Localisation for non-monotone Schrödinger operators

Elgart, Alexander, Shamis, Mira, and Sodin, Sasha. "Localisation for non-monotone Schrödinger operators." Journal of the European Mathematical Society 016.5 (2014): 909-924. <http://eudml.org/doc/277216>.

@article{Elgart2014,
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 $d$-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.},
author = {Elgart, Alexander, Shamis, Mira, Sodin, Sasha},
journal = {Journal of the European Mathematical Society},
keywords = {Anderson localisation; non-monotone; alloy-type models; Wegner estimate; Anderson localization; non-monotone; alloy-type models; Wegner estimate},
language = {eng},
number = {5},
pages = {909-924},
publisher = {European Mathematical Society Publishing House},
title = {Localisation for non-monotone Schrödinger operators},
url = {http://eudml.org/doc/277216},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Elgart, Alexander
AU - Shamis, Mira
AU - Sodin, Sasha
TI - Localisation for non-monotone Schrödinger operators
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 5
SP - 909
EP - 924
AB - 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 $d$-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.
LA - eng
KW - Anderson localisation; non-monotone; alloy-type models; Wegner estimate; Anderson localization; non-monotone; alloy-type models; Wegner estimate
UR - http://eudml.org/doc/277216
ER -