JournalsjemsVol. 16, No. 5pp. 909–924

Localisation for non-monotone Schrödinger operators

  • Alexander Elgart

    Virginia Tech, Blacksburg, USA
  • Mira Shamis

    Institute for Advanced Study, Princeton, USA
  • Sasha Sodin

    Princeton University, USA
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Abstract

We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schrödinger operators with non-monotone random potentials, on the dd-dimensional lattice. Our results include dynamical localisation, i.e. exponentially decaying bounds on the transition amplitude in the mean. They are derived through the study of fractional moments of the resolvent, which are finite due to resonance-diffusing effects of the disorder. One of the byproducts of the analysis is a nearly optimal Wegner estimate. A particular example of the class of systems covered by our results is the discrete alloy-type Anderson model.

Cite this article

Alexander Elgart, Mira Shamis, Sasha Sodin, Localisation for non-monotone Schrödinger operators. J. Eur. Math. Soc. 16 (2014), no. 5, pp. 909–924

DOI 10.4171/JEMS/451