On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials

Abstract

We consider discrete one-dimensional random Schroedinger operators with decaying matrix-valued, independent potentials. We show that if the l^2-norm of this potential has finite expectation value with respect to the product measure then almost surely the Schroedinger operator has an interval of purely absolutely continuous (ac) spectrum. We apply this result to Schroedinger operators on a strip. This work provides a new proof and generalizes a result obtained by Delyon, Simon, and Souillard.

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References in corpus (3)

• Graph Subspaces and the Spectral Shift Function
• Perturbation theory for Lyapunov exponents of an Anderson model on a strip
• Absolutely continuous spectrum for a random potential on a tree with strong transverse correlations and large weighted loops

Cited by in corpus (2)

• On absolutely continuous spectrum for one-channel unitary operators
• Some applications of almost analytic extensions to operator bounds in trace ideals