Localization for the random displacement model

Frédéric Klopp (1) , Michael Loss (2) , Shu Nakamura (3) , Gunter Stolz (4)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 School of Mathematics - Georgia Institute of Technology
3 Graduate School of Mathematical Sciences
4 Department of Mathematics

We prove spectral and dynamical localization for the multi-dimensional random displacement model near the bottom of its spectrum by showing that the approach through multiscale analysis is applicable. In particular, we show that a previously known Lifshitz tail bound can be extended to our setting and prove a new Wegner estimate. A key tool is given by a quantitative form of a property of a related single-site Neumann problem which can be described as ``bubbles tend to the corners''.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Théorie spectrale [math.SP]

Frédéric Klopp, Michael Loss, Shu Nakamura, Gunter Stolz. Localization for the random displacement model. 2010. ⟨hal-00499598v1⟩