Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line

Details Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line

2011-01-05

arxiv.org/abs/1101.0900v4

Physics

Mathematical Physics

In section 5, a proof of localization at the bottom of the spectrum for the displacement model in dimension 1 was added. This

Scientific paper

We present a proof of Minami type estimates for one dimensional random Schr\"odinger operators valid at all energies in the localization regime provided a Wegner estimate is known to hold. The Minami type estimates are then applied to various models to obtain results on their spectral statistics. The heuristics underlying our proof of Minami type estimates is that close by eigenvalues of a one-dimensional Schr\"odinger operator correspond either to eigenfunctions that live far away from each other in space or they come from some tunneling phenomena. In the second case, one can undo the tunneling and thus construct quasi-modes that live far away from each other in space.

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