Absolutely Continuous Spectrum For Schr\"odinger Operators With Random Decaying Matrix Potentials on The Strip

TL;DR

This paper proves that certain random Schr"odinger operators with decaying matrix potentials on a strip have almost surely purely absolutely continuous spectrum, except for some embedded eigenvalues that may cluster at band edges.

Contribution

It establishes the almost sure absolute continuity of the spectrum for a class of random Schr"odinger operators with decaying matrix potentials on the strip, including possible embedded eigenvalues.

Findings

Spectrum is almost surely purely absolutely continuous

Embedded eigenvalues may exist and accumulate at band edges

Results apply to random Schr"odinger operators with decaying matrix potentials

Abstract

We consider a family of random Schr\"odinger operators on the discrete strip with decaying random $\ell^2$ matrix potential. We prove that the spectrum is almost surely pure absolutely continuous, apart from random, possibly embedded eigenvalues, which may accumulate at band edges.