Random Schr"odinger operators on manifolds

Daniel Lenz; Norbert Peyerimhoff; Ivan Veselic'

Random Schr"odinger operators on manifolds

数学物理 2018-09-28 v1 math.MP 谱理论

作者: Daniel Lenz , Norbert Peyerimhoff , Ivan Veselic'

摘要

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.

关键词

schrödinger operators operator theory and quantum mechanics

引用

@article{arxiv.math-ph/0212057,
  title  = {Random Schr"odinger operators on manifolds},
  author = {Daniel Lenz and Norbert Peyerimhoff and Ivan Veselic'},
  journal= {arXiv preprint arXiv:math-ph/0212057},
  year   = {2018}
}

备注

10 pages, to appear in Markov Process. Related Fields, proceedings of the conference "Aspects Mathematiques des Systemes Aleatoires et de la Mecanique Statistique", held in the honour of L. Pastur, May 2002, Marseille

Random Schr"odinger operators on manifolds

摘要

关键词

引用

备注

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