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

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 1, page 53-143
- ISSN: 1435-9855

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topGerminet, 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 -

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