Random Schr"odinger operators on manifolds

Details Random Schr"odinger operators on manifolds Random Schr"odinger operators on manifolds

2002-12-19

arxiv.org/abs/math-ph/0212057v1

Physics

Mathematical Physics

10 pages, to appear in Markov Process. Related Fields, proceedings of the conference "Aspects Mathematiques des Systemes Aleat

Scientific paper

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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