has an interval of purely absolutely continuous spectrum, depending on the constant `potential' part of the Schrödinger operator. The proof is based on a study of the corresponding Green functions. The obtained result is applied to Schrödinger operators on a strip. This work provides a new proof and generalizes a result obtained by \textit{F. Delyon, B. Simon} and \textit{B. Souillard} [Ann. Inst. Henri Poincaré, Phys. Théor. 42, 283--309 (1985; Zbl 0579.60056)].
scientific article; zbMATH DE number 6048552
scientific article