Random Schrödinger operators with a background potential

2017/12/21 by Asatryan, Hayk, Kirsch, Werner
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1712.08095

Abstract

We consider one-dimensional random Schrödinger operators with a background potential, arising in the inverse problem of scattering. We study the influence of the background potential on the essential spectrum of the random Schrödinger operator and obtain Anderson Localization for a larger class of one-dimensional Schrödinger operators. Further, we prove the existence of the integrated density of states and give a formula for it.

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