A comprehensive proof of localization for continuous Anderson models with singular random potentials

Germinet, François, and Klein, Abel. "A comprehensive proof of localization for continuous Anderson models with singular random potentials." Journal of the European Mathematical Society 015.1 (2013): 53-143. <http://eudml.org/doc/277569>.

@article{Germinet2013,
abstract = {We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution), decay of eigenfunctions correlations, and decay of the Fermi projections. We also prove log-Hölder continuity of the integrated density of states at the bottom of the spectrum.},
author = {Germinet, François, Klein, Abel},
journal = {Journal of the European Mathematical Society},
keywords = {Anderson localization; dynamical localization; random Schrödinger operator; continuous Anderson model; integrated density of states; Anderson localization; dynamical localization; random Schrödinger operator; continuous Anderson model; integrated density of states},
language = {eng},
number = {1},
pages = {53-143},
publisher = {European Mathematical Society Publishing House},
title = {A comprehensive proof of localization for continuous Anderson models with singular random potentials},
url = {http://eudml.org/doc/277569},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Germinet, François
AU - Klein, Abel
TI - A comprehensive proof of localization for continuous Anderson models with singular random potentials
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 1
SP - 53
EP - 143
AB - We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution), decay of eigenfunctions correlations, and decay of the Fermi projections. We also prove log-Hölder continuity of the integrated density of states at the bottom of the spectrum.
LA - eng
KW - Anderson localization; dynamical localization; random Schrödinger operator; continuous Anderson model; integrated density of states; Anderson localization; dynamical localization; random Schrödinger operator; continuous Anderson model; integrated density of states
UR - http://eudml.org/doc/277569
ER -