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

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

2009-12-01

arxiv.org/abs/0912.0294v1

Physics

Mathematical Physics

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Scientific paper

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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