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Random Schr"odinger operators on manifolds

Daniel Lenz·Norbert Peyerimhoff·Ivan Veselic'
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Abstract

We consider a random family of Schr\"odinger operators on a cover $X$ of a compact Riemannian manifold $M = X/\Gamma$. We present several results on their spectral theory, in particular almost sure constancy of the spectral components and existence and non-randomness of an integrated density of states. We also sketch a groupoid based general framework which allows to treat basic features of random operators in different contexts in a unified way. Further topics of research are also discussed.

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Daniel Lenz, Norbert Peyerimhoff, Ivan Veselic'. 2002-12-19. Random Schr"odinger operators on manifolds. https://arxiv.org/abs/math-ph/0212057

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